diff --git a/src/core/group/group.h b/src/core/group/group.h
index 39b65a5..ec86d59 100644
--- a/src/core/group/group.h
+++ b/src/core/group/group.h
@@ -255,50 +255,63 @@ private:
     Toward toward_;
     uint32_t pattern_id_;
 
-    Group(uint32_t type_id, uint32_t pattern_id, Toward toward) {
-        type_id_ = type_id;
-        pattern_id_ = pattern_id;
-        toward_ = toward;
-    }
-
     /// Tiled merge of type_id and pattern_id.
     [[nodiscard]] constexpr uint32_t flat_id() const;
-};
 
-/// Spawn all the unsorted codes of the current group.
-std::vector<codec::RawCode> Group_extend(codec::RawCode raw_code, uint32_t reserve = 0);
+    /// Hidden constructor called from unsafe_create.
+    constexpr Group(uint32_t type_id, uint32_t pattern_id, Toward toward);
 
-class GroupCases {
+    // ------------------------------------------------------------------------------------- //
+};
+
+class CaseInfo {
 public:
     // ------------------------------------------------------------------------------------- //
 
-    // TODO: move to `::klotski::group::CaseInfo`
-    class CaseInfo {
-    public:
-        CaseInfo() = delete;
+    /// Get the original group.
+    [[nodiscard]] constexpr Group group() const;
 
-        [[nodiscard]] constexpr Group group() const;
+    /// Get the original case id.
+    [[nodiscard]] constexpr uint32_t case_id() const;
 
-        [[nodiscard]] constexpr uint32_t case_id() const;
+    /// Get the string form of current case.
+    [[nodiscard]] constexpr std::string to_string() const;
 
-        static CaseInfo unsafe_create(Group group, uint32_t case_id);
+    // ------------------------------------------------------------------------------------- //
 
-        static std::optional<CaseInfo> create(Group group, uint32_t case_id);
+    CaseInfo() = delete;
 
-        [[nodiscard]] std::string to_string() const;
+    /// Create CaseInfo without any check.
+    static constexpr CaseInfo unsafe_create(Group group, uint32_t case_id);
+
+    /// Create CaseInfo with validity check.
+    static constexpr std::optional<CaseInfo> create(Group group, uint32_t case_id);
+
+    // ------------------------------------------------------------------------------------- //
 
 #ifndef KLSK_NDEBUG
-        friend std::ostream& operator<<(std::ostream &out, CaseInfo self);
+    /// Output case info only for debug.
+    friend std::ostream& operator<<(std::ostream &out, CaseInfo self);
 #endif
 
-    private:
-        CaseInfo(Group group, uint32_t case_id) : group_(group), case_id_(case_id) {}
+    /// Compare the internal values of two CaseInfo.
+    friend constexpr auto operator==(const CaseInfo &lhs, const CaseInfo &rhs);
 
-        Group group_;
-        uint32_t case_id_;
-    };
+    // ------------------------------------------------------------------------------------- //
+
+private:
+    Group group_;
+    uint32_t case_id_;
+
+    /// Hidden constructor called from unsafe_create.
+    constexpr CaseInfo(Group group, uint32_t case_id);
 
     // ------------------------------------------------------------------------------------- //
+};
+
+class GroupCases {
+public:
+    // ------------------------------------------------------------------------------------- //
 
     /// Execute the build process.
     static void build();
@@ -308,15 +321,17 @@ public:
 
     // ------------------------------------------------------------------------------------- //
 
-    /// Get the CommonCode from CaseInfo.
-    static codec::CommonCode obtain_code(CaseInfo info);
-
     /// Get the Group which ShortCode is located.
     static Group obtain_group(codec::ShortCode short_code);
 
     /// Get the Group which CommonCode is located.
     static Group obtain_group(codec::CommonCode common_code);
 
+    // ------------------------------------------------------------------------------------- //
+
+    /// Get the CommonCode from CaseInfo.
+    static codec::CommonCode obtain_code(CaseInfo info);
+
     /// Get the CaseInfo corresponding to the ShortCode.
     static CaseInfo obtain_info(codec::ShortCode short_code);
 
@@ -364,14 +379,17 @@ private:
     // ------------------------------------------------------------------------------------- //
 };
 
+/// Spawn all the unsorted codes of the current group.
+std::vector<codec::RawCode> Group_extend(codec::RawCode raw_code, uint32_t reserve = 0);
+
 static_assert(std::is_standard_layout_v<Group>);
 static_assert(std::is_trivially_copyable_v<Group>);
 
 static_assert(std::is_standard_layout_v<GroupUnion>);
 static_assert(std::is_trivially_copyable_v<GroupUnion>);
 
-static_assert(std::is_standard_layout_v<GroupCases::CaseInfo>);
-static_assert(std::is_trivially_copyable_v<GroupCases::CaseInfo>);
+static_assert(std::is_standard_layout_v<CaseInfo>);
+static_assert(std::is_trivially_copyable_v<CaseInfo>);
 
 } // namespace klotski::group
 
@@ -379,9 +397,12 @@ static_assert(std::is_trivially_copyable_v<GroupCases::CaseInfo>);
 #include "internal/group_union.inl"
 #include "internal/group_cases.inl"
 #include "internal/group.inl"
+#include "internal/case_info.inl"
 
 // ----------------------------------------------------------------------------------------- //
 
+// TODO: move to `hash.inl`
+
 namespace std {
 
 template <>
@@ -401,6 +422,16 @@ struct std::hash<klotski::group::GroupUnion> {
 
 // TODO: add `std::hash` for CaseInfo
 
+template <>
+struct std::hash<klotski::group::CaseInfo> {
+    constexpr std::size_t operator()(const klotski::group::CaseInfo &info) const noexcept {
+        // TODO: perf hash alg
+        const auto h1 = std::hash<klotski::group::Group>{}(info.group());
+        const auto h2 = std::hash<uint32_t>{}(info.case_id());
+        return h1 ^ h2;
+    }
+};
+
 } // namespace std
 
 // ----------------------------------------------------------------------------------------- //
diff --git a/src/core/group/internal/case_info.inl b/src/core/group/internal/case_info.inl
new file mode 100644
index 0000000..49eacf8
--- /dev/null
+++ b/src/core/group/internal/case_info.inl
@@ -0,0 +1,37 @@
+#pragma once
+
+#include <format>
+
+namespace klotski::group {
+
+inline std::ostream& operator<<(std::ostream &out, CaseInfo self) {
+    out << self.to_string();
+    return out;
+}
+
+constexpr std::string CaseInfo::to_string() const {
+    return std::format("{}-{}", group_.to_string(), case_id_);
+}
+
+constexpr Group CaseInfo::group() const {
+    return group_;
+}
+
+constexpr uint32_t CaseInfo::case_id() const {
+    return case_id_;
+}
+
+constexpr std::optional<CaseInfo> CaseInfo::create(Group group, uint32_t case_id) {
+    if (case_id >= group.size()) {
+        return std::nullopt;
+    }
+    return unsafe_create(group, case_id);
+}
+
+constexpr CaseInfo CaseInfo::unsafe_create(Group group, uint32_t case_id) {
+    return {group, case_id};
+}
+
+constexpr CaseInfo::CaseInfo(Group group, uint32_t case_id) : group_(group), case_id_(case_id) {}
+
+} // namespace klotski::group
diff --git a/src/core/group/internal/group.inl b/src/core/group/internal/group.inl
index 96078fe..b1bff17 100644
--- a/src/core/group/internal/group.inl
+++ b/src/core/group/internal/group.inl
@@ -178,4 +178,10 @@ constexpr Group Group::to_horizontal_mirror() const {
     }
 }
 
+constexpr Group::Group(uint32_t type_id, uint32_t pattern_id, Toward toward) {
+    type_id_ = type_id;
+    pattern_id_ = pattern_id;
+    toward_ = toward;
+}
+
 } // namespace klotski::group
diff --git a/src/core/group/internal/group_cases.cc b/src/core/group/internal/group_cases.cc
index 10c6c5b..364ebea 100644
--- a/src/core/group/internal/group_cases.cc
+++ b/src/core/group/internal/group_cases.cc
@@ -12,6 +12,8 @@ using klotski::group::GroupCases;
 using klotski::group::GroupUnion;
 using klotski::cases::RangesUnion;
 
+using klotski::group::CaseInfo;
+
 using klotski::group::ALL_GROUP_NUM;
 using klotski::group::TYPE_ID_LIMIT;
 using klotski::cases::ALL_CASES_NUM_;
@@ -123,7 +125,7 @@ CommonCode GroupCases::fast_obtain_code(CaseInfo info) {
     return CommonCode::unsafe_create(head << 32 | range);
 }
 
-GroupCases::CaseInfo GroupCases::fast_obtain_info(ShortCode short_code) {
+CaseInfo GroupCases::fast_obtain_info(ShortCode short_code) {
     uint16_t type_id = GroupUnion::from_short_code(short_code).unwrap(); // NOTE: need to convert as CommonCode
     uint16_t pattern_id = (*rev_data)[short_code.unwrap()].pattern_id;
     uint16_t toward_id = (*rev_data)[short_code.unwrap()].toward_id;
@@ -133,7 +135,7 @@ GroupCases::CaseInfo GroupCases::fast_obtain_info(ShortCode short_code) {
     return CaseInfo::unsafe_create(group, case_id);
 }
 
-GroupCases::CaseInfo GroupCases::fast_obtain_info(CommonCode common_code) {
+CaseInfo GroupCases::fast_obtain_info(CommonCode common_code) {
     auto short_code = common_code.to_short_code();
     uint16_t type_id = GroupUnion::from_common_code(common_code).unwrap();
     uint16_t pattern_id = (*rev_data)[short_code.unwrap()].pattern_id;
@@ -193,7 +195,7 @@ static std::unordered_map<uint64_t, Group> build_map_data() {
     return data;
 }
 
-GroupCases::CaseInfo GroupCases::tiny_obtain_info(CommonCode common_code) {
+CaseInfo GroupCases::tiny_obtain_info(CommonCode common_code) {
     auto raw_codes = Group_extend(common_code.to_raw_code());
     std::vector<CommonCode> common_codes;
     common_codes.reserve(raw_codes.size());
diff --git a/src/core/group/internal/group_cases.inl b/src/core/group/internal/group_cases.inl
index b8b181f..a6b1535 100644
--- a/src/core/group/internal/group_cases.inl
+++ b/src/core/group/internal/group_cases.inl
@@ -1,37 +1,7 @@
 #pragma once
 
-#include <format>
-
 namespace klotski::group {
 
-inline std::ostream& operator<<(std::ostream &out, GroupCases::CaseInfo self) {
-    out << self.to_string();
-    return out;
-}
-
-inline std::string GroupCases::CaseInfo::to_string() const {
-    return std::format("{}-{}", group_.to_string(), case_id_);
-}
-
-constexpr Group GroupCases::CaseInfo::group() const {
-    return group_;
-}
-
-constexpr uint32_t GroupCases::CaseInfo::case_id() const {
-    return case_id_;
-}
-
-inline std::optional<GroupCases::CaseInfo> GroupCases::CaseInfo::create(klotski::group::Group group, uint32_t case_id) {
-    if (case_id >= group.size()) {
-        return std::nullopt;
-    }
-    return unsafe_create(group, case_id);
-}
-
-inline GroupCases::CaseInfo GroupCases::CaseInfo::unsafe_create(klotski::group::Group group, uint32_t case_id) {
-    return {group, case_id};
-}
-
 inline codec::CommonCode GroupCases::obtain_code(CaseInfo info) {
     if (fast_) {
         return fast_obtain_code(info);
@@ -39,7 +9,7 @@ inline codec::CommonCode GroupCases::obtain_code(CaseInfo info) {
     return tiny_obtain_code(info);
 }
 
-inline GroupCases::CaseInfo GroupCases::obtain_info(codec::CommonCode common_code) {
+inline CaseInfo GroupCases::obtain_info(codec::CommonCode common_code) {
     if (fast_) {
         return fast_obtain_info(common_code);
     }
@@ -60,7 +30,7 @@ inline Group GroupCases::obtain_group(codec::ShortCode short_code) {
     return Group::from_short_code(short_code);
 }
 
-inline GroupCases::CaseInfo GroupCases::obtain_info(codec::ShortCode short_code) {
+inline CaseInfo GroupCases::obtain_info(codec::ShortCode short_code) {
     if (fast_) {
         return fast_obtain_info(short_code);
     }