Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#14268661 |
| Fitting | C4×C113 ⋊ C16 |
| derived, Sylow | C113 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14268661 |
| commutator, hypocenter | C113 | C4×C16 |
| Frattini | C2 | C2×#14268661 |
| Fitting | C4×C113 | C16 |
| socle | C2×C113 | C2×C16 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C4 | |
58 conjugacy classes of subgroups.
92 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14268661, #28407833, D4⋊#14268661, … |
| maximal normal subgroup of | C8×#14268661, #28407833, D4⋊#14268661, … |
| maximal quotient of | C8×#14268661, #28407833, (C2×#14268661)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1674);