Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#14515358 |
| unambiguous semidirect product | #11757210⋊C8 |
| Fitting | C4×C241 ⋊ C8 |
| derived, Sylow | C241 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14515358 |
| commutator, hypocenter | C241 | C4×C8 |
| Frattini | C2 | C2×#14515358 |
| Fitting | C4×C241 | C8 |
| socle | C2×C241 | C2×C8 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
152 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14515358, #29508801, D4⋊#14515358, … |
| maximal normal subgroup of | C8×#14515358, #29508801, D4⋊#14515358, … |
| maximal quotient of | C8×#14515358, #29508801, (C2×#14515358)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 237);