Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16838778 |
| derived, Sylow | C241 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11757210 |
| commutator, hypocenter | C241 | C22×C8 |
| Frattini | C2 | C22×#11757210 |
| Fitting | C2×C4×C241 | C4 |
| socle | C22×C241 | C2×C4 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
| maximal subgroup of | #29508582, #29508590, #29508592, … |
| maximal normal subgroup of | #29508582, #29508590, #29508592, … |
| maximal quotient of | C2×C4×#14515356, C4×#16838778, #29508685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 229);