Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#14515356 |
| derived, Sylow | C241 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11757210 |
| commutator, hypocenter | C241 | C22×C8 |
| Frattini | C2 | C22×#11757210 |
| Fitting, socle | C23×C241 | C4 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C23 | |
76 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 228);