Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic241 |
| derived, Sylow | C241 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D241 |
| commutator, hypocenter | C241 | C23×C4 |
| Frattini | C2 | C23×D241 |
| Fitting, socle | C24×C241 | C2 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
1952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#21440549, C22⋊C4×Dic241, #29507575, … |
| maximal normal subgroup of | C2×#21440549, C22⋊C4×Dic241, #29507575, … |
| maximal quotient of | C22×C4×Dic241, C22×C22⋊Dic241, C22×C4⋊Dic241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 181);