Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16838780 |
| Sylow | C241 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
500 conjugacy classes — view the full character table.
| maximal subgroup of | #29508587, #29508593, #29508600, … |
| maximal normal subgroup of | #29508587, #29508593, #29508600, … |
| maximal quotient of | C2×#21440697, C4×#16838780, C2×#21440699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 232);