Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11757210 |
| unambiguous semidirect product | D241⋊(C4⋊C4) |
| Fitting | C2×C4×C241 ⋊ C4 |
| Sylow | C241 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
500 conjugacy classes — view the full character table.
| maximal subgroup of | #29508590, #29508591, #29508596, … |
| maximal normal subgroup of | #29508590, #29508591, #29508596, … |
| maximal quotient of | C2×(C2×#11757210)⋊C4, C4×C4⋊#11757210, #29508659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 224);