Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#11757210 |
| Fitting | D4×C241 ⋊ C4 |
| Sylow | C241 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11757210 |
| commutator, socle | C2×C241 | C22×C4 |
| Fitting | D4×C241 | C4 |
| hypercenter | D4 | #11757210 |
| hypocenter | C241 | C4×D4 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C2 ◁ D4 | |
94 conjugacy classes of subgroups.
320 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#11757210, SD16×#11757210, #29508756, … |
| maximal normal subgroup of | D8×#11757210, SD16×#11757210, #29508756, … |
| maximal quotient of | C22⋊C4×#11757210, C4⋊C4×#11757210, #29508664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 226);