Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#16838773 |
| derived, Sylow | C241 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11757210 |
| commutator, hypocenter | C241 | C2×C16 |
| Frattini | C4 | C2×#11757210 |
| Fitting | C2×C4×C241 | C4 |
| socle | C22×C241 | C8 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16838773, #29508603, #29508605, … |
| maximal normal subgroup of | C4×#16838773, #29508603, #29508605, … |
| maximal quotient of | C4×#16838773, C22⋊#16838773, C4⋊#16838773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 218);