Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#16838782 |
| derived, Sylow | C241 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14515358 |
| commutator, hypocenter | C241 | C2×C16 |
| Frattini | C2 | C2×#14515358 |
| Fitting, socle | C22×C241 | C8 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
152 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16838782, #29508811, C22⋊#16838782, … |
| maximal normal subgroup of | C4×#16838782, #29508811, C22⋊#16838782, … |
| maximal quotient of | C4×#16838782, C22⋊#16838782, C4⋊#16838782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 240);