Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#16838784 |
| Fitting, socle | C2×C241 ⋊ C16 |
| derived, Sylow | C241 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16838784 |
| commutator, hypocenter | C241 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C241 | C16 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
62 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16838784, C22⋊#16838784, C4⋊#16838784, … |
| maximal normal subgroup of | C4×#16838784, C22⋊#16838784, C4⋊#16838784, … |
| maximal quotient of | C4×#16838784, C22⋊#16838784, C4⋊#16838784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 246);