Finite Group DatabasebetaFinite Group Databasebeta| order | 7664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C479⋊C8 |
| unambiguous semidirect product | (C2×C479)⋊C8 |
| derived, Sylow | C479 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D479 |
| commutator, hypocenter | C479 | C2×C8 |
| Frattini | C4 | C2×D479 |
| Fitting | C2×C4×C479 | C2 |
| socle | C22×C479 | C4 |
| LCS | G ▷ C479 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic479, C4×C479⋊C8, #29506292, … |
| maximal normal subgroup of | C8×Dic479, C4×C479⋊C8, #29506292, … |
| maximal quotient of | C4×C479⋊C8, C22⋊(C479⋊C8), C4⋊(C479⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7664, 22);