Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×C67⋊C64 |
| unambiguous semidirect product | (C2×C67)⋊C64 |
| derived, Sylow | C67 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D67 |
| commutator, hypocenter | C67 | C2×C64 |
| Frattini | C32 | C2×D67 |
| Fitting | C2×C32×C67 | C2 |
| socle | C22×C67 | C32 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic67, C4×C67⋊C64, #30743635, … |
| maximal normal subgroup of | C64×Dic67, C4×C67⋊C64, #30743635, … |
| maximal quotient of | C4×C67⋊C64, C22⋊(C67⋊C64), C4⋊(C67⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2719);