Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C67⋊C32 |
| derived, Sylow | C67 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D67 |
| commutator, hypocenter | C67 | C4×C32 |
| Frattini | C2×C16 | C2×D67 |
| Fitting | C4×C16×C67 | C2 |
| socle | C22×C67 | C2×C16 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C67⋊C8, C8×C67⋊C32, #30743158, … |
| maximal normal subgroup of | C32×C67⋊C8, C8×C67⋊C32, #30743158, … |
| maximal quotient of | C8×C67⋊C32, #30743162, #30743518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2642);