Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×C67⋊C8 |
| unambiguous semidirect product | (C2×C67)⋊C82 |
| derived, Sylow | C67 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D67 |
| commutator, hypocenter | C67 | C2×C82 |
| Frattini | C42 | C22×D67 |
| Fitting | C2×C4×C8×C67 | C2 |
| socle | C23×C67 | C42 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C4×C8 | |
280 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742658, #30742662, #30742693, … |
| maximal normal subgroup of | #30742658, #30742662, #30742693, … |
| maximal quotient of | C4×C8×C67⋊C8, C2×C67⋊#1273, #30746254, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2783);