Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16863350 |
| Fitting | C2×C4×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×C4×C8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×C4×C8 | D67 |
| hypocenter | C67 | C2×#405 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
592 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30746360, #30746364, #30748689, … |
| maximal normal subgroup of | #30746360, #30746364, #30748689, … |
| maximal quotient of | C2×C8×#11761611, C2×#22558491, C2×#22558497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12921);