Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863329 |
| Sylow | C67 ⋊ C2×#398 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C23×C67 | C24 |
| Frattini | C23 | C23×D67 |
| Fitting | C22×C4⋊C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C4⋊C4 | D67 |
| hypocenter | C67 | C2×#398 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
692 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30777666, C4×#16863329, #30781216, … |
| maximal normal subgroup of | #30777666, C4×#16863329, #30781216, … |
| maximal quotient of | C2×#22558461, C2×#22558462, C2×#22558463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7743);