Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16863448 |
| Fitting | C2×C4⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#431 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C2×C4⋊C8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D67 |
| hypocenter | C67 | C2×#431 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
528 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30745288, #30745291, #30745309, … |
| maximal normal subgroup of | #30745288, #30745291, #30745309, … |
| maximal quotient of | C2×#22559953, C2×#22559966, C2×C4⋊C8×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13125);