Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C42×D67 |
| Fitting | C22×C42×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D67 |
| commutator, hypocenter | C67 | C23×C42 |
| Frattini | C22 | C24×D67 |
| Fitting | C22×C42×C67 | C2 |
| socle | C24×C67 | C23 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761047, #30761071, C4×#95×D67, … |
| maximal normal subgroup of | #30761047, #30761071, C4×#95×D67, … |
| maximal quotient of | C2×C43×D67, C22×C42×Dic67, C22×#95×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17664);