Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C43×D67 |
| Fitting | C43×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D67 |
| commutator, hypocenter | C67 | C2×C43 |
| Frattini | C23 | C23×D67 |
| Fitting | C43×C67 | C2 |
| socle | C23×C67 | C24 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C43 | |
1272 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1276×D67, #30745271, C42×C8×D67, … |
| maximal normal subgroup of | #1276×D67, #30745271, C42×C8×D67, … |
| maximal quotient of | C43×Dic67, C4×#95×D67, C4×#16863241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6831);