Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C24×C4×D67 |
| Fitting | C24×C4×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D67 |
| commutator, hypocenter | C67 | C25×C4 |
| Frattini | C2 | C25×D67 |
| Fitting | C24×C4×C67 | C2 |
| socle | C25×C67 | C22 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊#95×D67, C2×(C2×D67)⋊#95, #30777036, … |
| maximal normal subgroup of | C22⋊#95×D67, C2×(C2×D67)⋊#95, #30777036, … |
| maximal quotient of | C23×C42×D67, C24×C4×Dic67, C23×C22⋊C4×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19299);