Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D9 |
| unambiguous semidirect product | C9⋊C26 |
| unambiguous semidirect product | (C2×C9)⋊C25 |
| Fitting | C25×C9 ⋊ C2 |
| derived, Sylow | C9 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D9 |
| commutator, cosocle, hypocenter | C9 | C26 |
| Frattini | C3 | C25×D3 |
| Fitting | C25×C9 | C2 |
| socle | C25×C3 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C25 | |
8475 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#379, C2×#10588635, #11856154, … |
| maximal normal subgroup of | D9×#379, C2×#10588635, #11856154, … |
| maximal quotient of | C24×C4×D9, C25×Dic9, C23×D4×D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8267);