Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#63436 |
| Fitting | C2×C42×C9 ⋊ C2 |
| Sylow | C9 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D9 |
| commutator, cosocle | C22×C9 | C24 |
| Frattini | C22×C3 | C23×D3 |
| Fitting | C2×C42×C9 | C2 |
| socle | C23×C3 | C22×D3 |
| hypercenter | C2×C42 | D9 |
| hypocenter | C9 | C2×#127 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
747 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10588163, #11776255, #11776261, … |
| maximal normal subgroup of | C2×#10588163, #11776255, #11776261, … |
| maximal quotient of | C2×#10588615, C2×#10588619, C4×#63436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1459);