Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#3701 |
| Fitting | C22×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D9 |
| commutator, cosocle | C2×C9 | C25 |
| Frattini | C2×C3 | C24×D3 |
| Fitting | C22×Q8×C9 | C2 |
| socle | C23×C3 | C22×D3 |
| hypercenter | C22×Q8 | D9 |
| hypocenter | C9 | C22×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
1335 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11784674, #11784754, #11801868, … |
| maximal normal subgroup of | #11784674, #11784754, #11801868, … |
| maximal quotient of | C22×#63454, C22×#63455, C22×Q8×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5016);