Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×D3×Dic3 |
| derived, Sylow | C32 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D32 |
| commutator, hypocenter | C32 | C22×C42 |
| Frattini | C22 | C22×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle | C23×C32 | C23 |
| prime radical | C23×C3×D3 | C22 |
| cosocle | C22×C32 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C4 | |
1050 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4550, #11783086, D3×#4532, … |
| maximal normal subgroup of | D3×#4550, #11783086, D3×#4532, … |
| maximal quotient of | C42×D3×Dic3, C2×C4×Dic32, C2×D3×C3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6751);