Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5593 |
| Fitting | C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ #538 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C3 |
| Frattini | C22 | C23×C3×D3 |
| Fitting | C32×#120 | C2 |
| socle | C22×C32 | C24 |
| hypercenter | C3×#120 | D3 |
| hypocenter | C3 | C3×#538 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#120 | |
565 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#538, C2×C3×#5593, D3×#5593, … |
| maximal normal subgroup of | C3×D3×#538, C2×C3×#5593, D3×#5593, … |
| maximal quotient of | C3×#73820, C3×#74663, C3×#74383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7572);