Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#894 |
| Fitting | C32×C4⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C32×C4⋊C4 | C22 |
| prime radical | C2×D3×D12 | C2 |
| hypercenter | C4⋊C4 | D32 |
| hypocenter | C32 | C2×#123 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
723 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#123, C2×D3×#894, D3×#5627, … |
| maximal normal subgroup of | D32×#123, C2×D3×#894, D3×#5627, … |
| maximal quotient of | D3×#4664, D3×#4989, D3×#4665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6489);