Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#950 |
| Fitting | C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ C2×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D3×#67 |
| commutator, cosocle | C32×C4 | C24 |
| Frattini | C4 | C22×D32 |
| Fitting | C32×#41 | C22 |
| socle | C2×C32 | C22×D4 |
| hypercenter | #41 | D32 |
| hypocenter | C32 | C2×#135 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
563 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4824, D3×#5144, D3×#4823, … |
| maximal normal subgroup of | D3×#4824, D3×#5144, D3×#4823, … |
| maximal quotient of | D3×#5002, D3×#5233, D3×#4998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7334);