Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊C32 |
| unambiguous semidirect product | (C3×D3)⋊C32 |
| derived, Sylow | C32 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D32 |
| commutator, hypocenter | C32 | C2×C32 |
| Fitting, cosocle | C32×C16 | C22 |
| socle | C2×C32 | C2×C16 |
| prime radical | C2×C3×D3 | C16 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C16 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D32×C32, C2×D3×C3⋊C32, D3×#4447, … |
| maximal normal subgroup of | D32×C32, C2×D3×C3⋊C32, D3×#4447, … |
| maximal quotient of | Dic3×C3⋊C32, (C2×D3)⋊(C3⋊C32), Dic3⋊(C3⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 948);