Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#5111 |
| Fitting | C22×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ #435 |
286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#435, C2×C3×#5111, D3×#5111, … |
| maximal normal subgroup of | C3×D3×#435, C2×C3×#5111, D3×#5111, … |
| maximal quotient of | C3×#70841, C3×#70842, C3×#70933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4090);