Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D3×#137 |
| Fitting | C32×#137 ⋊ C2 |
| Sylow | C32 ⋊ C2×#137 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#455, D3×#5202, C3×D3×#456, … |
| maximal normal subgroup of | C3×D3×#455, D3×#5202, C3×D3×#456, … |
| maximal quotient of | C3×D3×#419, C3×D3×#417, C3×D3×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7755);