Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5638 |
| Fitting | C32×C22⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ #539 |
473 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#539, C2×C3×#5638, D3×#5638, … |
| maximal normal subgroup of | C3×D3×#539, C2×C3×#5638, D3×#5638, … |
| maximal quotient of | C3×#75296, C3×#74945, C3×#74006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7617);