Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5816 |
| Fitting | C22×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ #536 |
618 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70350, #11788726, C3×#70105, … |
| maximal normal subgroup of | C3×#70350, #11788726, C3×#70105, … |
| maximal quotient of | C3×#84062, C3×#82186, C3×#82157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7795);