Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5675 |
| Fitting | C32×#124 ⋊ C2 |
| Sylow | C32 ⋊ #536 |
578 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#69159, #11796441, C3×#69164, … |
| maximal normal subgroup of | C3×#69159, #11796441, C3×#69164, … |
| maximal quotient of | C3×#76610, C3×#76294, C3×#74225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7654);