Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5587 |
| Sylow | C32 ⋊ #551 |
561 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70998, C3×#69132, #11798571, … |
| maximal normal subgroup of | C3×#70998, C3×#69132, #11798571, … |
| maximal quotient of | C3×#73822, C3×#74392, C3×#74674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7566);