Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5825 |
| Sylow | C32 ⋊ #536 |
622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70046, C3×#72024, #11788723, … |
| maximal normal subgroup of | C3×#70046, C3×#72024, #11788723, … |
| maximal quotient of | C3×#82230, C3×#84087, C3×#82234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7804);