Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#5827 |
| Sylow | C32 ⋊ #520 |
670 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70297, C3×#70363, #11786692, … |
| maximal normal subgroup of | C3×#70297, C3×#70363, #11786692, … |
| maximal quotient of | C3×#82223, C3×#82317, C3×#82450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7806);