Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#948 |
| Sylow | C32 ⋊ C2×#131 |
614 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#70040, C3×#70133, #11783851, … |
| maximal normal subgroup of | C3×#70040, C3×#70133, #11783851, … |
| maximal quotient of | C2×C3×#4997, C3×C4×#948, C2×C3×#5234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7797);