Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64157 |
| Sylow | C32 ⋊ C2×#131 |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11783831, #11783834, #11783852, … |
| maximal normal subgroup of | #11783831, #11783834, #11783852, … |
| maximal quotient of | C2×#10592696, C4×#64157, C2×#10592933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8171);