Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#63771 |
| Sylow | C32 ⋊ C2×#108 |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11772386, #11772402, #11772432, … |
| maximal normal subgroup of | #11772386, #11772402, #11772432, … |
| maximal quotient of | C2×#10590172, C2×#10590171, #11776810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5652);