Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3744 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×#3746 |
| Sylow | C32 ⋊ C22×Q16 |
774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11787472, #11787478, #11787506, … |
| maximal normal subgroup of | #11787472, #11787478, #11787506, … |
| maximal quotient of | C22×#63643, C22×#63645, C2×C4×#3746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8095);