Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×Q8×C3⋊D3 |
| Fitting | C22×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C23×Q8 |
2550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11773484, #11784650, #11784659, … |
| maximal normal subgroup of | #11773484, #11784650, #11784659, … |
| maximal quotient of | C22×C4⋊C4×C3⋊D3, C2×C4×Q8×C3⋊D3, C22×#64096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8632);