Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64116 |
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ C2×#131 |
798 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 271 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11783822, #11783837, #11783842, … |
| maximal normal subgroup of | #11783822, #11783837, #11783842, … |
| maximal quotient of | C2×#10592407, C2×#10592821, C4×#64116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8097);