Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#64110 |
| Fitting | C22×C32×C8 ⋊ 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 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11783828, #11783836, #11783846, … |
| maximal normal subgroup of | #11783828, #11783836, #11783846, … |
| maximal quotient of | C2×#10592388, C2×#10592800, C4×#64110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8091);