Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D9×SD32 |
| Fitting | C9×SD32 ⋊ C2 |
| Sylow | C9 ⋊ C2×SD32 |
135 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×SD32, D9×#508, D9×#509, … |
| maximal normal subgroup of | C2×D9×SD32, D9×#508, D9×#509, … |
| maximal quotient of | D9×#357, D9×#358, D9×#367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 475);