Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | D9×M32 |
| Fitting | C9×M32 ⋊ C2 |
| Sylow | C9 ⋊ C2×M32 |
135 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#347, #11795928, D9×#349, … |
| maximal normal subgroup of | D9×#347, #11795928, D9×#349, … |
| maximal quotient of | D9×#346, M32×Dic9, #11795849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 468);