Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D9×#107 |
| Fitting | C9×#107 ⋊ C2 |
| Sylow | C9 ⋊ C2×#107 |
195 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#357, D9×#358, #11796666, … |
| maximal normal subgroup of | D9×#357, D9×#358, #11796666, … |
| maximal quotient of | D9×#335, #11776884, #11776999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 441);