Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | D9×#97 |
| Fitting | C9×#97 ⋊ C2 |
| Sylow | C9 ⋊ C2×#97 |
219 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 101 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 | D9×#329, D9×#330, #11775695, … |
| maximal normal subgroup of | D9×#329, D9×#330, #11775695, … |
| maximal quotient of | D9×#322, #11773583, #11773589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 267);