Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63382 |
| Sylow | C9 ⋊ C2×#101 |
219 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #11783795, C4×#63382, #11784649, … |
| maximal normal subgroup of | #11783795, C4×#63382, #11784649, … |
| maximal quotient of | C2×#10588145, #11773826, #11773867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 688);