Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | #41×C22⋊C9 |
| Sylow | C22×#41 ⋊ C9 |
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #104×C22⋊C9, #131×C22⋊C9, #135×C22⋊C9, … |
| maximal normal subgroup of | #104×C22⋊C9, #131×C22⋊C9, #135×C22⋊C9, … |
| maximal quotient of | #117×C22⋊C9, C4×D4×C22⋊C9, C4×Q8×C22⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4999);