Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C24 |
| direct product | C2×D4×C22⋊C9 |
| unambiguous semidirect product | C4⋊(C22×C22⋊C9) |
| unambiguous semidirect product | (C23×D4)⋊C9 |
| Sylow | C23×D4 ⋊ C9 |
580 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #99×C22⋊C9, #100×C22⋊C9, #102×C22⋊C9, … |
| maximal normal subgroup of | #99×C22⋊C9, #100×C22⋊C9, #102×C22⋊C9, … |
| maximal quotient of | C2×C22⋊C4×C22⋊C9, C2×C4⋊C4×C22⋊C9, C4×D4×C22⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4995);