Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C4⋊C4×C22⋊C9 |
| unambiguous semidirect product | C4⋊(C4×C22⋊C9) |
| unambiguous semidirect product | (C22×C4⋊C4)⋊C9 |
| Sylow | C22×C4⋊C4 ⋊ C9 |
200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #102×C22⋊C9, #103×C22⋊C9, #106×C22⋊C9, … |
| maximal normal subgroup of | #102×C22⋊C9, #103×C22⋊C9, #106×C22⋊C9, … |
| maximal quotient of | #95×C22⋊C9, C4⋊C4×Q8⋊C9, #2351⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1420);