Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | M16×C22⋊C9 |
| unambiguous semidirect product | (C22×M16)⋊C9 |
| Sylow | C22×M16 ⋊ C9 |
146 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 45 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 | #100×C22⋊C9, #101×C22⋊C9, #104×C22⋊C9, … |
| maximal normal subgroup of | #100×C22⋊C9, #101×C22⋊C9, #104×C22⋊C9, … |
| maximal quotient of | #97×C22⋊C9, C22⋊C8×C22⋊C9, C4⋊C8×C22⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1436);