Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×D3×M32 |
| Fitting | C32×M32 ⋊ C2 |
| Sylow | C32 ⋊ C2×M32 |
193 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#347, D3×#4512, C3×#69087, … |
| maximal normal subgroup of | C3×D3×#347, D3×#4512, C3×#69087, … |
| maximal quotient of | C3×D3×#346, C3×Dic3×M32, C3×#69071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3885);