Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#4518 |
| Fitting | C32×M32 ⋊ C2 |
| Sylow | C32 ⋊ #360 |
129 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 129 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#360, C2×C3×#4518, D3×#4518, … |
| maximal normal subgroup of | C3×D3×#360, C2×C3×#4518, D3×#4518, … |
| maximal quotient of | C3×#67516, C3×#67517, C3×#67526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1144);