Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#4497 |
| Fitting | C32×#108 ⋊ C2 |
| Sylow | C32 ⋊ #359 |
127 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 127 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×#359, C2×C3×#4497, D3×#4497, … |
| maximal normal subgroup of | C3×D3×#359, C2×C3×#4497, D3×#4497, … |
| maximal quotient of | C3×#67471, C3×#67472, C3×#67487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1123);