Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×D3×C22⋊C4 |
| Fitting | C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C2×C22⋊C4 |
281 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(6,8)(9,10,11)(12,13,14);(1,4,3,2)(5,6)(7,8);(13,14)90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#806, C3×D3×#99, #10594037, … |
| maximal normal subgroup of | D3×#806, C3×D3×#99, #10594037, … |
| maximal quotient of | C3×#4646, C3×D3×#95, C3×#4664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 651);