Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | Aut(G) = C2×D3×#120 (order 384) · Inn(G) = (C2×D3)⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#806 |
| Fitting | C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #99 |
121 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 121 conjugacy classes of subgroups — too many to draw. Only its 38 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) = 24 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2,3)(4,5,6)(7,9)(8,13,12,11)(10,14);(5,6)(7,8)(9,13)(10,12)(11,14)63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#806, #10590404, #10590405, … |
| maximal normal subgroup of | D3×#806, #10590404, #10590405, … |
| maximal quotient of | C3×#4451, C3×#4452, C3×#4467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 240);