Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#935 |
| Sylow | C32 ⋊ #123 |
183 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3)(4,5,6)(8,10)(13,17)(15,18);(11,13)(12,15)(14,17)(16,18);(5,6)(7,8)(9,10)(11,16,14,12)(13,18,17,15)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10589175, #10589176, C3×#4472, … |
| maximal normal subgroup of | #10589175, #10589176, C3×#4472, … |
| maximal quotient of | C3×#4943, C3×#4944, C3×#4946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 706);