Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#889 |
| Sylow | C32 ⋊ #125 |
125 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,6)(8,12)(11,14)(15,21,18,17)(16,22,20,19);(7,13,10,9)(8,14,12,11)(17,21)(19,22);(5,6)(7,8)(9,11)(10,12)(13,14)(15,20,18,16)(17,22,21,19)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10594314, #10594315, #10594316, … |
| maximal normal subgroup of | #10594314, #10594315, #10594316, … |
| maximal quotient of | C3×#4647, C3×#4650, C3×#4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 660);