Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#898 |
| Fitting | C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #126 |
133 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 133 conjugacy classes of subgroups — too many to draw. Only its 58 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)(16,22,19,20);(7,13,10,9)(8,14,12,11)(16,19)(17,21);(5,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,20)(18,19)(21,22)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10594405, #10594409, #10594414, … |
| maximal normal subgroup of | #10594405, #10594409, #10594414, … |
| maximal quotient of | C3×#4651, C3×#4654, C3×#4660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 669);