Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#909 |
| Fitting | C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #137 |
130 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 130 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) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,6)(7,16,17,10,11,19,9,20)(8,18,12,13,15,21,14,22);(7,17,11,9)(8,14,15,12)(10,16,20,19)(13,21,22,18);(5,6)(7,8)(9,12)(10,18)(11,15)(13,16)(14,17)(19,22)(20,21)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10590979, #10590981, #10590983, … |
| maximal normal subgroup of | #10590979, #10590981, #10590983, … |
| maximal quotient of | C3×#4702, C3×#4703, C3×#4710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 680);