Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#886 |
| Fitting | C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #123 |
173 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 173 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)(7,10,9,8)(12,16)(13,18);(11,13)(12,15)(14,18)(16,17);(5,6)(8,10)(11,12)(13,17)(14,16)(15,18)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10590408, C3×#4742, #10594077, … |
| maximal normal subgroup of | #10590408, C3×#4742, #10594077, … |
| maximal quotient of | C3×#4653, C3×#4659, C3×#4661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 657);