Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#896 |
| Fitting | C32×C4⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C22⋊Q8 |
161 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 161 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) = 96 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3)(4,5,6)(7,10,9,8)(12,16)(15,18);(8,10)(11,17,14,13)(12,18,16,15);(5,6)(8,10)(11,12)(13,15)(14,16)(17,18)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10594319, #10594328, #10594330, … |
| maximal normal subgroup of | #10594319, #10594328, #10594330, … |
| maximal quotient of | C3×#4646, C3×#4652, C3×#4657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 667);