Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#946 |
| Fitting | C2×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C22⋊Q8 |
167 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 70 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)(8,10)(11,18,14,13)(12,17,16,15);(11,16,14,12)(13,15,18,17);(5,6)(7,8)(9,10)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10591549, #10591551, #10591558, … |
| maximal normal subgroup of | #10591549, #10591551, #10591558, … |
| maximal quotient of | C3×#4972, C3×#4978, C3×#4982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 717);