Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#949 |
| Fitting | C32×#41 ⋊ C2 |
| Sylow | C32 ⋊ AGL(1,ℤ/8) |
156 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 156 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) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3)(4,5,6)(7,8)(9,14)(10,12)(11,13);(8,12)(11,14);(5,6)(8,11)(9,13)(12,14)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10591665, #10591667, #10591677, … |
| maximal normal subgroup of | #10591665, #10591667, #10591677, … |
| maximal quotient of | C3×#4995, C3×#5001, C3×#5003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 720);