Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×Dic6 |
| Sylow | C32 ⋊ C22×Q8 |
331 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 16 points:
(3,4,5)(6,7,8)(9,11,12,16)(10,13,14,15);(1,2)(4,5)(9,10,12,14)(11,15,16,13);(7,8);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#810, #10590600, #10590603, … |
| maximal normal subgroup of | D3×#810, #10590600, #10590603, … |
| maximal quotient of | #10593851, #10593853, #10593856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 942);