Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×C3⋊D3×3−1+2 |
| Fitting, Sylow | C33×3−1+2 ⋊ C22 |
1912 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1912 conjugacy classes of subgroups — too many to draw. Only its 154 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) = 108 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,3)(5,6)(7,8,9)(10,16,17,15,13,14,12,11,18);(4,5,6)(8,9)(11,13,16)(14,18,17);(1,2,3)198 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3)(5,6)(7,8,9)(10,16,17,15,13,14,12,11,18), (4,5,6)(8,9)(11,13,16)(14,18,17), (1,2,3));