Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | 3−1+2×C3⋊AGL(1,ℤ/9) |
| Fitting, Sylow | C3×3−1+22 ⋊ C2 |
3106 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 3106 conjugacy classes of subgroups — too many to draw. Only its 252 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 162 |
A minimal faithful permutation representation — 3 generators on 21 points:
(2,3)(4,7,12,6,10,8,9,5,11)(14,16)(15,19)(17,20)(18,21);(1,2,3)(14,17,21)(16,20,18);(5,7,10)(8,12,11)(13,17,16,15,21,18,19,14,20)231 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)(4,7,12,6,10,8,9,5,11)(14,16)(15,19)(17,20)(18,21), (1,2,3)(14,17,21)(16,20,18), (5,7,10)(8,12,11)(13,17,16,15,21,18,19,14,20));