Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C3×C3⋊D3×AΣL(1,𝔽27) |
| Fitting, Sylow | C33×AΣL(1,𝔽27) ⋊ C2 |
13504 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 13504 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) = 18 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3)(5,6)(8,9)(11,15,13)(14,17,18);(7,8,9)(10,15,17,12,13,14,16,11,18);(4,5,6)(11,13,15)306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#10624749 |
| maximal normal subgroup of | C3⋊D3×#10624749 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(5,6)(8,9)(11,15,13)(14,17,18), (7,8,9)(10,15,17,12,13,14,16,11,18), (4,5,6)(11,13,15));