Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×C4⋊AGL(2,𝔽3) |
| Fitting | C33×C4 ⋊ GL(2,𝔽3) |
591 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 40 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 — 2 generators on 16 points:
(1,2,3)(5,7)(8,11,16,12,9,15,14,10);(4,5,6,7)(9,10,14)(11,13,15)96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72259824 |
| maximal quotient of | C3×#72259824 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(5,7)(8,11,16,12,9,15,14,10), (4,5,6,7)(9,10,14)(11,13,15));