Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | D12×PSU(3,𝔽2)⋊C3 |
| Fitting | C33×C4 ⋊ C2×SL(2,𝔽3) |
634 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 54 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)(5,7)(8,9,13)(10,14,12)(11,15,16);(2,3)(4,5)(6,7)(9,15,14,11)(10,16,13,12)90 conjugacy classes — view the full character table.
| maximal subgroup of | #626×PSU(3,𝔽2)⋊C3 |
| maximal quotient of | #626×PSU(3,𝔽2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(5,7)(8,9,13)(10,14,12)(11,15,16), (2,3)(4,5)(6,7)(9,15,14,11)(10,16,13,12));