Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C23 |
| direct product | 3−1+2×#5934 |
| Fitting | 3−1+2×H(5,𝔽2) ⋊ D3 |
905 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 905 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,3,5,6)(2,4,7,8)(9,15,16,14,12,13,11,10,17);(2,3,5)(6,7,8)(10,12,15)(13,17,16)143 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#5934 |
| maximal normal subgroup of | AGL(1,ℤ/9)×#5934 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,3,5,6)(2,4,7,8)(9,15,16,14,12,13,11,10,17), (2,3,5)(6,7,8)(10,12,15)(13,17,16));