Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C22 |
| direct product | SL(2,ℤ/4)×#1094 |
946 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 108 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4)(6,8,7)(9,10,12,11)(13,19,20,15,14,21,18,16,17);(5,8)(6,7)(10,11,12)(14,16,19)(17,21,20)200 conjugacy classes — view the full character table.
| maximal quotient of | #72245336 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3,4)(6,8,7)(9,10,12,11)(13,19,20,15,14,21,18,16,17), (5,8)(6,7)(10,11,12)(14,16,19)(17,21,20));