Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C25 |
| direct product | #97×C22⋊A4 |
| Fitting, Sylow | C24×#97 ⋊ C3 |
5770 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 5770 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 20 points:
(6,7,8)(10,12,11)(13,14,15,18,16,17,19,20);(1,2,3,4)(9,12)(10,11)(14,17)(18,20);(5,8)(6,7)160 conjugacy classes — view the full character table.
| maximal subgroup of | A42×#97, #97×#1020 |
| maximal normal subgroup of | A42×#97, #97×#1020 |
| maximal quotient of | #72341744 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((6,7,8)(10,12,11)(13,14,15,18,16,17,19,20), (1,2,3,4)(9,12)(10,11)(14,17)(18,20), (5,8)(6,7));