Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | #104×#857 |
| Fitting | C42×#104 ⋊ D3 |
3337 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 3337 conjugacy classes of subgroups — too many to draw. Only its 77 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) = 24 |
A minimal faithful permutation representation — 3 generators on 20 points:
(2,5,7,6)(9,13,20)(10,11,19)(12,18,17)(14,16,15);(1,2)(3,5)(4,7)(6,8)(11,15)(13,17)(16,20)(18,19);(11,15)(13,17)(16,20)(18,19)140 conjugacy classes — view the full character table.
| maximal subgroup of | #8572, #72258767 |
| maximal normal subgroup of | #72258767 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,5,7,6)(9,13,20)(10,11,19)(12,18,17)(14,16,15), (1,2)(3,5)(4,7)(6,8)(11,15)(13,17)(16,20)(18,19), (11,15)(13,17)(16,20)(18,19));