Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
274 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,3,2,4)(5,43,14,39,17,32,6,48)(7,49,23,33,18,51,13,40)(8,50,12,29,19,52,22,41)(9,42,24,38,16,31,15,30)(10,36,21,47,20,46,11,37)(25,44,26,45,27,34,28,35)(53,56,54,55)(57,83,58,90,69,94,66,82)(59,102,65,93,70,104,75,81)(60,103,74,85,71,101,64,92)(61,95,67,100,68,84,76,91)(62,89,63,98,72,99,73,88)(77,97,80,96,79,87,78,86);(1,54)(2,53)(3,56)(4,55)(5,76,19,57,14,71,16,66,7,68,15,59,17,67,8,69,6,60,9,58,18,61,24,70)(10,65,28,62,22,80,11,74,25,63,23,77,20,75,26,72,12,78,21,64,27,73,13,79)(29,90,51,81,39,103,40,91,52,92,30,104,41,82,49,93,48,101,33,100,50,85,38,102)(31,96,47,83,45,99,32,97,36,84,34,88,42,86,37,94,35,89,43,87,46,95,44,98)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240638);