Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
341 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 20 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 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,67,40,52,29,71)(2,80,38,55,43,73)(3,92,42,65,8,72)(4,66,48,49,37,91)(5,89,36,62,9,83)(6,96,20,78,15,82)(7,79,21,50,23,57)(10,88,47,51,22,87)(11,86,19,54,24,56)(12,95,46,75,16,85)(13,69,18,58,28,93)(14,90,33,53,25,64)(17,84,32,61,34,63)(26,81,31,59,39,70)(27,68,44,60,35,77)(30,94,41,74,45,76);(1,87,16,54,39,91)(2,56,29,61,8,57)(3,86,36,60,31,90)(4,70,23,58,34,83,14,82,35,65,22,71)(5,63,43,74,15,64)(6,84,46,49,42,68)(7,72,25,59,45,85,27,93,37,78,24,73)(9,51,28,77,12,76)(10,96,21,52,41,80,17,81,44,62,19,95)(11,69,33,55,47,89,30,92,48,75,32,67)(13,94,40,50,20,66)(18,79,26,88,38,53)48 conjugacy classes — view the full character table.
| maximal subgroup of | #72276840, #72277090 |
| maximal normal subgroup of | #72277090 |
| maximal quotient of | #72276774, #72276971 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240631);