Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #4626 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C4 |
| direct product | C5×#67999 |
| derived | C42⋊C3 ⋊ C5×C8 |
102 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(6,7,8,10,9,11,12,13)(14,19,29,23)(15,26,25,24)(16,17,22,28)(18,27,21,20);(15,20,28)(16,21,22)(17,24,18)(19,25,26)(23,29,27)110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236356);