Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#73072 |
236 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 640 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(6,8,10,9)(7,11,12,13)(14,26,24,19,22,29,16,20,25,15,17,28)(18,21,23,27);(6,7,9,11,10,12,8,13)(15,19)(17,23)(18,22)(20,21)(24,25)(26,27)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236494);