Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#73061 |
372 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 72 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)(6,7,8,9)(11,13)(14,24,26)(15,25,29)(16,23,18)(19,28,21);(10,11)(12,13)(14,15,18,21)(16,22,24,20)(17,25,27,19)(23,29,26,28)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236483);