Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #73011 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#73021 |
| Fitting | C5×C8×Q8 ⋊ D3 |
236 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,10,9,11,12,13)(14,20,21)(15,19,17);(7,10)(8,12)(11,13)(15,18)(16,20)(19,21)185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236443);