Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #396⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#1443⋊C3 |
| unambiguous semidirect product | #1443⋊(C3×C5) |
| unambiguous semidirect product | (C5×#1443)⋊C3 |
| Fitting, Hall | C5×#1443 ⋊ C3 |
| derived | #95 ⋊ C3×C4×C5 |
| Sylow | #1443 ⋊ C3×C5 |
222 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 38 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) = 240 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,9)(10,11,14)(12,17,21,18,16,20)(13,15,19);(10,18,13,12)(11,15)(14,20)(19,21)180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236366);