Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #2017⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#2091⋊C3 |
| unambiguous semidirect product | #2091⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2091)⋊C3 |
| Fitting, Hall | C5×#2091 ⋊ C3 |
| derived | #338 ⋊ C2×C3×C5 |
| Sylow | #2091 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #127⋊C3 |
| commutator, cosocle, hypocenter | #338 | C2×C3×C5 |
| Frattini | C22×C4 | C2×C5×A4 |
| Fitting | C5×#2091 | C3 |
| socle | C2×C5 | #399⋊C3 |
| LCS | G ▷ #338 | |
| UCS | C1 ◁ C4×C5 | |
134 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 134 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) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(7,15,18,11,12,8)(13,17,21,20,19,14);(6,12,9,20,10,15,16,13)(7,8,21,17,11,18,14,19)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236396);