Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #11757163⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #11757163⋊C2 |
| Fitting, socle | C24 ⋊ S5 |
| derived | #11757163 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #11757163 | C2 |
| Fitting, socle | C24 | S5 |
| LCS | G ▷ #11757163 | |
| UCS | C1 | |
197 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 10 |
| transitive degree | μt(G) = 10 |
A minimal faithful permutation representation — 2 generators on 10 points:
(1,2)(3,8,5)(4,6)(7,9,10);(1,6,3)(2,7,4)(5,9)(8,10)18 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240996);