Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #14515297 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C25 ⋊ A5 |
| derived | #11757162 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | #11757162 | C2 |
| Frattini, socle, cosocle | C24 | C2×A5 |
| Fitting | C25 | A5 |
| LCS | G ▷ #11757162 | |
| UCS | C1 | |
265 conjugacy classes of subgroups; only the 5 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 5 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,5,11)(2,6,10)(3,7,9)(4,8,12)(13,14,15)(17,20,19);(1,8,16,17,9,4,7,14,18,12)(2,6,13,19,11,3,5,15,20,10)18 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240995);