Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C5×#332 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C22⋊C4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2)(19,20,21)(22,23,24,25,26);(4,7)(5,9)(8,10)(11,12,14,16,15,18,13,17);(3,4,6,8)(5,10,9,7)(12,16)(13,14)(17,18)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 271);