Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#2243 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C2×C3×C5×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,28)(20,25)(21,24)(22,30)(23,27)(26,29)(31,32);(10,13)(14,16)(17,18,21,25,22,26,28,32,23,27,31,19,29,30,20,24);(9,11,12,15)(10,14,13,16)(17,19,20,27,29,32,31,26,23,25,28,18,22,24,21,30)390 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 975);