Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2211 |
| 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 | |
316 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,23)(16,19)(17,29)(18,32)(20,25)(21,31)(22,28)(24,39)(26,43)(27,40)(30,38)(33,37)(34,41)(35,42)(36,44);(9,10,11,12)(14,19)(20,34)(21,35)(22,32)(23,39)(29,40)(36,38)(37,43);(13,15,16,24)(14,20,19,34)(17,30,27,44)(18,33,28,26)(21,37,35,43)(22,38,32,36)(23,40,39,29)(25,42,41,31)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 943);