Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#2249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C2×C3×C5×D16 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
368 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)(16,28)(17,20)(18,31)(19,25)(21,24)(22,29)(26,35)(27,42)(30,43)(32,41)(33,44)(34,39)(36,38)(37,40);(13,15,24,38,18,27,30,41,17,26,39,44,29,40,16,25)(14,19,28,37,22,33,34,35,20,32,43,42,31,36,21,23);(9,10,11,12)(14,20)(19,32)(21,34)(22,31)(23,35)(28,43)(33,36)(37,42)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 981);