Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#2194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| prime radical | C3×C5×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#131 ◁ G | |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,15,21)(11,22,25,38)(12,26,30,37)(13,20,14,19)(16,32,35,23)(17,31,36,24)(18,28,33,29)(27,39,40,34);(9,11)(10,16)(12,27)(13,24)(14,31)(15,25)(17,33)(18,36)(19,34)(20,39)(21,35)(22,26)(23,29)(28,32)(30,40)(37,38);(9,11)(10,17)(12,23)(13,31)(14,24)(15,25)(16,33)(18,35)(19,38)(20,22)(21,36)(26,39)(27,29)(28,40)(30,32)(34,37)345 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 926);