Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C28 |
| direct product | C3×C5×#3541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
2064 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 5 generators on 32 points:
(1,2,3)(4,5,6,7,8)(10,13)(11,15)(17,18)(19,25)(20,22)(21,28)(23,26)(24,29)(27,30)(31,32);(10,13)(14,16)(18,20)(19,26)(24,28)(27,32);(9,10)(11,14)(12,13)(15,16)(17,19)(18,23)(20,25)(21,27)(22,26)(24,30)(28,31)(29,32);(9,11)(10,14)(12,15)(13,16)(17,20,22,18)(19,25,26,23)(21,28,29,24)(27,31,32,30);(17,21,22,29)(18,24,20,28)(19,27,26,32)(23,30,25,31)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2273);