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×#3540 |
| 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 | |
2116 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)(19,26)(20,23)(21,29)(22,25)(24,30)(27,31)(28,32);(10,13)(14,16)(17,19,22,20)(18,23,25,26)(21,27,30,28)(24,31,29,32);(9,10)(11,14)(12,13)(15,16)(17,20,22,19)(18,23,25,26)(21,28,30,27)(24,31,29,32);(9,11)(10,14)(12,15)(13,16)(17,18)(19,26)(20,23)(21,24)(22,25)(27,32)(28,31)(29,30);(17,21,22,30)(18,24,25,29)(19,27,20,28)(23,31,26,32)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2272);