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×#3538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C3×C5 |
| prime radical | C3×C5×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ G | |
2028 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)(17,18,22,24)(19,25,27,20)(21,29,30,23)(26,28,32,31);(10,13)(14,16)(17,19,22,27)(18,20,24,25)(21,26,30,32)(23,28,29,31);(9,10)(11,14)(12,13)(15,16);(9,11)(10,14)(12,15)(13,16)(17,20)(18,19)(21,28)(22,25)(23,26)(24,27)(29,32)(30,31);(17,21,22,30)(18,23,24,29)(19,26,27,32)(20,28,25,31)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2270);