Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C5×#3131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C22×C3×C5 | C22×D4 |
| prime radical | C3×C5×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G | |
800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,25)(20,24)(21,26)(22,27)(23,28)(29,32)(30,31);(10,13)(14,16)(17,19,22,29,23,30,21,20)(18,24,26,31,28,32,27,25);(9,11,12,15)(10,14,13,16)(17,20,21,30,23,29,22,19)(18,25,27,32,28,31,26,24);(17,21,23,22)(18,26,28,27)(19,20,30,29)(24,31,32,25)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1863);