Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C5×#2381 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C24 |
| commutator | C22 | C23×C3×C4×C5 |
| Frattini, cosocle | C23 | C24×C3×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 36 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(14,17)(15,19)(22,26)(23,29)(28,31)(30,35);(14,17)(18,20)(21,22,25,26)(23,27,29,33)(24,31,32,28)(30,36,35,34);(13,14,16,17)(15,18,19,20)(21,23)(22,27)(24,30)(25,29)(26,33)(28,34)(31,36)(32,35);(13,15)(14,18)(16,19)(17,20)(21,24,25,32)(22,28,26,31)(23,30,29,35)(27,34,33,36)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1113);