Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2634 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
832 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)(14,17)(18,20)(21,22,26,24)(23,29,31,27)(25,28,33,32)(30,35,36,34);(10,12)(14,17)(18,20)(21,23,26,31)(22,27,24,29)(25,30,33,36)(28,34,32,35);(9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24,26,22)(23,27,31,29)(25,28,33,32)(30,35,36,34);(13,15,16,19)(14,18,17,20)(21,25)(22,28)(23,30)(24,32)(26,33)(27,34)(29,35)(31,36)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1366);