Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2074 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3×C5 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 36 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14)(15,18)(16,17)(19,20)(21,22)(23,26)(24,27)(25,28)(29,36)(30,34)(31,33)(32,35);(14,17)(18,20)(21,23,24,30)(22,26,27,34)(25,29,32,31)(28,36,35,33);(10,12)(13,15,16,19)(14,18,17,20)(22,27)(23,29)(25,32)(26,33)(30,31)(34,36)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 806);