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×#2097 |
| 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 | |
476 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)(13,14,16,18)(15,19,20,17)(21,22,24,28,25,29,33,26)(23,30,31,35,32,36,34,27);(9,10)(11,12)(13,15,16,20)(14,17,18,19)(22,26)(24,33)(27,30)(28,29)(31,34)(35,36);(10,12)(21,23,25,32)(22,27,29,35)(24,34,33,31)(26,30,28,36)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 829);