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×C4 |
| direct product | C3×C5×#2658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3×C5 |
| prime radical | C22×C3×C5×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
1224 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)(9,10,11,12)(18,22)(19,25)(24,30)(27,28);(13,14,15,16)(17,18)(19,26)(20,24)(21,22)(23,25)(27,32)(28,31)(29,30);(9,10)(11,12)(13,14)(15,16)(17,19)(18,23)(20,28)(21,25)(22,26)(24,32)(27,29)(30,31);(17,20,21,29)(18,24,22,30)(19,27,25,28)(23,31,26,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1390);