Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#2370 |
| 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 | |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10,12,11)(13,14,17,16)(15,19,20,18)(21,22)(23,27)(24,28)(25,26);(9,11,12,10)(14,16)(18,19)(22,26)(24,27);(13,15)(14,18)(16,19)(17,20)(21,23,25,28)(22,27,26,24);(13,16,17,14)(15,19,20,18)(21,24,25,27)(22,28,26,23)750 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1102);