Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C8 · Schur multiplier (H2) = C42 |
| direct product | C3×C5×#1274 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C42 |
| commutator | C4 | C3×C4×C5×C8 |
| Frattini, cosocle | C2×C42 | C22×C3×C5 |
| socle | C22×C3×C5 | #95 |
| prime radical | C23×C3×C5 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ G | |
336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10,11,13,12,14,15,16)(17,18)(19,25,27,31)(20,23)(21,24)(22,26,29,32)(28,30);(17,19)(18,22,24,29)(20,26)(21,27)(23,25,30,31)(28,32)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6);