Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1272 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C3×C5 | C22⋊C4 |
| commutator | C2×C4 | C2×C3×C5×C8 |
| Frattini, cosocle | C2×C42 | C22×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15,16,13)(12,14)(18,21,22,23)(25,26,27,29,28,30,31,32);(9,11)(10,13)(12,16)(14,15)(17,18,20,22)(19,23,24,21)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4);