Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×#1553 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C42 | C23×C3×C5 |
| prime radical | C3×C5×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,13)(12,14)(15,16)(17,18,21,24,22,25,20,29)(19,26,27,31,28,23,30,32);(10,13)(11,16)(14,15)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,26)(29,32);(10,14)(13,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,26,32)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 285);