Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#1811 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C22×C3×C5 | C2×C4⋊C4 |
| prime radical | C24×C3×C5 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C23×C3×C4×C5 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(13,14,17,20,18,21,16,26)(15,22,25,27,23,28,24,19);(13,15,16,24,18,23,17,25)(14,19,20,22,21,27,26,28);(10,12)(15,23)(19,27)(22,28)(24,25)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 543);