Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#1952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #121 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10,12,11)(14,19)(15,22)(16,17)(20,27)(21,25)(23,24);(9,11,12,10)(13,14)(15,20)(16,25)(17,19)(18,21)(22,26)(23,28)(24,27);(13,15,16,23,18,24,17,22)(14,20,25,28,21,27,19,26)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 684);