Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C3×C5×#3153 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C2×C3×C42×C5 ◁ G | |
1144 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(10,12)(13,14)(15,21)(16,24)(17,19)(18,23)(20,25)(22,27)(26,28);(13,15,16,23,17,22,25,28)(14,18,20,21,19,26,24,27);(9,10,11,12)(14,19)(18,26)(20,24)(21,27);(15,22)(18,26)(21,27)(23,28)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1885);