Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2176 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C2×D8 |
| commutator | C8 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1920 |
A minimal faithful permutation representation — 3 generators on 44 points:
(1,2,3)(4,5,6,7,8)(9,10,12,11)(13,14)(15,23)(16,27)(17,32)(18,20)(19,24)(21,30)(22,29)(25,43)(26,40)(28,38)(31,39)(33,37)(34,42)(35,44)(36,41);(13,15,18,26)(14,19,20,34)(16,28,31,44)(17,33,29,25)(21,37,36,43)(22,38,32,35)(23,39,40,27)(24,41,42,30);(9,11,12,10)(14,20)(19,34)(21,36)(22,32)(23,40)(27,39)(35,38)(37,43)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 908);