Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#2110 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C5×C8 | C42 |
| commutator | C4 | C2×C3×C42×C5 |
| Frattini, cosocle | C2×C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×#97 |
| prime radical | C23×C3×C5 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C8 ◁ G | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 40 points:
(1,2,3)(4,5,6,7,8)(9,10,12,16,13,18,24,32,14,17,25,31,26,33,39,40)(11,19,21,35,22,28,37,30,20,34,23,38,36,15,27,29);(9,11)(10,15,17,28)(12,23)(13,22)(14,20)(16,30,31,29)(18,19,33,34)(21,25)(24,27)(26,36)(32,38,40,35)(37,39);(11,20)(15,28)(19,34)(21,23)(22,36)(27,37)(29,30)(35,38)660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 842);