Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3104 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| socle | C22×C3×C5 | C22×D4 |
| prime radical | C23×C3×C5 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C2×C3×C42×C5 ◁ G | |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26);(10,13)(14,16);(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(9,11,12,15)(10,14,13,16)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1836);