Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C24 |
| direct product | C3×C5×#3191 |
| 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 ◁ C23×C3×C4×C5 ◁ G | |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,15)(12,14)(13,16)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32);(9,11)(10,13)(12,16)(14,15);(11,16)(13,15)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(10,14)(13,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 1923);