Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C4 |
| direct product | C3×C5×#1922 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C5 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle | C22×C3×C5 | C4×D4 |
| prime radical | C23×C3×C5 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C5 ◁ C22×C3×C5×C8 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,14)(12,13)(15,16)(17,18,21,25,22,20,29,24)(19,23,27,31,28,26,32,30);(10,13)(14,16)(17,19,21,27,22,28,29,32)(18,23,25,31,20,26,24,30);(9,11,12,15)(10,14,13,16)(17,20)(18,22)(19,26)(21,24)(23,28)(25,29)(27,30)(31,32)570 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 654);