Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C25 |
| direct product | C3×C5×#3270 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3×C5 |
| prime radical | C3×C5×#548 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C4×C5×D4 ◁ G | |
944 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,12)(14,18)(16,24)(19,27)(20,25)(21,28)(22,26);(13,14,17,20)(15,21,23,27)(16,25,24,18)(19,26,28,22);(10,12);(13,15,17,23)(14,19,20,28)(16,26,24,22)(18,27,25,21)435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 2002);