Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5×C19 · Schur multiplier (H2) = C22 |
| direct product | C5×C22⋊C4×C19 |
| unambiguous semidirect product | C22⋊(C4×C5×C19) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5×C19 | C22 |
| commutator | C2 | C2×C4×C5×C19 |
| Frattini, cosocle | C22 | C22×C5×C19 |
| prime radical | C23×C5×C19 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5×C19 ◁ G | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 760 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,3,4,5)(6,7,9,11)(8,10,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(7,10)(11,13)950 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 81);