Finite Group DatabasebetaFinite Group Databasebeta| order | 13020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14579600⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #13049959⋊C5 |
| commutator, hypocenter | C7×C31 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C7×C31 | C2×C3×C5 |
| prime radical | C2×#10620253⋊C5 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 868 |
A minimal faithful permutation representation — 2 generators on 42 points:
(2,7,21,20,11,6,4,15,25,5,3,13,9,26,24)(8,27,10,30,16,14,18,29,23,31,17,12,22,19,28)(33,36,37,34,35,38)(39,40,41,42);(1,2,5,12,20,6,14,26,9,21,24,30,28,18,15,27,4,10,13,11,25,31,22,29,23,3,8,19,7,16,17)(32,33,35,38,37,36,34)Polycyclic presentation:
2,3,5,7,31,2|a^2=f,d^a=d^6,d^b=d^2,e^b=e^25,e^c=e^1690 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13020, 67);