Finite Group DatabasebetaFinite Group Databasebeta| order | 13260 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17984471⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C17 | C3×C4 |
| prime radical | C5×C17⋊(D13⋊C3) | C2 |
| cosocle | C5×D221 | C2×C3 |
| LCS | G ▷ C5×C13×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1105 |
A minimal faithful permutation representation — 2 generators on 35 points:
(2,3,4,6)(5,8,9,14)(7,10,12,11)(13,15,16,17)(19,23,28,24,21,25,22,29,26,20,27,30)(32,33)(34,35);(1,2,5,10,3,7,13,15,8,14,17,16,12,6,11,9,4)(18,19,23,21,28,20,25,30,24,26,27,29,22)(31,32,34,35,33)Polycyclic presentation:
2,3,2,5,13,17|a^2=c,d^a=d^4,e^a=e^5,f^a=f^4,e^b=e^3,e^c=e^12,f^c=f^16169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13260, 51);