Finite Group DatabasebetaFinite Group Databasebeta| order | 13260 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1105⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C17⋊(D13⋊C3)) |
| commutator, hypocenter | C5×C13×C17 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C13×C17 | C2×C3 |
| prime radical | C2×C5×C17×C13⋊C3 | C2 |
| LCS | G ▷ C5×C13×C17 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4420 |
A minimal faithful permutation representation — 2 generators on 39 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,23,24,20,21,25)(22,29,28,26,27,30)(32,33)(34,35)(36,37,38,39);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,22,21,25,28,27,29,30,24,23,26,20)(31,32,34,35,33)Polycyclic presentation:
2,3,5,13,17,2|a^2=f,c^a=c^4,d^a=d^12,e^a=e^16,d^b=d^3604 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13260, 24);