Finite Group DatabasebetaFinite Group Databasebeta| order | 13020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊(C7⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C31 | C3×C4 |
| prime radical | C7×D5×C31⋊C3 | C2 |
| cosocle | C7×D5×C31 | C2×C3 |
| LCS | G ▷ C5×C7×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1085 |
A minimal faithful permutation representation — 2 generators on 43 points:
(2,6,7,3,4,8)(5,14,15,9,10,22)(11,25,26,17,18,30)(12,24,20,19,16,13)(21,23,31,27,28,29)(33,34)(35,36)(37,38)(40,41,42,43);(1,2,5,11,19,4,8,13,21,28,10,16,22,26,31,18,25,29,30,15,24,14,23,27,20,7,6,12,17,9,3)(32,33,35,37,38,36,34)(39,40,41,43,42)Polycyclic presentation:
2,3,2,5,7,31|a^2=c,d^a=d^2,e^a=e^6,f^a=f^30,f^b=f^5,d^c=d^4191 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13020, 124);