Finite Group DatabasebetaFinite Group Databasebeta| order | 13020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D217 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C31 | C22 |
| LCS | G ▷ C3×C5×C7×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 3255 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(32,33,35,37,38,36,34)(39,40)(41,42)(45,46);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(33,34)(35,36)(37,38)(40,41)(42,43)(44,45,46)Polycyclic presentation:
2^2,3,5,7,31|d^a=d^4,e^a=e^6,f^a=f^30,c^b=c^2,d^b=d^4984 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13020, 228);