Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13280 |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 points:
(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)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,56,57,61)(55,58,59,60)(63,70)(69,85)(71,80)(72,88)(73,89)(74,92)(86,90)(87,91);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(62,64,75,79,66,77,68,84)(63,69,73,91,70,85,89,87)(65,78,67,83,81,93,82,76)(71,90,72,74,80,86,88,92);(54,55,57,59)(56,60,61,58)(62,63,67,72,75,89,81,71,66,70,82,88,68,73,65,80)(64,74,78,69,84,86,76,91,77,92,93,85,79,90,83,87)Polycyclic presentation:
2^8,53|a^2=f,b^2=defg,c^2=eh,d^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,d^b=dg,f^b=fg,g^b=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88159);