Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2048 ⋊ C2 |
| Sylow | C53 ⋊ #25197 |
968 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,55,60,64)(56,61,68,77)(57,62,71,79)(58,72,59,63)(65,67,76,73)(66,75,84,81)(69,74,78,70)(80,82,85,83);(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)(54,57)(55,62)(56,66)(58,70)(59,74)(60,71)(61,75)(63,78)(64,79)(65,80)(67,82)(68,84)(69,72)(73,83)(76,85)(77,81);(54,56,59,67,60,68,58,73)(55,61,63,76,64,77,72,65)(57,66,70,83,71,84,74,82)(62,75,69,80,79,81,78,85);(54,55,59,63,60,64,58,72)(56,65,67,61,68,76,73,77)(57,69,70,79,71,78,74,62)(66,81,83,85,84,75,82,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,g^b=gh,f^c=fh,e^d=eh,i^d=i^52638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 217669);