Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2005 ⋊ C2 |
| Sylow | C53 ⋊ #25194 |
980 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(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)(58,62)(59,67)(60,72)(61,76)(63,79)(64,78)(65,80)(66,81)(68,84)(69,77)(70,85)(71,86)(73,88)(74,87)(75,89)(82,83);(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)(55,57)(58,61,65,60)(59,66,70,82)(62,76,80,72)(63,74,64,73)(67,81,85,83)(68,71,69,75)(77,89,84,86)(78,88,79,87);(54,55)(56,57)(58,60,64,73,65,61,63,74)(59,66,68,75,70,82,69,71)(62,76,78,87,80,72,79,88)(67,83,84,86,85,81,77,89);(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)(58,59,64,68,65,70,63,69)(60,71,73,66,61,75,74,82)(62,77,78,67,80,84,79,85)(72,81,88,89,76,83,87,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,d^b=dh,e^b=eh,f^c=fh,g^c=gh,i^c=i^52,e^d=eh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 217634);