Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2069 ⋊ C2 |
| Sylow | C53 ⋊ #32871 |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,57)(55,63)(56,68)(58,73)(59,72)(60,74)(61,75)(62,78)(64,80)(65,79)(66,81)(67,82)(69,83)(70,71)(76,84)(77,85);(55,62)(56,67)(57,72)(58,59)(63,79)(64,65)(66,76)(68,71)(69,70)(73,74)(75,84)(81,85);(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)(54,56,58,69,60,70,59,67)(55,61,64,66,65,77,62,76)(57,71,72,83,74,68,73,82)(63,75,78,84,79,85,80,81);(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)(54,55,59,64,60,65,58,62)(56,66,67,77,70,76,69,61)(57,63,72,80,74,79,73,78)(68,81,82,85,71,84,83,75)Polycyclic presentation:
2^8,53|a^2=gh,b^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,c^b=cg,d^b=def,f^b=fh,i^b=i^52,d^c=de,e^c=eh,f^c=fh,g^c=gh,e^d=eh,f^d=fh,i^d=i^52626 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 318169);