Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2081 ⋊ C2 |
| Sylow | C53 ⋊ #32699 |
538 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)(54,58,59,70)(55,63,64,78)(56,66,67,83)(57,68,61,75)(60,74,72,71)(62,77,73,82)(65,81,80,79)(69,85,76,84);(54,57)(55,62,64,73)(56,65,67,80)(58,68)(59,61)(60,69)(63,77,78,82)(66,81,83,79)(70,75)(71,84)(72,76)(74,85);(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)(55,61)(57,64)(58,66)(59,67)(60,73)(62,72)(63,68)(65,69)(70,83)(71,77)(74,82)(75,78)(76,80)(79,85)(81,84);(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)(54,55,60,65,59,64,72,80)(56,57,62,69,67,61,73,76)(58,63,71,79,70,78,74,81)(66,75,82,85,83,68,77,84)Polycyclic presentation:
2^8,53|a^2=g,c^2=efh,d^2=h,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,i^a=i^52,c^b=cg,d^b=de,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh,g^d=gh,i^d=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 316429);