Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1868 ⋊ C2 |
| Sylow | C53 ⋊ #27694 |
626 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)(54,58,59,77,61,78,60,69)(55,64,65,76,67,80,66,83)(56,70,71,79,72,57,74,75)(62,73,68,82,81,85,84,63);(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)(54,57)(55,63)(56,69)(58,71)(59,75)(60,79)(61,70)(62,80)(64,81)(65,73)(66,85)(67,82)(68,83)(72,77)(74,78)(76,84);(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)(54,56,59,71,61,72,60,74)(55,62,65,68,67,81,66,84)(57,69,75,58,70,77,79,78)(63,64,73,76,82,80,85,83);(54,55,59,66,61,67,60,65)(56,68,71,62,72,84,74,81)(57,73,75,63,70,85,79,82)(58,76,77,64,78,83,69,80)Polycyclic presentation:
2^8,53|a^2=eg,b^2=e,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,f^b=fh,i^b=i^52,d^c=dh,f^c=fh,i^c=i^52,i^d=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 251764);