Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1644 ⋊ C2 |
| Sylow | C53 ⋊ #19906 |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
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)(70,72,74,80)(71,77,76,85)(73,83,81,79)(75,84,82,78);(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)(55,60)(57,65)(59,66)(61,62)(63,69)(67,68)(71,76)(75,82)(77,85)(78,84);(54,56,58,64)(55,59,62,68)(57,63,65,69)(60,66,61,67)(70,71,74,76)(72,78,80,84)(73,82,81,75)(77,83,85,79);(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)(56,59)(57,60)(58,62)(61,65)(63,66)(64,68)(67,69)(71,75)(73,81)(76,82)(77,84)(78,85)(79,83)Polycyclic presentation:
2^8,53|b^2=gh,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^52,c^b=cg,d^b=de,e^b=eg,f^c=fh,i^c=i^52,e^d=eg,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 161135);