Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1881 ⋊ C2 |
| Sylow | C53 ⋊ #24422 |
1300 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)(55,61)(56,66)(58,71)(59,72)(60,76)(62,69)(63,79)(64,80)(65,81)(67,83)(68,84)(70,75)(73,82)(74,78)(77,85);(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)(54,55)(56,65)(57,61)(58,74)(59,62)(60,73)(63,75)(64,67)(66,81)(68,77)(69,72)(70,79)(71,78)(76,82)(80,83)(84,85);(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)(54,56,59,68)(55,60,62,64)(57,66,72,84)(58,73,75,67)(61,76,69,80)(63,65,74,77)(70,83,71,82)(78,85,79,81);(54,55,58,63,59,62,75,74)(56,64,67,65,68,60,73,77)(57,69,70,79,72,61,71,78)(66,76,82,81,84,80,83,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh,g^c=gh,i^c=i^52,f^d=fh,i^d=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 207106);