Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#1891 ⋊ C2 |
| Sylow | C53 ⋊ #23883 |
1696 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)(55,63)(58,59)(61,66)(62,78)(64,65)(68,74)(70,79)(71,72)(75,81)(76,80)(77,85)(82,84);(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)(54,57,60,73)(55,62,65,79)(56,67,69,83)(58,72,59,71)(61,75,76,77)(63,78,64,70)(66,81,80,85)(68,84,74,82);(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)(57,67)(58,74)(59,68)(60,69)(62,77)(63,66)(64,80)(65,76)(70,81)(71,84)(72,82)(73,83)(75,79)(78,85);(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)(56,66)(57,70)(58,63)(59,64)(60,65)(61,68)(62,72)(67,75)(69,80)(71,79)(73,78)(74,76)(77,83)(81,82)(84,85)Polycyclic presentation:
2^8,53|c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,e^b=eh,i^b=i^52,e^c=eh,f^c=fh,i^c=i^52,e^d=eh,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, 200994);