Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1902 ⋊ C2 |
| Sylow | C53 ⋊ #23362 |
706 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)(55,62,64,63)(56,66)(60,75,76,80)(61,78,79,68)(65,82)(67,73)(69,83)(74,77,84,85);(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)(54,57,70,81,58,71,59,72)(55,61,63,68,64,79,62,78)(56,65,73,69,66,82,67,83)(60,74,75,77,76,84,80,85);(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)(55,60)(57,69)(58,66)(59,73)(61,77)(62,75)(63,80)(64,76)(65,81)(67,70)(68,74)(71,83)(72,82)(78,84)(79,85);(54,55)(56,60,66,76)(57,68,71,78)(58,64)(59,63)(61,72,79,81)(62,70)(65,77)(67,75,73,80)(69,74)(82,85)(83,84)Polycyclic presentation:
2^8,53|a^2=g,c^2=ef,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,c^b=cef,d^b=de,f^b=fh,g^b=gh,i^b=i^52,g^c=gh,i^c=i^52,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196151);