Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1841 ⋊ C2 |
| Sylow | C53 ⋊ #27833 |
442 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)(54,58,59,71,61,70,60,56)(55,64,65,62,67,68,66,78)(57,73,74,84,75,85,76,69)(63,79,72,77,81,82,80,83);(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)(58,73)(59,74)(60,76)(61,75)(62,77)(64,79)(65,72)(66,80)(67,81)(68,82)(70,85)(71,84)(78,83);(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)(54,56,60,70,61,71,59,58)(55,62,66,64,67,78,65,68)(57,73,74,84,75,85,76,69)(63,79,72,77,81,82,80,83);(54,55,60,65,61,67,59,66)(56,68,70,78,71,64,58,62)(57,72,76,81,75,80,74,63)(69,83,85,79,84,77,73,82)Polycyclic presentation:
2^8,53|a^2=efg,b^2=f,d^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,i^b=i^52,f^c=fh,g^c=gh,i^c=i^52,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 253667);