Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1910 ⋊ C2 |
| Sylow | C53 ⋊ #22284 |
796 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)(54,58,59,75,60,76,77,61)(55,63,64,56,66,68,65,69)(57,72,73,82,74,85,84,78)(62,79,80,67,81,71,70,83);(54,57,60,74)(55,62)(56,67)(58,72,76,85)(59,73,77,84)(61,78,75,82)(63,79)(64,80)(65,70)(66,81)(68,71)(69,83);(54,56,59,68,60,69,77,63)(55,61,64,58,66,75,65,76)(57,71,84,67,74,79,73,83)(62,72,70,78,81,85,80,82);(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)(54,55)(56,58)(57,70,74,80)(59,65)(60,66)(61,68)(62,73,81,84)(63,75)(64,77)(67,82,83,78)(69,76)(71,72,79,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=ef,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=ce,f^b=fh,g^c=gh,i^d=i^52800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 183474);