Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#3028 ⋊ C2 |
| Sylow | C53 ⋊ #25798 |
1430 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)(54,57,58,70,59,71,73,83)(55,61,62,69,63,75,72,82)(56,66,67,80,68,81,78,85)(60,74,64,76,65,79,77,84);(54,55)(56,65,68,60)(57,61)(58,62)(59,63)(64,67,77,78)(66,79,81,74)(69,70)(71,75)(72,73)(76,80,84,85)(82,83);(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)(54,56,58,67,59,68,73,78)(55,60,62,64,63,65,72,77)(57,66,70,80,71,81,83,85)(61,74,69,76,75,79,82,84);(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)(54,55)(56,64)(57,69)(58,72)(59,63)(60,67)(61,70)(62,73)(65,78)(66,79)(68,77)(71,82)(74,81)(75,83)(76,80)(84,85)Polycyclic presentation:
2^8,53|b^2=e,c^2=f,d^2=e,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,g^a=gh,i^a=i^52,c^b=cg,f^b=fh,i^b=i^52,g^c=gh,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 225163);