Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1742 ⋊ C2 |
| Sylow | C53 ⋊ #11090 |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(55,61)(56,64)(58,71)(59,69)(60,73)(62,67)(63,78)(65,68)(66,82)(70,72)(74,79)(75,85)(76,77)(80,81)(83,84);(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)(54,56)(55,60)(57,68,69,64)(58,66)(59,65)(61,73,67,79)(62,74)(63,75)(70,82,71,80)(72,81)(76,83,78,85)(77,84);(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)(54,55,58,63,59,62,72,77)(56,60,66,75,65,74,81,84)(57,67,70,78,69,61,71,76)(64,79,80,85,68,73,82,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,g^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fh,i^a=i^52,c^b=cf,f^b=fh,i^b=i^52,d^c=dh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76778);