Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1388 ⋊ C2 |
| Sylow | C53 ⋊ #12822 |
400 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)(55,63)(56,67)(58,71)(59,76)(60,72)(61,73)(62,77)(64,78)(65,81)(66,80)(68,83)(69,84)(70,75)(74,79)(82,85);(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)(54,56,58,68,61,69,60,59)(55,62,64,65,66,75,74,82)(57,67,71,83,73,84,72,76)(63,77,78,81,80,70,79,85);(54,55,60,64,61,66,58,74)(56,65,59,75,69,82,68,62)(57,70,72,85,73,77,71,81)(63,76,78,84,80,83,79,67)Polycyclic presentation:
2^8,53|a^2=f,b^2=d,d^2=h,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^b=i^52,e^c=eg,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85663);