Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#349 ⋊ C2 |
| Sylow | C53 ⋊ #13201 |
420 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)(54,57,58,75,61,77,60,67)(55,62,64,73,66,71,63,82)(56,69,70,74,72,65,78,83)(59,76,68,81,80,84,79,85);(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)(54,56,68,82,58,78,80,71,61,72,79,73,60,70,59,62)(55,57,74,85,63,75,69,76,66,77,83,81,64,67,65,84);(54,55,59,65,60,64,79,83,61,66,80,69,58,63,68,74)(56,67,71,85,70,77,82,84,72,75,62,81,78,57,73,76)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=e,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,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, 87777);