Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1277 ⋊ C2 |
| Sylow | C53 ⋊ #8996 |
484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 77 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)(54,57,58,59)(55,60,56,61)(62,64,66,72)(63,69,70,77)(65,74,68,71)(67,75,73,76);(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)(54,56,58,55)(57,61,59,60)(62,63,68,67,66,70,65,73)(64,69,71,75,72,77,74,76);(54,55,59,60,58,56,57,61)(63,67,70,73)(64,71,72,74)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,i^c=i^521508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64461);