Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1640 ⋊ C2 |
| Sylow | C53 ⋊ #18666 |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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)(54,56,58,57)(55,60,61,59)(62,64,66,71)(63,68,69,75)(65,70,72,76)(67,74,73,77);(54,56,58,57)(55,59,61,60)(62,63)(64,68)(65,73)(66,69)(67,72)(70,77)(71,75)(74,76);(54,55)(56,59)(57,60)(58,61)(65,72)(67,73)(70,76)(74,77);(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)(55,59)(56,57)(60,61)(63,67)(65,72)(68,74)(69,73)(70,76)(75,77)Polycyclic presentation:
2^8,53|c^2=g,d^2=gh,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,i^a=i^52,d^b=dg,e^b=eg,f^b=fh,e^c=eh,f^c=fh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 147175);