Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1668 ⋊ C2 |
| Sylow | C53 ⋊ #19762 |
728 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)(62,65,67,73)(63,69,70,77)(64,71,66,75)(68,76,74,72);(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)(55,58)(56,61)(59,60)(62,64,67,66)(63,68,70,74)(65,71,73,75)(69,76,77,72);(62,63,67,70)(64,68,66,74)(65,72,73,76)(69,75,77,71);(54,55)(56,58)(57,60)(59,61)(63,68)(64,66)(69,76)(70,74)(71,75)(72,77)Polycyclic presentation:
2^8,53|b^2=g,c^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=de,e^b=eg,f^c=fh,i^c=i^52,e^d=eg,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 159015);