Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1910 ⋊ C2 |
| Sylow | C53 ⋊ #22286 |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(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)(54,58,65,78,60,73,59,72)(55,62,56,67,64,79,63,71)(57,68,74,84,70,82,69,81)(61,75,66,80,77,85,76,83);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57,60,70)(55,61)(56,66)(58,68,73,82)(59,69,65,74)(62,75)(63,76)(64,77)(67,80)(71,83)(72,81,78,84)(79,85);(54,56,59,55,60,63,65,64)(57,61,74,66,70,77,69,76)(58,67,72,62,73,71,78,79)(68,75,84,80,82,85,81,83);(54,55,60,64)(56,65,63,59)(57,66)(58,71,73,67)(61,74)(62,78,79,72)(68,75)(69,77)(70,76)(80,81)(82,85)(83,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=ef,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^c=gh,i^d=i^52800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 183492);