Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3230 ⋊ C2 |
| Sylow | C53 ⋊ #19417 |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(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)(70,72,74,79)(71,76,78,83)(73,80,81,85)(75,82,77,84);(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)(71,75)(73,81)(76,82)(77,78)(80,85)(83,84);(54,56,63,67,58,65,57,64)(55,59,66,69,61,68,60,62)(72,79)(76,83)(80,85)(82,84);(54,55,58,61)(56,62,65,69)(57,66,63,60)(59,67,68,64)(70,71,74,78)(72,76,79,83)(73,75,81,77)(80,82,85,84)Polycyclic presentation:
2^8,53|a^2=gh,b^2=eg,d^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=dh,f^c=fh,i^c=i^52881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 155063);