Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2145 ⋊ C2 |
| Sylow | C53 ⋊ #33468 |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(54,58,61,60)(55,64,66,75)(56,69,70,76)(57,72,73,59)(62,78,79,80)(63,71,81,65)(67,82,77,83)(68,84,85,74);(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)(54,57,60,59,61,73,58,72)(55,63,64,71,66,81,75,65)(56,68,76,74,70,85,69,84)(62,77,78,83,79,67,80,82);(54,56)(55,62)(57,68)(58,69)(59,74)(60,76)(61,70)(63,77)(64,78)(65,82)(66,79)(67,81)(71,83)(72,84)(73,85)(75,80);(54,55)(56,67,70,77)(57,71)(58,64)(59,63)(60,75)(61,66)(62,68,79,85)(65,73)(69,82,76,83)(72,81)(74,78,84,80)Polycyclic presentation:
2^8,53|a^2=f,c^2=fg,d^2=h,e^2=g,g^2=h,b^a=be,c^a=cg,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,e^c=eh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323014);