Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1796 ⋊ C2 |
| Sylow | C53 ⋊ #12717 |
944 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,57)(55,62)(56,67)(58,70)(59,74)(60,71)(61,75)(63,78)(64,80)(65,79)(66,69)(68,81)(72,83)(73,84)(76,85)(77,82);(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)(54,56,60,59)(55,61,65,77)(57,67,71,74)(58,72,73,68)(62,75,79,82)(63,64,76,66)(69,78,80,85)(70,83,84,81);(54,55)(56,66)(57,69,71,80)(58,63,73,76)(59,64)(60,65)(61,68,77,72)(62,67,79,74)(70,82)(75,84)(78,83)(81,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dh,f^b=fgh,i^b=i^52,e^c=eh,f^c=fh,f^d=fh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85143);