Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1632 ⋊ C2 |
| Sylow | C53 ⋊ #18597 |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
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)(56,63)(59,68)(62,69)(64,66)(70,72,74,79)(71,76,77,83)(73,78,80,84)(75,82,81,85);(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)(70,71)(72,76)(73,81)(74,77)(75,80)(78,85)(79,83)(82,84);(54,56,58,63)(55,59,61,68)(57,66,67,64)(60,69,65,62)(73,80)(75,81)(78,84)(82,85);(54,55,58,61)(56,62,63,69)(57,65,67,60)(59,66,68,64)(71,75)(73,80)(76,82)(77,81)(78,84)(83,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,d^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=dg,e^b=eg,f^b=fh,e^c=eh,f^c=fh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 146406);