Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #18698 |
834 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)(70,73,75,81)(71,77,78,85)(72,79,74,80)(76,83,82,84);(54,56)(55,59)(57,66)(58,63)(60,69)(61,68)(62,64)(65,67)(70,72,75,74)(71,76,78,82)(73,80,81,79)(77,84,85,83);(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)(54,55,58,61)(56,59,63,68)(57,65,64,60)(62,69,66,67)(70,71)(72,76)(73,77)(74,82)(75,78)(79,83)(80,84)(81,85);(56,62)(57,64)(59,67)(60,65)(63,66)(68,69)(71,76)(72,74)(77,83)(78,82)(79,80)(84,85)Polycyclic presentation:
2^8,53|b^2=h,c^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh,f^c=fh716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 147511);