Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12918 |
376 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)(55,63)(56,68)(58,72)(59,67)(60,73)(61,74)(62,76)(64,71)(65,78)(66,69)(70,83)(75,80)(77,79)(81,85)(82,84);(54,56,59,70,60,63,76,78,61,71,77,85,58,69,75,84)(55,62,65,74,64,79,81,72,66,80,82,57,68,67,83,73);(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)(54,55,59,65,60,64,76,81,61,66,77,82,58,68,75,83)(56,67,70,73,63,62,78,74,71,79,85,72,69,80,84,57)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^52,d^b=dh,e^c=eh1832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86061);