Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12686 |
904 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)(55,62)(58,73)(61,76)(63,65)(66,79)(68,72)(71,74)(75,84);(54,56)(55,61)(57,70)(58,72)(59,67)(60,69)(62,76)(63,79)(64,81)(65,66)(68,73)(71,84)(74,75)(77,78)(80,83)(82,85);(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)(54,55,58,64,59,65,74,82,60,62,73,78,57,63,71,80)(56,66,68,83,67,76,84,81,69,79,72,85,70,61,75,77)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,d^b=dh,f^b=fh,f^c=fh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85025);