Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #23753 |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(57,72)(62,70)(66,81)(71,82)(73,74)(76,85)(78,83)(79,84);(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)(54,57,58,73,59,72,60,74)(55,62,63,79,64,70,75,84)(56,66,67,82,69,81,68,71)(61,76,65,78,77,85,80,83);(54,56,60,67,59,69,58,68)(55,61,75,65,64,77,63,80)(57,71,74,66,72,82,73,81)(62,78,84,85,70,83,79,76);(54,55,58,63,59,64,60,75)(56,65,67,77,69,80,68,61)(57,70,73,84,72,62,74,79)(66,78,82,85,81,83,71,76)Polycyclic presentation:
2^8,53|a^2=e,b^2=ef,c^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,g^b=gh,d^c=dh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 199550);