Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #23649 |
892 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)(57,69)(61,75)(65,68)(70,83)(73,84)(76,85)(79,80)(81,82);(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)(54,57,58,70,59,69,72,83)(55,61,62,76,63,75,78,85)(56,65,66,81,67,68,71,82)(60,73,64,79,74,84,77,80);(54,56)(55,60)(57,68)(58,71)(59,67)(61,73)(62,77)(63,74)(64,78)(65,69)(66,72)(70,81)(75,84)(76,80)(79,85)(82,83);(54,55)(56,64,67,77)(57,61)(58,62)(59,63)(60,66,74,71)(65,80,68,79)(69,75)(70,76)(72,78)(73,82,84,81)(83,85)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,d^c=dh,g^c=gh,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, 198494);