Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1796 ⋊ C2 |
| Sylow | C53 ⋊ #21784 |
1278 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)(54,56)(55,60)(57,65)(58,66)(59,67)(61,74)(62,64)(63,75)(68,85)(69,82)(70,83)(71,73)(72,84)(76,77)(78,79)(80,81);(54,57,59,70)(55,61,62,77)(56,65,67,83)(58,72,73,69)(60,74,64,76)(63,80,78,68)(66,84,71,82)(75,81,79,85);(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)(54,56)(55,60)(57,65)(58,71)(59,67)(61,76)(62,64)(63,79)(66,73)(68,85)(69,84)(70,83)(72,82)(74,77)(75,78)(80,81);(54,55)(56,64,67,60)(57,68,70,80)(58,63)(59,62)(61,69,77,72)(65,81)(66,79,71,75)(73,78)(74,82)(76,84)(83,85)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,i^b=i^52,f^c=fh,g^c=gh,g^d=gh800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 178772);