Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2916 ⋊ C2 |
| Sylow | C53 ⋊ #22695 |
808 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)(54,58)(55,64)(56,69)(57,70)(59,78)(60,77)(61,74)(62,73)(63,81)(65,85)(66,84)(67,79)(68,83)(71,76)(72,75)(80,82);(54,57,60,75,61,76,59,69)(55,63,66,73,67,83,65,82)(56,58,70,77,72,74,71,78)(62,79,68,85,80,64,81,84);(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)(54,56)(55,62)(57,74)(58,76)(59,71)(60,70)(61,72)(63,64)(65,81)(66,68)(67,80)(69,77)(73,84)(75,78)(79,83)(82,85);(54,55,59,66,61,67,60,65)(56,68,71,80,72,81,70,62)(57,73,69,83,76,82,75,63)(58,64,78,84,74,79,77,85)Polycyclic presentation:
2^8,53|a^2=g,c^2=f,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,c^b=ch,d^b=de,e^b=eh,i^b=i^52,e^d=eh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 188095);