Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#2911 ⋊ C2 |
| Sylow | C53 ⋊ #21075 |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,62,64,63)(59,67,68,78)(60,71,73,72)(61,75,77,76)(65,69,80,83)(66,81,74,89)(70,85,87,86)(79,82,88,84);(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)(58,61,63,76,64,77,62,75)(59,66,67,81,68,74,78,89)(60,70,72,86,73,87,71,85)(65,79,69,82,80,88,83,84);(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)(54,56,57,55)(58,60,63,72,64,73,62,71)(59,65,67,69,68,80,78,83)(61,70,76,86,77,87,75,85)(66,79,81,82,74,88,89,84);(54,55,57,56)(58,59)(60,69)(61,74)(62,67)(63,78)(64,68)(65,72)(66,77)(70,84)(71,80)(73,83)(75,89)(76,81)(79,85)(82,87)(86,88)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^b=i^52,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 172115);