Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1764 ⋊ C2 |
| Sylow | C53 ⋊ #22895 |
1008 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)(58,61)(59,66)(60,71)(62,79)(63,76)(64,77)(65,80)(67,87)(68,84)(69,85)(70,88)(72,89)(73,75)(74,78)(81,83)(82,86);(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)(58,60)(59,65)(61,75)(62,72)(63,78)(64,73)(66,83)(67,70)(68,86)(69,81)(71,77)(74,79)(76,89)(80,85)(82,87)(84,88);(54,56,57,55)(58,60)(59,65)(61,74)(62,78)(63,72)(64,73)(66,82)(67,86)(68,70)(69,81)(71,76)(75,79)(77,89)(80,84)(83,87)(85,88);(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)(54,55,57,56)(58,59,64,69)(60,70,73,86)(61,66,77,85)(62,68,63,67)(65,78,81,72)(71,88,75,82)(74,83,89,80)(76,87,79,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=gh,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=de,e^b=eh,d^c=dh,f^c=fh,i^c=i^52,e^d=eh1514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 190409);