Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2052 ⋊ C2 |
| Sylow | C53 ⋊ #24804 |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(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)(58,62,65,74,64,73,63,60)(59,68,70,66,71,82,69,80)(61,76,78,88,79,87,77,72)(67,83,85,81,84,89,75,86);(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)(55,57)(58,61)(59,67)(60,72)(62,76)(63,77)(64,79)(65,78)(66,81)(68,83)(69,75)(70,85)(71,84)(73,87)(74,88)(80,86)(82,89);(54,55)(56,57)(58,60,63,73,64,74,65,62)(59,66,69,68,71,80,70,82)(61,72,77,87,79,88,78,76)(67,81,75,83,84,86,85,89);(58,59,65,69,64,71,63,70)(60,68,62,80,74,82,73,66)(61,75,77,67,79,85,78,84)(72,86,87,83,88,81,76,89)Polycyclic presentation:
2^8,53|a^2=fh,b^2=e,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^c=fh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 212098);