Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1784 ⋊ C2 |
| Sylow | C53 ⋊ #24282 |
1308 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)(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)(58,62,64,74,65,60,63,75)(59,68,70,72,71,66,69,80)(61,77,81,87,79,73,78,88)(67,83,85,86,84,82,76,89);(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)(55,57)(58,61)(59,67)(60,73)(62,77)(63,78)(64,81)(65,79)(66,82)(68,83)(69,76)(70,85)(71,84)(72,86)(74,87)(75,88)(80,89);(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)(56,57)(58,60,64,75,65,62,63,74)(59,66,70,80,71,68,69,72)(61,73,81,88,79,77,78,87)(67,82,85,89,84,83,76,86);(58,59,65,71)(60,72,62,80)(61,76,79,85)(63,70,64,69)(66,75,68,74)(67,81,84,78)(73,83,77,82)(86,88,89,87)Polycyclic presentation:
2^8,53|a^2=h,b^2=eh,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,i^b=i^52,f^c=fh,i^c=i^52,i^d=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 205444);