Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1967 ⋊ C2 |
| Sylow | C53 ⋊ #28496 |
1022 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)(58,62,64,73,65,72,63,60)(59,68,79,66,70,85,69,78)(61,75,80,87,77,86,76,71)(67,82,74,81,84,88,83,89);(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)(60,71)(62,75)(63,76)(64,80)(65,77)(66,81)(68,82)(69,83)(70,84)(72,86)(73,87)(74,79)(78,89)(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)(54,55,56,57)(58,60,63,72,65,73,64,62)(59,66,69,68,70,78,79,85)(61,71,76,86,77,87,80,75)(67,81,83,82,84,89,74,88);(58,59,64,69,65,70,63,79)(60,68,62,78,73,85,72,66)(61,74,76,84,77,83,80,67)(71,81,86,88,87,89,75,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=eg,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,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, 261421);