Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2068 ⋊ C2 |
| Sylow | C53 ⋊ #25957 |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 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)(66,69,71,68)(67,74,73,72)(70,77,81,79)(75,76,80,78);(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)(58,60,61,65)(59,62,63,64)(67,73)(72,74)(75,80)(76,78);(54,55)(56,57)(66,68,71,69)(67,72,73,74)(70,79,81,77)(75,78,80,76);(58,59,61,63)(60,64,65,62)(66,67,71,73)(68,76,69,78)(70,80,81,75)(72,79,74,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=fh,d^2=h,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,i^c=i^52,e^d=eh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 226725);