Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #11048 |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(58,61,63,73)(59,65,66,71)(60,68,69,83)(62,74,75,72)(64,76,77,79)(67,82,81,80)(70,86,85,84)(78,89,88,87);(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)(59,64)(61,68)(62,70)(63,69)(65,79)(66,77)(67,78)(71,76)(72,84)(73,83)(74,86)(75,85)(80,89)(81,88)(82,87);(55,57)(58,59,62,67,63,66,75,81)(60,64,70,78,69,77,85,88)(61,71,72,82,73,65,74,80)(68,76,84,87,83,79,86,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fh,c^b=cf,e^b=eh,i^b=i^52,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76516);