Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1661 ⋊ C2 |
| Sylow | C53 ⋊ #18998 |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 85 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)(55,60)(59,68)(61,65)(62,69);(57,67)(61,65)(62,69)(63,66)(70,72)(71,75)(73,83)(74,79)(76,85)(77,84)(78,81)(80,82);(54,56,58,64)(55,59,60,68)(57,66,67,63)(61,69,65,62)(73,82)(76,81)(78,85)(80,83);(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)(54,55,58,60)(56,62,64,69)(57,65,67,61)(59,66,68,63)(70,71,74,77)(72,78,79,85)(73,81,82,76)(75,83,84,80)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fgh,i^a=i^52,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150831);