Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2133 ⋊ C2 |
| Sylow | C53 ⋊ #33370 |
1208 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(56,65)(61,74)(66,79)(67,80)(72,75)(76,84)(81,82)(83,85);(54,56)(55,61)(57,66)(58,67)(59,65)(60,72)(62,75)(63,76)(64,74)(68,79)(69,81)(70,82)(71,80)(73,83)(77,85)(78,84);(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)(55,60)(57,68)(61,72)(62,64)(63,77)(66,79)(69,70)(73,78)(74,75)(76,85)(81,82)(83,84);(54,55,58,63,59,64,71,78)(56,61,67,76,65,74,80,84)(57,62,69,77,68,60,70,73)(66,75,81,85,79,72,82,83)Polycyclic presentation:
2^8,53|a^2=f,e^2=h,f^2=h,b^a=be,e^a=eg,g^a=gh,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh,i^d=i^52,f^e=fh644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322421);