Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13271 |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(54,57,59,73,61,74,60,58)(55,63,65,72,66,64,76,84)(56,68,70,85,71,69,77,75)(62,78,79,80,82,83,81,67);(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)(54,56)(55,62,66,82)(57,68)(58,75)(59,70)(60,77)(61,71)(63,78,64,83)(65,79,76,81)(67,72,80,84)(69,74)(73,85);(54,55,58,64,60,65,74,84,61,66,73,63,59,76,57,72)(56,67,68,79,70,83,85,62,71,80,69,81,77,78,75,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=def,c^2=e,d^2=g,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,d^b=dg,f^b=fgh,g^b=gh,i^b=i^52,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88121);