Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#1861 ⋊ C2 |
| Sylow | C53 ⋊ #32703 |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,68,70,69)(57,73)(61,77,78,66)(62,80)(67,83,84,72)(71,81)(74,75)(76,79,82,85);(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)(54,57,58,74,60,73,59,75)(55,62,63,81,65,80,64,71)(56,67,69,83,70,84,68,72)(61,76,66,79,78,82,77,85);(54,56)(55,61)(57,72)(58,68)(59,69)(60,70)(62,79)(63,77)(64,66)(65,78)(67,75)(71,82)(73,83)(74,84)(76,81)(80,85);(54,55,59,63,60,65,58,64)(56,66,69,61,70,77,68,78)(57,71,75,62,73,81,74,80)(67,82,83,79,84,76,72,85)Polycyclic presentation:
2^8,53|a^2=efg,c^2=e,d^2=ef,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fh,c^b=cg,d^b=de,e^b=eh,g^b=gh,d^c=dh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 316460);