Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3160 ⋊ C2 |
| Sylow | C53 ⋊ #33637 |
524 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)(54,58,61,59)(55,64,67,66)(56,60,71,70)(57,73,75,74)(62,68,76,65)(63,78,79,81)(69,77,84,83)(72,82,85,80);(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)(55,63)(56,69)(58,73)(59,74)(60,77)(61,75)(62,72)(64,78)(65,80)(66,81)(67,79)(68,82)(70,83)(71,84)(76,85);(54,56,59,70,61,71,58,60)(55,62,64,68,67,76,66,65)(57,69,74,83,75,84,73,77)(63,72,78,82,79,85,81,80);(54,55)(56,68)(57,72,75,85)(58,64)(59,66)(60,76)(61,67)(62,70)(63,69,79,84)(65,71)(73,82,74,80)(77,81,83,78)Polycyclic presentation:
2^8,53|a^2=eg,b^2=e,d^2=h,e^2=h,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fg,g^a=gh,f^c=fgh,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, 324307);