Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13024 |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,64)(56,59)(58,72)(60,71)(61,70)(62,76)(63,65)(66,73)(67,83)(68,69)(74,79)(75,77)(78,82)(80,84)(81,85);(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)(54,56,61,74,62,72,77,71)(55,63,67,73,68,82,84,81)(57,59,70,79,76,58,75,60)(64,65,83,66,69,78,80,85);(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)(54,55,60,66,61,67,59,78,62,68,79,85,77,84,58,65)(56,69,70,82,71,83,57,73,72,64,75,63,74,80,76,81)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^52,d^c=dgh,e^c=eg,f^c=fgh,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86711);