Finite Group Databasebeta

← Group #152541

Character table — Group #152541

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222222222222244444444444448888888888888888888888161616161616161632323232
order12222444488161616168888888161616161616441616161632323232323232323232323232323232224488882288
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ9111-1-111-1-111-1-1-1-11-1ii−i−i-111-1-111i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i1-1i−i
χ10111-1-111-1-111-1-1-1-11-1ii−i−i-111-1-111i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-11−ii
χ11111-1-111-1-111-1-1-1-11-1ii−i−i-111-1-111i−iii−i−i−i−i−i−iiiii-1-1-1-111111-11-1ii−i−i-11−ii
χ12111-1-111-1-111-1-1-1-11-1ii−i−i-111-1-111i−iii−i−i−i−i−i−iiiii-1-1-1-11111-11-11−i−iii1-1i−i
χ13111-1-111-1-111-1-1-1-11-1−i−iii-111-1-111−ii−i−iiiiiii−i−i−i−i-1-1-1-111111-11-1−i−iii-11i−i
χ14111-1-111-1-111-1-1-1-11-1−i−iii-111-1-111−ii−i−iiiiiii−i−i−i−i-1-1-1-11111-11-11ii−i−i1-1−ii
χ15111-1-111-1-111-1-1-1-11-1−i−iii-111-1-111−ii−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii1-1−ii
χ16111-1-111-1-111-1-1-1-11-1−i−iii-111-1-111−ii−i−iii−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-11i−i
χ1722222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222-2-20000-2-22222-2000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ20222222222-2-20000-2-22222-2000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ21222222222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−222000000000000
χ22222222222-2-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−2000000000000
χ2322222-2-2-2-20022−2−2002i−2i2i−2i02−22−22−200i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ2422222-2-2-2-20022−2−2002i−2i2i−2i02−22−22−200i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ2522222-2-2-2-20022−2−200−2i2i−2i2i02−22−22−200−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ2622222-2-2-2-20022−2−200−2i2i−2i2i02−22−22−200−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ2722222-2-2-2-200−2−222002i−2i2i−2i0−22−22−2200−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ2822222-2-2-2-200−2−222002i−2i2i−2i0−22−22−2200−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ2922222-2-2-2-200−2−22200−2i2i−2i2i0−22−22−2200i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3022222-2-2-2-200−2−22200−2i2i−2i2i0−22−22−2200i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ31222-2-222-2-22222222-22i2i−2i−2i-2-2-222-2-22i−2i−2i−2i2i2i0000000000000000000000000000
χ32222-2-222-2-22222222-2−2i−2i2i2i-2-2-222-2-2−2i2i2i2i−2i−2i0000000000000000000000000000
χ33222-2-222-2-2-2-20000-222i2i−2i−2i2000000−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ34222-2-222-2-2-2-20000-222i2i−2i−2i2000000−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ35222-2-222-2-2-2-20000-22−2i−2i2i2i20000002i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ36222-2-222-2-2-2-20000-22−2i−2i2i2i20000002i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ37222-2-2-2-2220022−2−2002-2-220−222−2−2200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ38222-2-2-2-2220022−2−2002-2-220−222−2−2200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ39222-2-2-2-2220022−2−200-222-20−222−2−22002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ40222-2-2-2-2220022−2−200-222-20−222−2−22002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ41222-2-2-2-22200−2−222002-2-2202−2−222−2002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ42222-2-2-2-22200−2−222002-2-2202−2−222−2002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ43222-2-2-2-22200−2−22200-222-202−2−222−200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ44222-2-2-2-22200−2−22200-222-202−2−222−200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4522-22-2-222-2222222-220000-2-2-2-2-222000000000000000000000022-2-200000000
χ4622-22-2-222-2222222-220000-2-2-2-2-2220000000000000000000000-2-22200000000
χ4722-22-2-222-222-2-2-2-2-220000-22222-2-2000000000000000000000000002i−2i2i−2i0000
χ4822-22-2-222-222-2-2-2-2-220000-22222-2-200000000000000000000000000−2i2i−2i2i0000
χ4922-2-22-22-22222222-2-20000222-2-2-2-2000000000000000000000000002-2-220000
χ5022-2-22-22-22222222-2-20000222-2-2-2-200000000000000000000000000-222-20000
χ5122-2-22-22-2222-2-2-2-2-2-200002-2-2222200000000000000000000002-2-2200000000
χ5222-2-22-22-2222-2-2-2-2-2-200002-2-222220000000000000000000000-222-200000000
χ5344-44-44-4-44002222−22−220000000−2222−222222−220000000000000000000000000000000000
χ5444-44-44-4-4400−22−222222000000022−2222−22−22220000000000000000000000000000000000
χ5544-44-4-444-4-4-400004-4000040000000000000000000000000000000000000000
χ5644-4-444-44-4002222−22−22000000022−22−2222−22220000000000000000000000000000000000
χ5744-4-444-44-400−22−2222220000000−222222−2222−220000000000000000000000000000000000
χ5844-4-44-44-44-4-40000440000-40000000000000000000000000000000000000000
χ598-8000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000000000000000000000000000000000000000000000
χ608-8000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000000000000000000000000000000000000000000000
χ618-80000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000000000000000000000000000000000000000000000
χ628-80000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.