Finite Group Databasebeta

← Group #490446

Character table — Group #490446

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222222244444444488888888888888883232111122222222222244444444488888888888888883232
order122244448888888848888888822448888161616161616161622222244448888888848888888822448888161616161616161622
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ61111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11
χ71111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ81111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1
χ922222222-2-22222-2-22-2-222-2-2-2-200000000000000000022222222-2-22222-2-22-2-222-2-2-2-2000000000000000000
χ1022222222-2-2-2-2-2-2-2-22-2-2-2-2222200000000000000000022222222-2-2-2-2-2-2-2-22-2-2-2-22222000000000000000000
χ11222222-2-222000022-2-2-200000022-2-200000000000000222222-2-222000022-2-2-200000022-2-200000000000000
χ12222222-2-222000022-2-2-2000000-2-22200000000000000222222-2-222000022-2-2-2000000-2-22200000000000000
χ13222222-2-2-2-20000-2-2-22200000000002i2i−2i−2i0000000000222222-2-2-2-20000-2-2-22200000000002i2i−2i−2i0000000000
χ14222222-2-2-2-20000-2-2-2220000000000−2i−2i2i2i0000000000222222-2-2-2-20000-2-2-2220000000000−2i−2i2i2i0000000000
χ152222-2-22200222200-200-2-200000000000022−2−222−2−2002222-2-22200222200-200-2-200000000000022−2−222−2−200
χ162222-2-22200222200-200-2-2000000000000−2−222−2−222002222-2-22200222200-200-2-2000000000000−2−222−2−22200
χ172222-2-22200-2-2-2-200-2002200000000000022−2−2−2−222002222-2-22200-2-2-2-200-2002200000000000022−2−2−2−22200
χ182222-2-22200-2-2-2-200-20022000000000000−2−22222−2−2002222-2-22200-2-2-2-200-20022000000000000−2−22222−2−200
χ1922-2-22-2002222−2−2-2-20002−222−2−2002i−2ii2−i2i2−i2000000000022-2-22-2002222−2−2-2-20002−222−2−2002i−2ii2−i2i2−i20000000000
χ2022-2-22-2002222−2−2-2-20002−222−2−200−2i2i−i2i2−i2i2000000000022-2-22-2002222−2−2-2-20002−222−2−200−2i2i−i2i2−i2i20000000000
χ2122-2-22-20022−2−222-2-2000−22−2−222002i−2i−i2i2−i2i2000000000022-2-22-20022−2−222-2-2000−22−2−222002i−2i−i2i2−i2i20000000000
χ2222-2-22-20022−2−222-2-2000−22−2−22200−2i2ii2−i2i2−i2000000000022-2-22-20022−2−222-2-2000−22−2−22200−2i2ii2−i2i2−i20000000000
χ2322-2-22-200-2-222−2−2220002−2−2−2222-2002−2−22000000000022-2-22-200-2-222−2−2220002−2−2−2222-2002−2−220000000000
χ2422-2-22-200-2-222−2−2220002−2−2−222-2200−222−2000000000022-2-22-200-2-222−2−2220002−2−2−222-2200−222−20000000000
χ2522-2-22-200-2-2−2−22222000−2222−2−22-200−222−2000000000022-2-22-200-2-2−2−22222000−2222−2−22-200−222−20000000000
χ2622-2-22-200-2-2−2−22222000−2222−2−2-22002−2−22000000000022-2-22-200-2-2−2−22222000−2222−2−2-22002−2−220000000000
χ272-2-2200-222−22-22-22−202−2002−22−200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5002-2-2200-222−22-22-22−202−2002−22−200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ282-2-2200-222−22-22-22−202−2002−22−200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5002-2-2200-222−22-22-22−202−2002−22−200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ292-2-2200-222−2-22-222−202−200−22−2200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5002-2-2200-222−2-22-222−202−200−22−2200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ302-2-2200-222−2-22-222−202−200−22−2200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5002-2-2200-222−2-22-222−202−200−22−2200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ312-2-2200-22−222-22-2−220−2200−22−2200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7002-2-2200-22−222-22-2−220−2200−22−2200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ322-2-2200-22−222-22-2−220−2200−22−2200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7002-2-2200-22−222-22-2−220−2200−22−2200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ332-2-2200-22−22-22-22−220−22002−22−200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7002-2-2200-22−22-22-22−220−22002−22−200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ342-2-2200-22−22-22-22−220−22002−22−200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7002-2-2200-22−22-22-22−220−22002−22−200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ354444-4-4-4-4000000004000000000000000000000000004444-4-4-4-400000000400000000000000000000000000
χ3644-4-4-4400002222−22−2200000−2222000000000000000000000044-4-4-4400002222−22−2200000−22220000000000000000000000
χ3744-4-4-440000−22−2222220000022−22000000000000000000000044-4-4-440000−22−2222220000022−220000000000000000000000
χ384-44-4000022−2222−22−2222−2222000002-2-220000000000000000004-44-4000022−2222−22−2222−2222000002-2-22000000000000000000
χ394-44-4000022−22−222222−22−222200000-222-20000000000000000004-44-4000022−22−222222−22−222200000-222-2000000000000000000
χ404-44-40000−222222−22−222222−2200000-222-20000000000000000004-44-40000−222222−22−222222−2200000-222-2000000000000000000
χ414-44-40000−2222−222222−2222−22000002-2-220000000000000000004-44-40000−2222−222222−2222−22000002-2-22000000000000000000
χ424-4-44004-422−22000022−220−22220000000000000000000000004-4-44004-422−22000022−220−2222000000000000000000000000
χ434-4-44004-4−22220000−2222022−220000000000000000000000004-4-44004-4−22220000−2222022−22000000000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ45111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ461111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ471111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ481111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11
χ491111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1
χ501111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1
χ511111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11
χ5222222222-2-22222-2-22-2-222-2-2-2-2000000000000000000-2-2-2-2-2-2-2-222-2-2-2-222-222-2-22222000000000000000000
χ5322222222-2-2-2-2-2-2-2-22-2-2-2-22222000000000000000000-2-2-2-2-2-2-2-222222222-22222-2-2-2-2000000000000000000
χ54222222-2-222000022-2-2-200000022-2-200000000000000-2-2-2-2-2-222-2-20000-2-2222000000-2-22200000000000000
χ55222222-2-222000022-2-2-2000000-2-22200000000000000-2-2-2-2-2-222-2-20000-2-222200000022-2-200000000000000
χ56222222-2-2-2-20000-2-2-22200000000002i2i−2i−2i0000000000-2-2-2-2-2-222220000222-2-20000000000−2i−2i2i2i0000000000
χ57222222-2-2-2-20000-2-2-2220000000000−2i−2i2i2i0000000000-2-2-2-2-2-222220000222-2-200000000002i2i−2i−2i0000000000
χ582222-2-22200222200-200-2-200000000000022−2−222−2−200-2-2-2-222-2-200-2-2-2-20020022000000000000−2−222−2−22200
χ592222-2-22200222200-200-2-2000000000000−2−222−2−22200-2-2-2-222-2-200-2-2-2-2002002200000000000022−2−222−2−200
χ602222-2-22200-2-2-2-200-2002200000000000022−2−2−2−22200-2-2-2-222-2-200222200200-2-2000000000000−2−22222−2−200
χ612222-2-22200-2-2-2-200-20022000000000000−2−22222−2−200-2-2-2-222-2-200222200200-2-200000000000022−2−2−2−22200
χ6222-2-22-2002222−2−2-2-20002−222−2−2002i−2ii2−i2i2−i20000000000-2-222-2200-2-2−2−22222000−22−2−22200−2i2i−i2i2−i2i20000000000
χ6322-2-22-2002222−2−2-2-20002−222−2−200−2i2i−i2i2−i2i20000000000-2-222-2200-2-2−2−22222000−22−2−222002i−2ii2−i2i2−i20000000000
χ6422-2-22-20022−2−222-2-2000−22−2−222002i−2i−i2i2−i2i20000000000-2-222-2200-2-222−2−2220002−222−2−200−2i2ii2−i2i2−i20000000000
χ6522-2-22-20022−2−222-2-2000−22−2−22200−2i2ii2−i2i2−i20000000000-2-222-2200-2-222−2−2220002−222−2−2002i−2i−i2i2−i2i20000000000
χ6622-2-22-200-2-222−2−2220002−2−2−2222-2002−2−220000000000-2-222-220022−2−222-2-2000−2222−2−2-2200−222−20000000000
χ6722-2-22-200-2-222−2−2220002−2−2−222-2200−222−20000000000-2-222-220022−2−222-2-2000−2222−2−22-2002−2−220000000000
χ6822-2-22-200-2-2−2−22222000−2222−2−22-200−222−20000000000-2-222-22002222−2−2-2-20002−2−2−222-22002−2−220000000000
χ6922-2-22-200-2-2−2−22222000−2222−2−2-22002−2−220000000000-2-222-22002222−2−2-2-20002−2−2−2222-200−222−20000000000
χ702-2-2200-222−22-22-22−202−2002−22−200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500-222-2002-2−22-22-22−220−2200−22−2200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ712-2-2200-222−22-22-22−202−2002−22−200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500-222-2002-2−22-22-22−220−2200−22−2200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ722-2-2200-222−2-22-222−202−200−22−2200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500-222-2002-2−222-22-2−220−22002−22−200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ732-2-2200-222−2-22-222−202−200−22−2200000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500-222-2002-2−222-22-2−220−22002−22−200000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ742-2-2200-22−222-22-2−220−2200−22−2200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700-222-2002-22−2-22-222−202−2002−22−200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ752-2-2200-22−222-22-2−220−2200−22−2200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700-222-2002-22−2-22-222−202−2002−22−200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ762-2-2200-22−22-22-22−220−22002−22−200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700-222-2002-22−22-22-22−202−200−22−2200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ772-2-2200-22−22-22-22−220−22002−22−200000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700-222-2002-22−22-22-22−202−200−22−2200000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ784444-4-4-4-400000000400000000000000000000000000-4-4-4-4444400000000-400000000000000000000000000
χ7944-4-4-4400002222−22−2200000−22220000000000000000000000-4-4444-40000−22−2222220000022−220000000000000000000000
χ8044-4-4-440000−22−2222220000022−220000000000000000000000-4-4444-400002222−22−2200000−22220000000000000000000000
χ814-44-4000022−2222−22−2222−2222000002-2-22000000000000000000-44-440000−2222−222222−2222−2200000-222-2000000000000000000
χ824-44-4000022−22−222222−22−222200000-222-2000000000000000000-44-440000−222222−22−222222−22000002-2-22000000000000000000
χ834-44-40000−222222−22−222222−2200000-222-2000000000000000000-44-44000022−22−222222−22−2222000002-2-22000000000000000000
χ844-44-40000−2222−222222−2222−22000002-2-22000000000000000000-44-44000022−2222−22−2222−222200000-222-2000000000000000000
χ854-4-44004-422−22000022−220−2222000000000000000000000000-444-400-44−22220000−2222022−22000000000000000000000000
χ864-4-44004-4−22220000−2222022−22000000000000000000000000-444-400-4422−22000022−220−2222000000000000000000000000

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