Finite Group Databasebeta

← Group #93091

Character table — Group #93091

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244444444888888888888448888888888888888881616161616161616161616161616161616161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111-1-1-1-1-11111-1111111-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-1-1-1-11111-1111111-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-1-1-1-11111-1111111-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-1-1-1-11111-1111111-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−i
χ141111-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii
χ151111-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−ii
χ161111-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−i
χ17222222222222222222-2-222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-222-2-222-2-222-2-222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1922222222-222-2-2-2222200220022-2-2-2-200-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-222-2-2-2222200220022-2-2-2-200-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-222-2-2-2-2-2-2-200-2-200-2-2-2-222002200000000000000000000000000002−22−2−22−220000
χ2222222222-222-2-2-2-2-2-2-200-2-200-2-2-2-22200220000000000000000000000000000−22−222−22−20000
χ23222222-2-22-2-2222000022002200-2-200-2-20022-2-20000000022−2−222−2−222−2−222−2−2000000000000
χ24222222-2-22-2-2222000022002200-2-200-2-20022-2-200000000−2−222−2−222−2−222−2−222000000000000
χ25222222-2-22-2-22220000-2-200-2-200-2-2002200-2-22200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222222-2-22-2-22220000-2-200-2-200-2-2002200-2-22200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ272222-2-222-2-2-222-20000220022002-200-2-200-2-22200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ282222-2-222-2-2-222-20000220022002-200-2-200-2-22200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ292222-2-222-2-2-222-20000-2-200-2-2002-200220022-2-20000000022−2−2−2−222−2−22222−2−2000000000000
χ302222-2-222-2-2-222-20000-2-200-2-2002-200220022-2-200000000−2−22222−2−222−2−2−2−222000000000000
χ312222-2-2-2-2222-2-22222200-2-200-2-22-2-2-200220000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ322222-2-2-2-2222-2-22222200-2-200-2-22-2-2-200220000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ332222-2-2-2-2222-2-22-2-2-2-2002200222-22200-2-200000000000000000000000000002−2−22−222−20000
χ342222-2-2-2-2222-2-22-2-2-2-2002200222-22200-2-20000000000000000000000000000−222−22−2−220000
χ352222-2-2-2-2-22222-22222-2-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-2-22222-2-2-2-2-222222222-22-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ3722-2-22-2002002-2-222−2−2222−2-2-22−2002−2002−22-20022−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3822-2-22-2002002-2-222−2−2222−2-2-22−2002−2002−22-20022−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3922-2-22-2002002-2-222−2−2-2-22−2222−2002−2002−2-2200−2−222−2−222ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4022-2-22-2002002-2-222−2−2-2-22−2222−2002−2002−2-2200−2−222−2−222−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4122-2-22-2002002-2-2−2−22222−22-2-2−2200−2200−222-200−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4222-2-22-2002002-2-2−2−22222−22-2-2−2200−2200−222-200−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4322-2-22-2002002-2-2−2−222-2-2−2222−2200−2200−22-220022−2−222−2−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4422-2-22-2002002-2-2−2−222-2-2−2222−2200−2200−22-220022−2−222−2−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4522-2-2-2200-2002-2222−2−222−22-2-2−22002−200−22-220022−2−2−2−222ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4622-2-2-2200-2002-2222−2−222−22-2-2−22002−200−22-220022−2−2−2−222−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4722-2-2-2200-2002-2222−2−2-2-2−2222−22002−200−222-200−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4822-2-2-2200-2002-2222−2−2-2-2−2222−22002−200−222-200−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4922-2-2-2200-2002-22−2−222222−2-2-22−200−22002−2-2200−2−22222−2−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ5022-2-2-2200-2002-22−2−222222−2-2-22−200−22002−2-2200−2−22222−2−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ5122-2-2-2200-2002-22−2−222-2-22−2222−200−22002−22-20022−2−2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ5222-2-2-2200-2002-22−2−222-2-22−2222−200−22002−22-20022−2−2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ53444444-4-4-4-4-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ544444-4-4444-4-4-4-44000000000000-440000000000000000000000000000000000000000000000
χ5544-4-44-400-400-4442222−22−220022−220022−2200−222200−22220000000000000000000000000000000000000000
χ5644-4-44-400-400-444−22−22222200−222200−22220022−220022−220000000000000000000000000000000000000000
χ5744-4-4-4400400-44-42222−22−2200−222200−222200−22220022−220000000000000000000000000000000000000000
χ5844-4-4-4400400-44-4−22−2222220022−220022−220022−2200−22220000000000000000000000000000000000000000
χ594-44-4000004-4000000022−224422−22-4-4000022−22000000000022−2222−220000000000000000000000000000
χ604-44-4000004-4000000022−22-4-422−2244000022−220000000000−2222−22220000000000000000000000000000
χ614-44-4000004-40000000−222244−2222-4-40000−22220000000000−2222−22220000000000000000000000000000
χ624-44-4000004-40000000−2222-4-4−2222440000−2222000000000022−2222−220000000000000000000000000000
χ634-44-400000-440004i−4i4i−4i22−220022−22000000−22220000002i2−2i22i2−2i200000000000000000000000000000000
χ644-44-400000-440004i−4i4i−4i−222200−222200000022−22000000−2i22i2−2i22i200000000000000000000000000000000
χ654-44-400000-44000−4i4i−4i4i22−220022−22000000−2222000000−2i22i2−2i22i200000000000000000000000000000000
χ664-44-400000-44000−4i4i−4i4i−222200−222200000022−220000002i2−2i22i2−2i200000000000000000000000000000000
χ674-4-44004i−4i0000002i2−2i2−2i22i222−2222−22−2222−222200000000002i2−2i22i−2i−2i2i2-2-220000000000000000000000000000
χ684-4-44004i−4i0000002i2−2i2−2i22i2−222222−2222−22−22220000000000−2i22i2−2i2i2i−2i-222-20000000000000000000000000000
χ694-4-44004i−4i000000−2i22i22i2−2i222−22−2222−222222−2200000000002i2−2i2−2i2i2i−2i-222-20000000000000000000000000000
χ704-4-44004i−4i000000−2i22i22i2−2i2−2222−222222−2222−220000000000−2i22i22i−2i−2i2i2-2-220000000000000000000000000000
χ714-4-4400−4i4i0000002i2−2i2−2i22i222−22−2222−222222−220000000000−2i22i22i−2i−2i2i-222-20000000000000000000000000000
χ724-4-4400−4i4i0000002i2−2i2−2i22i2−2222−222222−2222−2200000000002i2−2i2−2i2i2i−2i2-2-220000000000000000000000000000
χ734-4-4400−4i4i000000−2i22i22i2−2i222−2222−22−2222−22220000000000−2i22i2−2i2i2i−2i2-2-220000000000000000000000000000
χ744-4-4400−4i4i000000−2i22i22i2−2i2−222222−2222−22−222200000000002i2−2i22i−2i−2i2i-222-20000000000000000000000000000

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