Finite Group Databasebeta

← Group #151663

Character table — Group #151663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222222222222444444444444444444444448888888888888888323232326464
order122244448888161616161616161648816161616323232323232323232323232323232322488161616163232323232323232888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1
χ9222222222222-2-2-2-2-2-2-2-2222-2-2-2-200000000000000002222-2-2-2-200000000000000
χ10222222222222-2-2-2-2-2-2-2-2222-2-2-2-20000000000000000-2-2-2-2222200000000000000
χ1122222222-2-2-2-2000000002-2-200002222−2−2−2−22222−2−2−2−222-2-200002222−2−2−2−2000000
χ1222222222-2-2-2-2000000002-2-200002222−2−2−2−22222−2−2−2−2-2-2220000−2−2−2−22222000000
χ1322222222-2-2-2-2000000002-2-20000−2−2−2−22222−2−2−2−2222222-2-20000−2−2−2−22222000000
χ1422222222-2-2-2-2000000002-2-20000−2−2−2−22222−2−2−2−22222-2-22200002222−2−2−2−2000000
χ15222222-2-2222222222222-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000
χ16222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ17222222-2-22222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000
χ18222222-2-22222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000
χ19222222-2-2-2-2-2-200000000-22200002222−2−2−2−2−2−2−2−2222200002i2i−2i−2ii2i2−i2−i2−i2−i2i2i2000000
χ20222222-2-2-2-2-2-200000000-22200002222−2−2−2−2−2−2−2−222220000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2000000
χ21222222-2-2-2-2-2-200000000-2220000−2−2−2−222222222−2−2−2−200002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2000000
χ22222222-2-2-2-2-2-200000000-2220000−2−2−2−222222222−2−2−2−20000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2000000
χ232222-2-222000022−2−222−2−2-20022−2−2ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ102-2002−22−2ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10000000
χ242222-2-222000022−2−222−2−2-20022−2−2ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10-2200−22−22−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10000000
χ252222-2-222000022−2−222−2−2-20022−2−2−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ102-2002−22−2−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10000000
χ262222-2-222000022−2−222−2−2-20022−2−2−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10-2200−22−22ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10000000
χ272222-2-2220000−2−222−2−222-200−2−222ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ142-200−22−22ζ6−ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14000000
χ282222-2-2220000−2−222−2−222-200−2−222ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14-22002−22−2−ζ6+ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14000000
χ292222-2-2220000−2−222−2−222-200−2−222−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ142-200−22−22−ζ6+ζ10ζ6−ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14ζ2−ζ14−ζ2+ζ14000000
χ302222-2-2220000−2−222−2−222-200−2−222−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14-22002−22−2ζ6−ζ10−ζ6+ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14−ζ2+ζ14ζ2−ζ14000000
χ312222-2-2-2-2000022−2−222−2−2200−2−222ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10002i−2ii2−i2−i2i2ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10000000
χ322222-2-2-2-2000022−2−222−2−2200−2−222ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ1000−2i2i−i2i2i2−i2−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10000000
χ332222-2-2-2-2000022−2−222−2−2200−2−222−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10002i−2ii2−i2−i2i2−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10000000
χ342222-2-2-2-2000022−2−222−2−2200−2−222−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ1000−2i2i−i2i2i2−i2ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10000000
χ352222-2-2-2-20000−2−222−2−22220022−2−2ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14002i−2i−i2i2i2−i2−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14000000
χ362222-2-2-2-20000−2−222−2−22220022−2−2ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ1400−2i2ii2−i2−i2i2ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14000000
χ372222-2-2-2-20000−2−222−2−22220022−2−2−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14002i−2i−i2i2i2−i2ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14000000
χ382222-2-2-2-20000−2−222−2−22220022−2−2−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ1400−2i2ii2−i2−i2i2−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14000000
χ392-22-2-2200-2-222-2-2-2-222220000000000000002-22-22-22-20000000000000000i2−i2i2−i200
χ402-22-2-2200-2-222-2-2-2-222220000000000000002-22-22-22-20000000000000000−i2i2−i2i200
χ412-22-2-2200-2-222-2-2-2-22222000000000000000-22-22-22-220000000000000000i2−i2−i2i200
χ422-22-2-2200-2-222-2-2-2-22222000000000000000-22-22-22-220000000000000000−i2i2i2−i200
χ4344-4-4000022−2222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ1000000002ζ−2ζ15−2ζ+2ζ152ζ7−2ζ9−2ζ7+2ζ92ζ3−2ζ13−2ζ3+2ζ132ζ5−2ζ11−2ζ5+2ζ11000000000000000000000000000000
χ4444-4-4000022−2222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ100000000−2ζ+2ζ152ζ−2ζ15−2ζ7+2ζ92ζ7−2ζ9−2ζ3+2ζ132ζ3−2ζ13−2ζ5+2ζ112ζ5−2ζ11000000000000000000000000000000
χ4544-4-4000022−2222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ1000000002ζ7−2ζ9−2ζ7+2ζ9−2ζ+2ζ152ζ−2ζ15−2ζ5+2ζ112ζ5−2ζ112ζ3−2ζ13−2ζ3+2ζ13000000000000000000000000000000
χ4644-4-4000022−2222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ100000000−2ζ7+2ζ92ζ7−2ζ92ζ−2ζ15−2ζ+2ζ152ζ5−2ζ11−2ζ5+2ζ11−2ζ3+2ζ132ζ3−2ζ13000000000000000000000000000000
χ4744-4-40000−2222−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ1400000002ζ3−2ζ13−2ζ3+2ζ13−2ζ5+2ζ112ζ5−2ζ11−2ζ7+2ζ92ζ7−2ζ9−2ζ+2ζ152ζ−2ζ15000000000000000000000000000000
χ4844-4-40000−2222−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ140000000−2ζ3+2ζ132ζ3−2ζ132ζ5−2ζ11−2ζ5+2ζ112ζ7−2ζ9−2ζ7+2ζ92ζ−2ζ15−2ζ+2ζ15000000000000000000000000000000
χ4944-4-40000−2222−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ1400000002ζ5−2ζ11−2ζ5+2ζ112ζ3−2ζ13−2ζ3+2ζ13−2ζ+2ζ152ζ−2ζ152ζ7−2ζ9−2ζ7+2ζ9000000000000000000000000000000
χ5044-4-40000−2222−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ140000000−2ζ5+2ζ112ζ5−2ζ11−2ζ3+2ζ132ζ3−2ζ132ζ−2ζ15−2ζ+2ζ15−2ζ7+2ζ92ζ7−2ζ9000000000000000000000000000000
χ514-44-44-40000002222−22−22−22−2222220000000000000002ζ6−2ζ10−2ζ6+2ζ10−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ2−2ζ14−2ζ2+2ζ140000000000000000000000
χ524-44-44-40000002222−22−22−22−222222000000000000000−2ζ6+2ζ102ζ6−2ζ102ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ2+2ζ142ζ2−2ζ140000000000000000000000
χ534-44-44-4000000−22−2222222222−22−220000000000000002ζ2−2ζ14−2ζ2+2ζ14−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ6+2ζ102ζ6−2ζ100000000000000000000000
χ544-44-44-4000000−22−2222222222−22−22000000000000000−2ζ2+2ζ142ζ2−2ζ142ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ6−2ζ10−2ζ6+2ζ100000000000000000000000
χ554-44-4-440044-4-40000000000000000000000022−2222−22−2222−22220000000000000000000000
χ564-44-4-440044-4-400000000000000000000000−2222−222222−2222−220000000000000000000000
χ574-44-4-4400-4-4444444-4-4-4-4000000000000000000000000000000000000000000000
χ584-4-44004-422−22−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14022−222ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ1400000000000000000000000000000000000000
χ594-4-44004-422−22−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14022−22−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ1400000000000000000000000000000000000000
χ604-4-44004-4−222222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ100−22222ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ1000000000000000000000000000000000000000
χ614-4-44004-4−222222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ100−2222−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ1000000000000000000000000000000000000000
χ624-4-4400-4422−22−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ140−2222−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ1400000000000000000000000000000000000000
χ634-4-4400-4422−22−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ140−22222ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ1400000000000000000000000000000000000000
χ644-4-4400-44−222222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10022−22−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ1000000000000000000000000000000000000000
χ654-4-4400-44−222222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10022−222ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ1000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 32 (ζ32 = 1); i = ζ8.