Finite Group Databasebeta

← Group #153316

Character table — Group #153316

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122222444488881616161616161616881616161632323232323232323232323232323232448816161616323232323232323244448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ112222222222-2-2-2-200000000-2-2000022222222−2−2−2−2−2−2−2−222-2-200002222−2−2−2−200000000
χ122222222222-2-2-2-200000000-2-2000022222222−2−2−2−2−2−2−2−2-2-2220000−2−2−2−2222200000000
χ132222222222-2-2-2-200000000-2-20000−2−2−2−2−2−2−2−22222222222-2-20000−2−2−2−2222200000000
χ142222222222-2-2-2-200000000-2-20000−2−2−2−2−2−2−2−222222222-2-22200002222−2−2−2−200000000
χ15222222-2-2-2-2000022−2−222−2−20022−2−2ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10002i−2ii2i2−i2−i2ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ1000000000
χ16222222-2-2-2-2000022−2−222−2−20022−2−2ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ1000−2i2i−i2−i2i2i2−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ1000000000
χ17222222-2-2-2-2000022−2−222−2−20022−2−2−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10002i−2ii2i2−i2−i2−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ1000000000
χ18222222-2-2-2-2000022−2−222−2−20022−2−2−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ1000−2i2i−i2−i2i2i2ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ1000000000
χ19222222-2-2-2-20000−2−222−2−22200−2−222ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14002i−2i−i2−i2i2i2−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ1400000000
χ20222222-2-2-2-20000−2−222−2−22200−2−222ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ1400−2i2ii2i2−i2−i2ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ1400000000
χ21222222-2-2-2-20000−2−222−2−22200−2−222−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14002i−2i−i2−i2i2i2ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ1400000000
χ22222222-2-2-2-20000−2−222−2−22200−2−222−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ1400−2i2ii2i2−i2−i2−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ1400000000
χ232222-2-222-2-2222222222222-2-2-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000
χ242222-2-222-2-2222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000
χ252222-2-222-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ262222-2-222-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ272222-2-222-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−22200002i−2i2i−2ii2−i2i2−i2−i2i2−i2i200000000
χ282222-2-222-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000−2i2i−2i2i−i2i2−i2i2i2−i2i2−i200000000
χ292222-2-222-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−200002i−2i2i−2i−i2i2−i2i2i2−i2i2−i200000000
χ302222-2-222-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000−2i2i−2i2ii2−i2i2−i2−i2i2−i2i200000000
χ312222-2-2-2-222000022−2−222−2−200−2−222ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ102-2002−2−22ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ1000000000
χ322222-2-2-2-222000022−2−222−2−200−2−222ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10-2200−222−2−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ1000000000
χ332222-2-2-2-222000022−2−222−2−200−2−222−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ102-2002−2−22−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ1000000000
χ342222-2-2-2-222000022−2−222−2−200−2−222−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10-2200−222−2ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ1000000000
χ352222-2-2-2-2220000−2−222−2−2220022−2−2ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ142-200−222−2ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ1400000000
χ362222-2-2-2-2220000−2−222−2−2220022−2−2ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14-22002−2−22−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ1400000000
χ372222-2-2-2-2220000−2−222−2−2220022−2−2−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ142-200−222−2−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ1400000000
χ382222-2-2-2-2220000−2−222−2−2220022−2−2−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14-22002−2−22ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ1400000000
χ392-2-222-22-22-222-2-22222-2-2-2-22-22-22-2000000000000000000000000000000000000002i−2i
χ402-2-222-22-22-222-2-22222-2-2-2-22-22-22-200000000000000000000000000000000000000−2i2i
χ412-2-222-22-22-222-2-2-2-2-2-222222-2-22-2200000000000000000000000000000000002-20000
χ422-2-222-22-22-222-2-2-2-2-2-222222-2-22-220000000000000000000000000000000000-220000
χ432-2-22-222-2-2222-2-22222-2-2-2-2-22-22-220000000000000000000000000000000000002i−2i00
χ442-2-22-222-2-2222-2-22222-2-2-2-2-22-22-22000000000000000000000000000000000000−2i2i00
χ452-2-22-222-2-2222-2-2-2-2-2-22222-222-22-2000000000000000000000000000000002-2000000
χ462-2-22-222-2-2222-2-2-2-2-2-22222-222-22-200000000000000000000000000000000-22000000
χ4744-4-400000022−2222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10000000002ζ−2ζ15−2ζ+2ζ15002ζ7−2ζ9−2ζ7+2ζ9002ζ3−2ζ13−2ζ3+2ζ13002ζ5−2ζ11−2ζ5+2ζ11000000000000000000000000
χ4844-4-400000022−2222−222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ1000000000−2ζ+2ζ152ζ−2ζ1500−2ζ7+2ζ92ζ7−2ζ900−2ζ3+2ζ132ζ3−2ζ1300−2ζ5+2ζ112ζ5−2ζ11000000000000000000000000
χ4944-4-400000022−2222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10000000002ζ7−2ζ9−2ζ7+2ζ900−2ζ+2ζ152ζ−2ζ1500−2ζ5+2ζ112ζ5−2ζ11002ζ3−2ζ13−2ζ3+2ζ13000000000000000000000000
χ5044-4-400000022−2222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ1000000000−2ζ7+2ζ92ζ7−2ζ9002ζ−2ζ15−2ζ+2ζ15002ζ5−2ζ11−2ζ5+2ζ1100−2ζ3+2ζ132ζ3−2ζ13000000000000000000000000
χ5144-4-4000000−2222−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14000000002ζ3−2ζ13−2ζ3+2ζ1300−2ζ5+2ζ112ζ5−2ζ1100−2ζ7+2ζ92ζ7−2ζ900−2ζ+2ζ152ζ−2ζ15000000000000000000000000
χ5244-4-4000000−2222−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ1400000000−2ζ3+2ζ132ζ3−2ζ13002ζ5−2ζ11−2ζ5+2ζ11002ζ7−2ζ9−2ζ7+2ζ9002ζ−2ζ15−2ζ+2ζ15000000000000000000000000
χ5344-4-4000000−2222−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14000000002ζ5−2ζ11−2ζ5+2ζ11002ζ3−2ζ13−2ζ3+2ζ1300−2ζ+2ζ152ζ−2ζ15002ζ7−2ζ9−2ζ7+2ζ9000000000000000000000000
χ5444-4-4000000−2222−2222−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ1400000000−2ζ5+2ζ112ζ5−2ζ1100−2ζ3+2ζ132ζ3−2ζ13002ζ−2ζ15−2ζ+2ζ1500−2ζ7+2ζ92ζ7−2ζ9000000000000000000000000
χ554-44-400000022−22−22222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ100000002ζ7−2ζ9−2ζ7+2ζ9002ζ−2ζ15−2ζ+2ζ15002ζ5−2ζ11−2ζ5+2ζ11002ζ3−2ζ13−2ζ3+2ζ1300000000000000000000000000
χ564-44-400000022−22−22222ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ10000000−2ζ7+2ζ92ζ7−2ζ900−2ζ+2ζ152ζ−2ζ1500−2ζ5+2ζ112ζ5−2ζ1100−2ζ3+2ζ132ζ3−2ζ1300000000000000000000000000
χ574-44-400000022−22−2222−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ100000002ζ−2ζ15−2ζ+2ζ1500−2ζ7+2ζ92ζ7−2ζ900−2ζ3+2ζ132ζ3−2ζ13002ζ5−2ζ11−2ζ5+2ζ1100000000000000000000000000
χ584-44-400000022−22−2222−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10000000−2ζ+2ζ152ζ−2ζ15002ζ7−2ζ9−2ζ7+2ζ9002ζ3−2ζ13−2ζ3+2ζ1300−2ζ5+2ζ112ζ5−2ζ1100000000000000000000000000
χ594-44-4000000−222222−222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ140000002ζ5−2ζ11−2ζ5+2ζ1100−2ζ3+2ζ132ζ3−2ζ13002ζ−2ζ15−2ζ+2ζ15002ζ7−2ζ9−2ζ7+2ζ900000000000000000000000000
χ604-44-4000000−222222−222ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14000000−2ζ5+2ζ112ζ5−2ζ11002ζ3−2ζ13−2ζ3+2ζ1300−2ζ+2ζ152ζ−2ζ1500−2ζ7+2ζ92ζ7−2ζ900000000000000000000000000
χ614-44-4000000−222222−22−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ140000002ζ3−2ζ13−2ζ3+2ζ13002ζ5−2ζ11−2ζ5+2ζ11002ζ7−2ζ9−2ζ7+2ζ900−2ζ+2ζ152ζ−2ζ1500000000000000000000000000
χ624-44-4000000−222222−22−2ζ6+2ζ102ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ14000000−2ζ3+2ζ132ζ3−2ζ1300−2ζ5+2ζ112ζ5−2ζ1100−2ζ7+2ζ92ζ7−2ζ9002ζ−2ζ15−2ζ+2ζ1500000000000000000000000000
χ634-4-444-44-44-4-4-44400000000-4400000000000000000000000000000000000000000000
χ644-4-444-4-44-4400002222−22−22−22−2222220022−22−22220000000000000000000000000000000000000000
χ654-4-444-4-44-440000−22−2222222222−22−2200−222222−220000000000000000000000000000000000000000
χ664-4-44-444-4-44-4-444000000004-400000000000000000000000000000000000000000000
χ674-4-44-44-444-400002222−22−22−22−22222200−222222−220000000000000000000000000000000000000000
χ684-4-44-44-444-40000−22−2222222222−22−220022−22−22220000000000000000000000000000000000000000

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