Finite Group Databasebeta

← Group #153263

Character table — Group #153263

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order124422244488881616161616161616881616161632323232323232323232323232323232248816161616323232323232323224448888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
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
χ1522222-2-2-22-2222222222222-2-2-2-2-2-200000000000000000000000022-2-222-2-200000000
χ1622222-2-2-22-2222222222222-2-2-2-2-2-2000000000000000000000000-2-222-2-22200000000
χ1722222-2-2-22-22222-2-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ1822222-2-2-22-22222-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ1922222-2-2-22-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i2i−2i−2i22−2−2−2−22200000000
χ2022222-2-2-22-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i−2i2i2i−2−22222−2−200000000
χ2122222-2-2-22-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i2i−2i−2i−2−22222−2−200000000
χ2222222-2-2-22-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i−2i2i2i22−2−2−2−22200000000
χ2322-2-2222-2-2-200002222−2−2−2−20022−2−2ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10002i−2ii2−i2i2−i2ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ6+ζ10−ζ6−ζ10ζ6+ζ10−ζ6−ζ1000000000
χ2422-2-2222-2-2-200002222−2−2−2−20022−2−2ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ1000−2i2i−i2i2−i2i2−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10−ζ6−ζ10ζ6+ζ1000000000
χ2522-2-2222-2-2-200002222−2−2−2−20022−2−2−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10002i−2ii2−i2i2−i2−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ6−ζ10ζ6+ζ10−ζ6−ζ10ζ6+ζ1000000000
χ2622-2-2222-2-2-200002222−2−2−2−20022−2−2−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ1000−2i2i−i2i2−i2i2ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ6+ζ10−ζ6−ζ10ζ6+ζ10−ζ6−ζ1000000000
χ2722-2-2222-2-2-20000−2−2−2−2222200−2−222ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14002i−2i−i2i2−i2i2−ζ6−ζ10ζ6+ζ10−ζ6−ζ10ζ6+ζ10ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ2−ζ1400000000
χ2822-2-2222-2-2-20000−2−2−2−2222200−2−222ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ1400−2i2ii2−i2i2−i2ζ6+ζ10−ζ6−ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ2+ζ1400000000
χ2922-2-2222-2-2-20000−2−2−2−2222200−2−222−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14002i−2i−i2i2−i2i2ζ6+ζ10−ζ6−ζ10ζ6+ζ10−ζ6−ζ10−ζ2−ζ14ζ2+ζ14−ζ2−ζ14ζ2+ζ1400000000
χ3022-2-2222-2-2-20000−2−2−2−2222200−2−222−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10−ζ6+ζ10−ζ6+ζ10ζ6−ζ10ζ6−ζ10ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ14ζ2−ζ14ζ2−ζ14−ζ2+ζ14−ζ2+ζ1400−2i2ii2−i2i2−i2−ζ6−ζ10ζ6+ζ10−ζ6−ζ10ζ6+ζ10ζ2+ζ14−ζ2−ζ14ζ2+ζ14−ζ2−ζ1400000000
χ3122-2-22-2-22-2200002222−2−2−2−200−2−222ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ102-2002−2−22ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ1000000000
χ3222-2-22-2-22-2200002222−2−2−2−200−2−222ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10-2200−222−2−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ1000000000
χ3322-2-22-2-22-2200002222−2−2−2−200−2−222−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ102-2002−2−22−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ1000000000
χ3422-2-22-2-22-2200002222−2−2−2−200−2−222−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10-2200−222−2ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ1000000000
χ3522-2-22-2-22-220000−2−2−2−222220022−2−2ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ142-200−222−2ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ1400000000
χ3622-2-22-2-22-220000−2−2−2−222220022−2−2ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14-22002−2−22−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ1400000000
χ3722-2-22-2-22-220000−2−2−2−222220022−2−2−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ142-200−222−2−ζ6−ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10ζ2+ζ14−ζ2−ζ14−ζ2−ζ14ζ2+ζ1400000000
χ3822-2-22-2-22-220000−2−2−2−222220022−2−2−ζ6−ζ10−ζ6−ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10ζ6+ζ10−ζ6−ζ10−ζ6−ζ10−ζ2−ζ14−ζ2−ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ14−ζ2−ζ14-22002−2−22ζ6+ζ10−ζ6−ζ10−ζ6−ζ10ζ6+ζ10−ζ2−ζ14ζ2+ζ14ζ2+ζ14−ζ2−ζ1400000000
χ3922-2-2-22-222-2-2-22222-2-222-2-22-22-22-20000000000000000000000000000000000002i−2i00
χ4022-2-2-22-222-2-2-22222-2-222-2-22-22-22-2000000000000000000000000000000000000−2i2i00
χ4122-2-2-22-222-2-2-222-2-222-2-2222-2-22-2200000000000000000000000000000000002i−2i0000
χ4222-2-2-22-222-2-2-222-2-222-2-2222-2-22-220000000000000000000000000000000000−2i2i0000
χ4322-2-2-2-22-222-2-22222-2-222-2-2-22-22-22000000000000000000000000000000002-2000000
χ4422-2-2-2-22-222-2-22222-2-222-2-2-22-22-2200000000000000000000000000000000-22000000
χ4522-2-2-2-22-222-2-222-2-222-2-222-222-22-2000000000000000000000000000000000000002-2
χ4622-2-2-2-22-222-2-222-2-222-2-222-222-22-200000000000000000000000000000000000000-22
χ474444-44-4-4-4400002222−22−22−22−2222220022−22−22220000000000000000000000000000000000000000
χ484444-44-4-4-440000−22−2222222222−22−2200−222222−220000000000000000000000000000000000000000
χ494444-4-444-4-400002222−22−22−22−22222200−222222−220000000000000000000000000000000000000000
χ504444-4-444-4-40000−22−2222222222−22−220022−22−22220000000000000000000000000000000000000000
χ5144-4-4-44-444-444-4-400000000-4400000000000000000000000000000000000000000000
χ5244-4-4-4-44-44444-4-4000000004-400000000000000000000000000000000000000000000
χ534-44i−4i0000002i2−2i222−222ζ2−2ζ14−2ζ2+2ζ142ζ2+2ζ14−2ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ6+2ζ10−2ζ6−2ζ100000002ζ−2ζ2ζ9−2ζ92ζ15−2ζ152ζ7−2ζ72ζ13−2ζ132ζ5−2ζ52ζ3−2ζ32ζ11−2ζ11000000000000000000000000
χ544-44i−4i0000002i2−2i222−222ζ2−2ζ14−2ζ2+2ζ142ζ2+2ζ14−2ζ2−2ζ142ζ6−2ζ10−2ζ6+2ζ102ζ6+2ζ10−2ζ6−2ζ10000000−2ζ2ζ−2ζ92ζ9−2ζ152ζ15−2ζ72ζ7−2ζ132ζ13−2ζ52ζ5−2ζ32ζ3−2ζ112ζ11000000000000000000000000
χ554-44i−4i0000002i2−2i222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ2−2ζ142ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ6−2ζ102ζ6+2ζ100000002ζ9−2ζ9−2ζ2ζ2ζ7−2ζ7−2ζ152ζ15−2ζ52ζ52ζ13−2ζ13−2ζ112ζ112ζ3−2ζ3000000000000000000000000
χ564-44i−4i0000002i2−2i222−22−2ζ2+2ζ142ζ2−2ζ14−2ζ2−2ζ142ζ2+2ζ14−2ζ6+2ζ102ζ6−2ζ10−2ζ6−2ζ102ζ6+2ζ10000000−2ζ92ζ92ζ−2ζ−2ζ72ζ72ζ15−2ζ152ζ5−2ζ5−2ζ132ζ132ζ11−2ζ11−2ζ32ζ3000000000000000000000000
χ574-44i−4i000000−2i22i2−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ6−2ζ102ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ2+2ζ14−2ζ2−2ζ140000002ζ13−2ζ13−2ζ52ζ52ζ3−2ζ3−2ζ112ζ112ζ9−2ζ92ζ−2ζ2ζ7−2ζ72ζ15−2ζ15000000000000000000000000
χ584-44i−4i000000−2i22i2−22222ζ6−2ζ10−2ζ6+2ζ10−2ζ6−2ζ102ζ6+2ζ10−2ζ2+2ζ142ζ2−2ζ142ζ2+2ζ14−2ζ2−2ζ14000000−2ζ132ζ132ζ5−2ζ5−2ζ32ζ32ζ11−2ζ11−2ζ92ζ9−2ζ2ζ−2ζ72ζ7−2ζ152ζ15000000000000000000000000
χ594-44i−4i000000−2i22i2−2222−2ζ6+2ζ102ζ6−2ζ102ζ6+2ζ10−2ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ2−2ζ142ζ2+2ζ140000002ζ5−2ζ52ζ13−2ζ132ζ11−2ζ112ζ3−2ζ32ζ−2ζ−2ζ92ζ92ζ15−2ζ15−2ζ72ζ7000000000000000000000000
χ604-44i−4i000000−2i22i2−2222−2ζ6+2ζ102ζ6−2ζ102ζ6+2ζ10−2ζ6−2ζ102ζ2−2ζ14−2ζ2+2ζ14−2ζ2−2ζ142ζ2+2ζ14000000−2ζ52ζ5−2ζ132ζ13−2ζ112ζ11−2ζ32ζ3−2ζ2ζ2ζ9−2ζ9−2ζ152ζ152ζ7−2ζ7000000000000000000000000
χ614-4−4i4i0000002i2−2i2−22222ζ6−2ζ10−2ζ6+2ζ102ζ6+2ζ10−2ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ2−2ζ142ζ2+2ζ140000002ζ3−2ζ3−2ζ112ζ112ζ13−2ζ13−2ζ52ζ52ζ7−2ζ72ζ15−2ζ152ζ9−2ζ92ζ−2ζ000000000000000000000000
χ624-4−4i4i0000002i2−2i2−22222ζ6−2ζ10−2ζ6+2ζ102ζ6+2ζ10−2ζ6−2ζ10−2ζ2+2ζ142ζ2−2ζ14−2ζ2−2ζ142ζ2+2ζ14000000−2ζ32ζ32ζ11−2ζ11−2ζ132ζ132ζ5−2ζ5−2ζ72ζ7−2ζ152ζ15−2ζ92ζ9−2ζ2ζ000000000000000000000000
χ634-4−4i4i0000002i2−2i2−2222−2ζ6+2ζ102ζ6−2ζ10−2ζ6−2ζ102ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ2+2ζ14−2ζ2−2ζ140000002ζ11−2ζ112ζ3−2ζ32ζ5−2ζ52ζ13−2ζ132ζ15−2ζ15−2ζ72ζ72ζ−2ζ−2ζ92ζ9000000000000000000000000
χ644-4−4i4i0000002i2−2i2−2222−2ζ6+2ζ102ζ6−2ζ10−2ζ6−2ζ102ζ6+2ζ102ζ2−2ζ14−2ζ2+2ζ142ζ2+2ζ14−2ζ2−2ζ14000000−2ζ112ζ11−2ζ32ζ3−2ζ52ζ5−2ζ132ζ13−2ζ152ζ152ζ7−2ζ7−2ζ2ζ2ζ9−2ζ9000000000000000000000000
χ654-4−4i4i000000−2i22i222−222ζ2−2ζ14−2ζ2+2ζ14−2ζ2−2ζ142ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ6−2ζ102ζ6+2ζ100000002ζ15−2ζ152ζ7−2ζ72ζ−2ζ2ζ9−2ζ92ζ3−2ζ32ζ11−2ζ112ζ13−2ζ132ζ5−2ζ5000000000000000000000000
χ664-4−4i4i000000−2i22i222−222ζ2−2ζ14−2ζ2+2ζ14−2ζ2−2ζ142ζ2+2ζ142ζ6−2ζ10−2ζ6+2ζ10−2ζ6−2ζ102ζ6+2ζ10000000−2ζ152ζ15−2ζ72ζ7−2ζ2ζ−2ζ92ζ9−2ζ32ζ3−2ζ112ζ11−2ζ132ζ13−2ζ52ζ5000000000000000000000000
χ674-4−4i4i000000−2i22i222−22−2ζ2+2ζ142ζ2−2ζ142ζ2+2ζ14−2ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ6+2ζ10−2ζ6−2ζ100000002ζ7−2ζ7−2ζ152ζ152ζ9−2ζ9−2ζ2ζ−2ζ112ζ112ζ3−2ζ3−2ζ52ζ52ζ13−2ζ13000000000000000000000000
χ684-4−4i4i000000−2i22i222−22−2ζ2+2ζ142ζ2−2ζ142ζ2+2ζ14−2ζ2−2ζ14−2ζ6+2ζ102ζ6−2ζ102ζ6+2ζ10−2ζ6−2ζ10000000−2ζ72ζ72ζ15−2ζ15−2ζ92ζ92ζ−2ζ2ζ11−2ζ11−2ζ32ζ32ζ5−2ζ5−2ζ132ζ13000000000000000000000000

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