Finite Group Databasebeta

← Group #239352

Character table — Group #239352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222222224444444444888888881616161616161616111122222222224444444444888888881616161616161616
order12222222224444448888888844448888244444442222222222444444888888884444888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ92222222222-2-2-2-2-2-20000000022-2-20000000000002222222222-2-2-2-2-2-20000000022-2-2000000000000
χ102222222222-2-2-2-2-2-200000000-2-2220000000000002222222222-2-2-2-2-2-200000000-2-222000000000000
χ1122222-2-2-22-222-2-22-200000000000000000000002i−2i22222-2-2-22-222-2-22-200000000000000000000002i−2i
χ1222222-2-2-22-222-2-22-20000000000000000000000−2i2i22222-2-2-22-222-2-22-20000000000000000000000−2i2i
χ1322222-2-2-22-2-2-222-2200000000000000002-200000022222-2-2-22-2-2-222-2200000000000000002-2000000
χ1422222-2-2-22-2-2-222-220000000000000000-2200000022222-2-2-22-2-2-222-220000000000000000-22000000
χ152222-22-2-2-2222-2-2-22000000000000000000002i−2i002222-22-2-2-2222-2-2-22000000000000000000002i−2i00
χ162222-22-2-2-2222-2-2-2200000000000000000000−2i2i002222-22-2-2-2222-2-2-2200000000000000000000−2i2i00
χ172222-22-2-2-22-2-2222-20000000000000000002-200002222-22-2-2-22-2-2222-20000000000000000002-20000
χ182222-22-2-2-22-2-2222-2000000000000000000-2200002222-22-2-2-22-2-2222-2000000000000000000-220000
χ192222-2-222-2-22222-2-200000000000022-2-2000000002222-2-222-2-22222-2-200000000000022-2-200000000
χ202222-2-222-2-22222-2-2000000000000-2-222000000002222-2-222-2-22222-2-2000000000000-2-22200000000
χ212222-2-222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000002222-2-222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000
χ222222-2-222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002222-2-222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000
χ2322-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i20000000022-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i200000000
χ2422-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i20000000022-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i200000000
χ2522-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i20000000022-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i200000000
χ2622-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i20000000022-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i200000000
χ2722-2-2-222-22-200000022−2−2−2−2222i−2i00i2−i2−i2i20000000022-2-2-222-22-200000022−2−2−2−2222i−2i00i2−i2−i2i200000000
χ2822-2-2-222-22-200000022−2−2−2−222−2i2i00−i2i2i2−i20000000022-2-2-222-22-200000022−2−2−2−222−2i2i00−i2i2i2−i200000000
χ2922-2-2-222-22-2000000−2−22222−2−22i−2i00−i2i2i2−i20000000022-2-2-222-22-2000000−2−22222−2−22i−2i00−i2i2i2−i200000000
χ3022-2-2-222-22-2000000−2−22222−2−2−2i2i00i2−i2−i2i20000000022-2-2-222-22-2000000−2−22222−2−2−2i2i00i2−i2−i2i200000000
χ3144-4-444-44-4-400000000000000000000000000000044-4-444-44-4-4000000000000000000000000000000
χ3244-4-4-4-4-444400000000000000000000000000000044-4-4-4-4-4444000000000000000000000000000000
χ334-44-40000004i−4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000004-44-40000004i−4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ344-44-40000004i−4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000004-44-40000004i−4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ354-44-4000000−4i4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000004-44-4000000−4i4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ364-44-4000000−4i4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000004-44-4000000−4i4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ374-4-44000000004-4002i−2i−2i2i−2i2i2i−2i00000000000000004-4-44000000004-4002i−2i−2i2i−2i2i2i−2i0000000000000000
χ384-4-44000000004-400−2i2i2i−2i2i−2i−2i2i00000000000000004-4-44000000004-400−2i2i2i−2i2i−2i−2i2i0000000000000000
χ394-4-4400000000-44002-2-222-2-2200000000000000004-4-4400000000-44002-2-222-2-220000000000000000
χ404-4-4400000000-4400-222-2-222-200000000000000004-4-4400000000-4400-222-2-222-20000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ43111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ44111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ451111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ461111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ471111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ481111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ492222222222-2-2-2-2-2-20000000022-2-2000000000000-2-2-2-2-2-2-2-2-2-222222200000000-2-222000000000000
χ502222222222-2-2-2-2-2-200000000-2-222000000000000-2-2-2-2-2-2-2-2-2-22222220000000022-2-2000000000000
χ5122222-2-2-22-222-2-22-200000000000000000000002i−2i-2-2-2-2-2222-22-2-222-220000000000000000000000−2i2i
χ5222222-2-2-22-222-2-22-20000000000000000000000−2i2i-2-2-2-2-2222-22-2-222-2200000000000000000000002i−2i
χ5322222-2-2-22-2-2-222-2200000000000000002-2000000-2-2-2-2-2222-2222-2-22-20000000000000000-22000000
χ5422222-2-2-22-2-2-222-220000000000000000-22000000-2-2-2-2-2222-2222-2-22-200000000000000002-2000000
χ552222-22-2-2-2222-2-2-22000000000000000000002i−2i00-2-2-2-22-2222-2-2-2222-200000000000000000000−2i2i00
χ562222-22-2-2-2222-2-2-2200000000000000000000−2i2i00-2-2-2-22-2222-2-2-2222-2000000000000000000002i−2i00
χ572222-22-2-2-22-2-2222-20000000000000000002-20000-2-2-2-22-2222-222-2-2-22000000000000000000-220000
χ582222-22-2-2-22-2-2222-2000000000000000000-220000-2-2-2-22-2222-222-2-2-220000000000000000002-20000
χ592222-2-222-2-22222-2-200000000000022-2-200000000-2-2-2-222-2-222-2-2-2-222000000000000-2-22200000000
χ602222-2-222-2-22222-2-2000000000000-2-22200000000-2-2-2-222-2-222-2-2-2-22200000000000022-2-200000000
χ612222-2-222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000-2-2-2-222-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000
χ622222-2-222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000-2-2-2-222-2-2222222-2-22i2i2i2i−2i−2i−2i−2i0000000000000000
χ6322-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i200000000-2-222-22-222-2000000−i2−i2i2i2−i2−i2i2i200-22−i2i2−i2i200000000
χ6422-2-22-22-2-22000000i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i200000000-2-222-22-222-2000000−i2−i2i2i2−i2−i2i2i2002-2i2−i2i2−i200000000
χ6522-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i200000000-2-222-22-222-2000000i2i2−i2−i2i2i2−i2−i200-22i2−i2i2−i200000000
χ6622-2-22-22-2-22000000−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i200000000-2-222-22-222-2000000i2i2−i2−i2i2i2−i2−i2002-2−i2i2−i2i200000000
χ6722-2-2-222-22-200000022−2−2−2−2222i−2i00i2−i2−i2i200000000-2-2222-2-22-22000000−2−22222−2−2−2i2i00−i2i2i2−i200000000
χ6822-2-2-222-22-200000022−2−2−2−222−2i2i00−i2i2i2−i200000000-2-2222-2-22-22000000−2−22222−2−22i−2i00i2−i2−i2i200000000
χ6922-2-2-222-22-2000000−2−22222−2−22i−2i00−i2i2i2−i200000000-2-2222-2-22-2200000022−2−2−2−222−2i2i00i2−i2−i2i200000000
χ7022-2-2-222-22-2000000−2−22222−2−2−2i2i00i2−i2−i2i200000000-2-2222-2-22-2200000022−2−2−2−2222i−2i00−i2i2i2−i200000000
χ7144-4-444-44-4-4000000000000000000000000000000-4-444-4-44-444000000000000000000000000000000
χ7244-4-4-4-4-4444000000000000000000000000000000-4-444444-4-4-4000000000000000000000000000000
χ734-44-40000004i−4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000-44-44000000−4i4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ744-44-40000004i−4i0000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000-44-44000000−4i4i00002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ754-44-4000000−4i4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000-44-440000004i−4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ764-44-4000000−4i4i0000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000-44-440000004i−4i00002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ774-4-44000000004-4002i−2i−2i2i−2i2i2i−2i0000000000000000-444-400000000-4400−2i2i2i−2i2i−2i−2i2i0000000000000000
χ784-4-44000000004-400−2i2i2i−2i2i−2i−2i2i0000000000000000-444-400000000-44002i−2i−2i2i−2i2i2i−2i0000000000000000
χ794-4-4400000000-44002-2-222-2-220000000000000000-444-4000000004-400-222-2-222-20000000000000000
χ804-4-4400000000-4400-222-2-222-20000000000000000-444-4000000004-4002-2-222-2-220000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.