Finite Group Databasebeta

← Group #141253

Character table — Group #141253

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222224444444488888888888844888888888888888888888888888888888816161616161616164444
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
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-2-2-2-2-2002222-2-2-2-2002-2000000-2-222000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-2-2-2-2-2-2002222-2-2-2-2002-2000000-2-222000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-2-2-2-2-2-200-2-2-2-22222002-200000022-2-2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2222222222-2-2-2-2-2-200-2-2-2-22222002-200000022-2-2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ23222222-2-222-2-222220000000022-2-222-2-2-2-20000000000000000000022-2-222-2-2000000000000
χ24222222-2-222-2-222220000000022-2-222-2-2-2-200000000000000000000-2-222-2-222000000000000
χ25222222-2-222-2-222-2-200000000-2-2-2-2-2-222220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ26222222-2-222-2-222-2-200000000-2-2-2-2-2-22222000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ272222-2-22222-2-2-2-2222222-2-2-2-222-22-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ282222-2-22222-2-2-2-222-2-2-2-2222222-22-2-2-2-222-2-2222222-2-2-2-20000000000000000000000000000
χ292222-2-222-2-22222002222222200-2-2000000-2-2-2-20000000000000000000000002−2−222−2−220000
χ302222-2-222-2-22222002222222200-2-2000000-2-2-2-2000000000000000000000000−222−2−222−20000
χ312222-2-222-2-2222200-2-2-2-2-2-2-2-200-2-200000022220000000000000000000000002−2−22−222−20000
χ322222-2-222-2-2222200-2-2-2-2-2-2-2-200-2-20000002222000000000000000000000000−222−22−2−220000
χ332222-2-2-2-22222-2-22200000000222-2-2-222-2-200000000000022-2-2-2-22200000000000000000000
χ342222-2-2-2-22222-2-22200000000222-2-2-222-2-2000000000000-2-22222-2-200000000000000000000
χ352222-2-2-2-22222-2-2-2-200000000-2-22-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ362222-2-2-2-22222-2-2-2-200000000-2-22-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ372-2-222-2002-2002-22222−2−222−2−2-2-2002-200002−22−222−2−222−2−2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i000000000000
χ382-2-222-2002-2002-22222−2−222−2−2-2-2002-200002−22−222−2−222−2−2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i000000000000
χ392-2-222-2002-2002-222−2−222−2−222-2-2002-20000−22−22−2−222−2−222i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i000000000000
χ402-2-222-2002-2002-222−2−222−2−222-2-2002-20000−22−22−2−222−2−222−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i000000000000
χ412-2-222-2002-2002-2-2-222−2−222−2−22200-2200002−22−2−2−222−2−2222−2−222−2−222-2002-200000000000000
χ422-2-222-2002-2002-2-2-222−2−222−2−22200-2200002−22−2−2−222−2−222−222−2−222−2-2200-2200000000000000
χ432-2-222-2002-2002-2-2-2−2−222−2−2222200-220000−22−2222−2−222−2−22−2−222−2−22-2200-2200000000000000
χ442-2-222-2002-2002-2-2-2−2−222−2−2222200-220000−22−2222−2−222−2−2−222−2−222−22-2002-200000000000000
χ452-2-22-22002-200-222222−2−2−2−222-2-200-2200002−2−22−2−22222−2−2i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i00000000000000
χ462-2-22-22002-200-222222−2−2−2−222-2-200-2200002−2−22−2−22222−2−2−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i00000000000000
χ472-2-22-22002-200-2222−2−22222−2−2-2-200-220000−222−222−2−2−2−222i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i00000000000000
χ482-2-22-22002-200-2222−2−22222−2−2-2-200-220000−222−222−2−2−2−222−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i00000000000000
χ492-2-22-22002-200-22-2-222−2−2−2−22222002-200002−2−2222−2−2−2−2222−22−2−22−22002-200-22000000000000
χ502-2-22-22002-200-22-2-222−2−2−2−22222002-200002−2−2222−2−2−2−222−22−222−22−200-22002-2000000000000
χ512-2-22-22002-200-22-2-2−2−22222−2−222002-20000−222−2−2−22222−2−22−22−2−22−2200-22002-2000000000000
χ522-2-22-22002-200-22-2-2−2−22222−2−222002-20000−222−2−2−22222−2−2−22−222−22−2002-200-22000000000000
χ53444444-4-4-4-444-4-4000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4-444000000000000440000000000000000000000000000000000000000000000
χ5544-4-40000004-40022−2222−2222−2222−2222−2222−22000022−220000002-22-22-22-20000000000000000000000000000
χ5644-4-40000004-40022−22−2222−2222−2222−222222−22000022−22000000-22-22-22-220000000000000000000000000000
χ5744-4-40000004-400−222222−2222−2222−2222−22−22220000−2222000000-22-22-22-220000000000000000000000000000
χ5844-4-40000004-400−2222−2222−2222−2222−2222−22220000−22220000002-22-22-22-20000000000000000000000000000
χ5944-4-4000000-440022−2222−2222−22−2222−222222−220000−2222000000-22-222-22-20000000000000000000000000000
χ6044-4-4000000-440022−22−2222−222222−2222−2222−220000−22220000002-22-2-22-220000000000000000000000000000
χ6144-4-4000000-4400−222222−2222−22−2222−2222−2222000022−220000002-22-2-22-220000000000000000000000000000
χ6244-4-4000000-4400−2222−2222−222222−2222−22−2222000022−22000000-22-222-22-20000000000000000000000000000
χ634-44-4004-400000022−2200004-4-44−222200000022−22000022−22−222200000000000000000000000000000000
χ644-44-4004-400000022−220000-444-4−222200000022−220000−222222−2200000000000000000000000000000000
χ654-44-4004-4000000−222200004-4-4422−22000000−22220000−222222−2200000000000000000000000000000000
χ664-44-4004-4000000−22220000-444-422−22000000−2222000022−22−222200000000000000000000000000000000
χ674-44-400-4400000022−224-4-440000−2222000000−22220000000022−22−22220000000000000000000000000000
χ684-44-400-4400000022−22-444-40000−2222000000−222200000000−222222−220000000000000000000000000000
χ694-44-400-44000000−22224-4-44000022−2200000022−2200000000−222222−220000000000000000000000000000
χ704-44-400-44000000−2222-444-4000022−2200000022−220000000022−22−22220000000000000000000000000000
χ714-4-444-400-4400-44002222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ724-4-444-400-4400-4400−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000
χ734-4-44-4400-44004-4002222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000
χ744-4-44-4400-44004-400−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).