Finite Group Databasebeta

← Group #200412

Character table — Group #200412

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222222244442222444444444444444444888888888888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1111-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1111-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1111-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ12111111111-1-1-1-1-1-11-1-111-1-111-1-111-1-111-1-1111-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ13111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-111111-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-111111-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-111111-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-111111-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1711111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ2211111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ2311111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ2411111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ2511111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ2611111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ2711111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-111-1-111-1
χ2811111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-11-1-111-1-11
χ2911111-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-111-11-1-11-111-1
χ3011111-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-11-1-11-111-11-1-11
χ3111111-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-111-1-111-11-1-11
χ3211111-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11-1-111-1-11-111-1
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χ35222222222-2-2-2-2-2-22-2-2-2-22222-2-222-2-2-2-222-2-2-2222-2-222000000000000000000000000000000000000000000000000
χ36222222222-2-2-2-2-2-22-2-2-2-222-2-222-2-22222-2-2-2-2-222222-2-2000000000000000000000000000000000000000000000000
χ3722222-2-2-2-22222-2-22-2-222222222-2-2-2-2-2-2-2-2-2-22-2-222222000000000000000000000000000000000000000000000000
χ3822222-2-2-2-22222-2-22-2-22222-2-2-2-222222222-2-22-2-22-2-2-2-2000000000000000000000000000000000000000000000000
χ3922222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-222-2-222-2-2222-222-2-2000000000000000000000000000000000000000000000000
χ4022222-2-2-2-2-2-2-2-22222222-2-2-2-22222-2-222-2-2-2-2222-2-2-222000000000000000000000000000000000000000000000000
χ412222-222-2-222-2-22-2-22-222220000000000002-2-22-2-20000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ422222-222-2-222-2-22-2-22-222220000000000002-2-22-2-200000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ432222-222-2-222-2-22-2-22-2-2-2-2-2000000000000-222-22200002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ442222-222-2-222-2-22-2-22-2-2-2-2-2000000000000-222-2220000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ452222-222-2-2-2-222-22-2-2222-2-20000000000002-2-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ462222-222-2-2-2-222-22-2-2222-2-20000000000002-2-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ472222-222-2-2-2-222-22-2-22-2-222000000000000-2222-2-2000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ482222-222-2-2-2-222-22-2-22-2-222000000000000-2222-2-20000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ492222-2-2-22222-2-2-22-2-222222000000000000-22-2-22-2000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ502222-2-2-22222-2-2-22-2-222222000000000000-22-2-22-20000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ512222-2-2-22222-2-2-22-2-22-2-2-2-20000000000002-222-22000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ522222-2-2-22222-2-2-22-2-22-2-2-2-20000000000002-222-2200000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ532222-2-2-222-2-2222-2-22-222-2-2000000000000-22-22-2200002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ542222-2-2-222-2-2222-2-22-222-2-2000000000000-22-22-220000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ552222-2-2-222-2-2222-2-22-2-2-2220000000000002-22-22-20000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ562222-2-2-222-2-2222-2-22-2-2-2220000000000002-22-22-200000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ5722-2-222-22-22-22-222-2-2-200002-22-22-22-2000000000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−20000000000000000
χ5822-2-222-22-22-22-222-2-2-200002-22-22-22-200000000000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−220000000000000000
χ5922-2-222-22-22-22-222-2-2-20000-22-22-22-22000000000000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−220000000000000000
χ6022-2-222-22-22-22-222-2-2-20000-22-22-22-2200000000000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−20000000000000000
χ6122-2-222-22-2-22-22-2-2-22200002-2-222-2-2200000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6222-2-222-22-2-22-22-2-2-22200002-2-222-2-2200000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ6322-2-222-22-2-22-22-2-2-2220000-222-2-222-200000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ6422-2-222-22-2-22-22-2-2-2220000-222-2-222-200000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6522-2-22-22-222-22-2-2-2-22200002-22-2-22-2200000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ6622-2-22-22-222-22-2-2-2-22200002-22-2-22-2200000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ6722-2-22-22-222-22-2-2-2-2220000-22-222-22-200000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ6822-2-22-22-222-22-2-2-2-2220000-22-222-22-200000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ6922-2-22-22-22-22-2222-2-2-200002-2-22-222-2000000000000002−22−2−22−22−22−222−22−22−22−2−22−22−22−222−22−20000000000000000
χ7022-2-22-22-22-22-2222-2-2-200002-2-22-222-200000000000000−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−220000000000000000
χ7122-2-22-22-22-22-2222-2-2-20000-222-22-2-22000000000000002−22−2−22−22−22−222−22−2−22−222−22−22−22−2−22−220000000000000000
χ7222-2-22-22-22-22-2222-2-2-20000-222-22-2-2200000000000000−22−222−22−22−22−2−22−222−22−2−22−22−22−222−22−20000000000000000
χ7322-2-2-22-2-222-2-222-22-220000000000002i−2i2i−2i0000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i22−2−222−2−222−2−222−2−220000000000000000
χ7422-2-2-22-2-222-2-222-22-220000000000002i−2i2i−2i0000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−222−2−222−2−222−2−222−20000000000000000
χ7522-2-2-22-2-222-2-222-22-22000000000000−2i2i−2i2i000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−222−2−222−2−222−2−222−20000000000000000
χ7622-2-2-22-2-222-2-222-22-22000000000000−2i2i−2i2i000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i22−2−222−2−222−2−222−2−220000000000000000
χ7722-2-2-22-2-22-222-2-2222-20000000000002i−2i−2i2i0000002i−2i−2i2i2−2−222−2−22−222−2−222−2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ7822-2-2-22-2-22-222-2-2222-20000000000002i−2i−2i2i0000002i−2i−2i2i−222−2−222−22−2−222−2−22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7922-2-2-22-2-22-222-2-2222-2000000000000−2i2i2i−2i000000−2i2i2i−2i2−2−222−2−22−222−2−222−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ8022-2-2-22-2-22-222-2-2222-2000000000000−2i2i2i−2i000000−2i2i2i−2i−222−2−222−22−2−222−2−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ8122-2-2-2-222-22-2-22-2222-20000000000002i−2i2i−2i000000−2i2i−2i2i2−2−22−222−22−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ8222-2-2-2-222-22-2-22-2222-20000000000002i−2i2i−2i000000−2i2i−2i2i−222−22−2−22−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ8322-2-2-2-222-22-2-22-2222-2000000000000−2i2i−2i2i0000002i−2i2i−2i2−2−22−222−22−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ8422-2-2-2-222-22-2-22-2222-2000000000000−2i2i−2i2i0000002i−2i2i−2i−222−22−2−22−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ8522-2-2-2-222-2-222-22-22-220000000000002i−2i−2i2i000000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i22−2−22−222−2−222−22−2−220000000000000000
χ8622-2-2-2-222-2-222-22-22-220000000000002i−2i−2i2i000000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−222−22−2−222−2−22−222−20000000000000000
χ8722-2-2-2-222-2-222-22-22-22000000000000−2i2i2i−2i0000002i−2i−2i2ii2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−222−22−2−222−2−22−222−20000000000000000
χ8822-2-2-2-222-2-222-22-22-22000000000000−2i2i2i−2i0000002i−2i−2i2i−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i22−2−22−222−2−222−22−2−220000000000000000
χ898-88-800000000000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-80000000000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88000000000000008-8000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800000000000000-88000000000000000000000000000000000000000000000000000000000000000000000000

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