Finite Group Databasebeta

← Group #357665

Character table — Group #357665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size11111111111111112222222244444444444444444444444488888888888888881111111111111111222222224444444444444444444444448888888888888888
order12222222222222224444444422224444888888888888888844444444444444442222222222222222444444442222444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii1111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ121111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i1111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ131111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii1111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ141111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i1111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ151111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i1111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii1111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-2-2-22-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000002222222-2-2-2-2-22-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-2-22-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000002222222-2-2-2-2-22-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ212222-2-2-22222-2-2-2-2-2000000002-22-2000022−2−222−2−222−2−222−2−200000000000000002222-2-2-22222-2-2-2-2-2000000002-22-2000022−2−222−2−222−2−222−2−20000000000000000
χ222222-2-2-22222-2-2-2-2-2000000002-22-20000−2−222−2−222−2−222−2−22200000000000000002222-2-2-22222-2-2-2-2-2000000002-22-20000−2−222−2−222−2−222−2−2220000000000000000
χ232222-2-2-22222-2-2-2-2-200000000-22-22000022−2−222−2−2−2−222−2−22200000000000000002222-2-2-22222-2-2-2-2-200000000-22-22000022−2−222−2−2−2−222−2−2220000000000000000
χ242222-2-2-22222-2-2-2-2-200000000-22-220000−2−222−2−22222−2−222−2−200000000000000002222-2-2-22222-2-2-2-2-200000000-22-220000−2−222−2−22222−2−222−2−20000000000000000
χ252222-2-2-2-2-2-2-22-2222000000002-2-22000022−2−2−2−22222−2−2−2−22200000000000000002222-2-2-2-2-2-2-22-2222000000002-2-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ262222-2-2-2-2-2-2-22-2222000000002-2-220000−2−22222−2−2−2−22222−2−200000000000000002222-2-2-2-2-2-2-22-2222000000002-2-220000−2−22222−2−2−2−22222−2−20000000000000000
χ272222-2-2-2-2-2-2-22-222200000000-222-2000022−2−2−2−222−2−22222−2−200000000000000002222-2-2-2-2-2-2-22-222200000000-222-2000022−2−2−2−222−2−22222−2−20000000000000000
χ282222-2-2-2-2-2-2-22-222200000000-222-20000−2−22222−2−222−2−2−2−22200000000000000002222-2-2-2-2-2-2-22-222200000000-222-20000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-2-222-222-2-22-2-2-220000000000002i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000022-2-222-222-2-22-2-2-220000000000002i−2i2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3022-2-222-222-2-22-2-2-220000000000002i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000022-2-222-222-2-22-2-2-220000000000002i−2i2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3122-2-222-222-2-22-2-2-22000000000000−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000022-2-222-222-2-22-2-2-22000000000000−2i2i−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-2-222-222-2-22-2-2-22000000000000−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000022-2-222-222-2-22-2-2-22000000000000−2i2i−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-2-222-2-2-222-2-222-20000000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000000022-2-222-2-2-222-2-222-20000000000002i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ3422-2-222-2-2-222-2-222-20000000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000000022-2-222-2-2-222-2-222-20000000000002i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ3522-2-222-2-2-222-2-222-2000000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000022-2-222-2-2-222-2-222-2000000000000−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ3622-2-222-2-2-222-2-222-2000000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000000022-2-222-2-2-222-2-222-2000000000000−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ3722-2-2-2-2222-2-2-2222-22222-2-2-2-200000000000000002i−2i−2i2i2i−2i−2i2i000000000000000022-2-2-2-2222-2-2-2222-22222-2-2-2-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ3822-2-2-2-2222-2-2-2222-22222-2-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000022-2-2-2-2222-2-2-2222-22222-2-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ3922-2-2-2-2222-2-2-2222-2-2-2-2-22222000000002-2-222-2-2200000000000000000000000022-2-2-2-2222-2-2-2222-2-2-2-2-22222000000002-2-222-2-22000000000000000000000000
χ4022-2-2-2-2222-2-2-2222-2-2-2-2-2222200000000-222-2-222-200000000000000000000000022-2-2-2-2222-2-2-2222-2-2-2-2-2222200000000-222-2-222-2000000000000000000000000
χ4122-2-2-2-22-2-22222-2-2222-2-222-2-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000000022-2-2-2-22-2-22222-2-2222-2-222-2-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ4222-2-2-2-22-2-22222-2-2222-2-222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000022-2-2-2-22-2-22222-2-2222-2-222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4322-2-2-2-22-2-22222-2-22-2-222-2-222000000002-2-22-222-200000000000000000000000022-2-2-2-22-2-22222-2-22-2-222-2-222000000002-2-22-222-2000000000000000000000000
χ4422-2-2-2-22-2-22222-2-22-2-222-2-22200000000-222-22-2-2200000000000000000000000022-2-2-2-22-2-22222-2-22-2-222-2-22200000000-222-22-2-22000000000000000000000000
χ452-22-22-2-22-22-2222-2-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i2-22-22-2-22-22-2222-2-22-22-22-22-20000000000000000000000000000000000002i−2i2i−2i
χ462-22-22-2-22-22-2222-2-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i2-22-22-2-22-22-2222-2-22-22-22-22-2000000000000000000000000000000000000−2i2i−2i2i
χ472-22-22-2-22-22-2222-2-2-22-22-22-2200000000000000000000000000002i−2i2i−2i000000002-22-22-2-22-22-2222-2-2-22-22-22-2200000000000000000000000000002i−2i2i−2i00000000
χ482-22-22-2-22-22-2222-2-2-22-22-22-220000000000000000000000000000−2i2i−2i2i000000002-22-22-2-22-22-2222-2-2-22-22-22-220000000000000000000000000000−2i2i−2i2i00000000
χ492-22-22-2-2-22-22-22-2222-2-22-222-20000000000000000000000000000000000002-2-222-22-22-2-2-22-22-22-2222-2-22-222-20000000000000000000000000000000000002-2-22
χ502-22-22-2-2-22-22-22-2222-2-22-222-2000000000000000000000000000000000000-222-22-22-22-2-2-22-22-22-2222-2-22-222-2000000000000000000000000000000000000-222-2
χ512-22-22-2-2-22-22-22-222-222-22-2-2200000000000000000000000000002-2-22000000002-22-22-2-2-22-22-22-222-222-22-2-2200000000000000000000000000002-2-2200000000
χ522-22-22-2-2-22-22-22-222-222-22-2-220000000000000000000000000000-222-2000000002-22-22-2-2-22-22-22-222-222-22-2-220000000000000000000000000000-222-200000000
χ532-2-22-22-22-2-22-222-222-22-2-22-220000000000000000000000002-22-20000000000002-2-22-22-22-2-22-222-222-22-2-22-220000000000000000000000002-22-2000000000000
χ542-2-22-22-22-2-22-222-222-22-2-22-22000000000000000000000000-22-220000000000002-2-22-22-22-2-22-222-222-22-2-22-22000000000000000000000000-22-22000000000000
χ552-2-22-22-22-2-22-222-22-22-222-22-2000000000000000000000000000000002-22-200002-2-22-22-22-2-22-222-22-22-222-22-2000000000000000000000000000000002-22-20000
χ562-2-22-22-22-2-22-222-22-22-222-22-200000000000000000000000000000000-22-2200002-2-22-22-22-2-22-222-22-22-222-22-200000000000000000000000000000000-22-220000
χ572-2-22-22-2-222-222-22-22-2-222-2-220000000000000000000000002i−2i−2i2i0000000000002-2-22-22-2-222-222-22-22-2-222-2-220000000000000000000000002i−2i−2i2i000000000000
χ582-2-22-22-2-222-222-22-22-2-222-2-22000000000000000000000000−2i2i2i−2i0000000000002-2-22-22-2-222-222-22-22-2-222-2-22000000000000000000000000−2i2i2i−2i000000000000
χ592-2-22-22-2-222-222-22-2-222-2-222-2000000000000000000000000000000002i−2i−2i2i00002-2-22-22-2-222-222-22-2-222-2-222-2000000000000000000000000000000002i−2i−2i2i0000
χ602-2-22-22-2-222-222-22-2-222-2-222-200000000000000000000000000000000−2i2i2i−2i00002-2-22-22-2-222-222-22-2-222-2-222-200000000000000000000000000000000−2i2i2i−2i0000
χ614-44-4-4444-44-4-4-4-4440000000000000000000000000000000000000000000000004-44-4-4444-44-4-4-4-444000000000000000000000000000000000000000000000000
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χ651111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ66111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ6711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111
χ6811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1
χ69111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ70111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ72111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ731111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-111111-1111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii
χ741111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-111111-1111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i
χ751111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-111111-1111-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ761111111-1-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-111111-1111-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ771111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-111111-1111-1-11111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ781111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-111111-1111-1-11111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ791111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-111111-1111-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ801111111-1-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-111111-1111-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
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χ10222-2-2-2-2222-2-2-2222-22222-2-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000-2-22222-2-2-2222-2-2-22-2-2-2-2222200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
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χ1284-4-444-44-444-4-4-44-44000000000000000000000000000000000000000000000000-444-4-44-44-4-4444-44-4000000000000000000000000000000000000000000000000

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