Finite Group Databasebeta

← Group #10796327

Character table — Group #10796327

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111111111112222222222222222444444444444444444446666666666666666888888888888888888888888888888881212121212121212121212121212121224242424
order12222222444444443666666612121212121212122244888888888888888822222222444444442444666612121212121212122424242424242424242424242424242488888888888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i-11-11
χ1811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii1-11-1
χ1911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1
χ2011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-11
χ2111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1
χ2211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-11
χ2311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii-11-11
χ2411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i1-11-1
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-1-1-1-111111111-1-1-1-1-11-11-1-1-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-111
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii1111-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-11111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-1-1-1-111111111-1-1-1-1-11-11-1-1-1-111-1-11111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-111
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222222200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ342222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-1-1111111-1-111-1-1-1-1-1-1-1-11111111100000000000000000000
χ352222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2-1-1111111-1-11111111111-1-1-1-1-1-1-1-100000000000000000000
χ362222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ372222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000002-2-2211-1-1111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000
χ382222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-222-21111-1-1-1-11111-1-1-1-111111111-1-1-1-100000000000000000000
χ392222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-222-21111-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000000000000000
χ402222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000002-2-2211-1-1111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000022-2-2-1-1-1-1-1-1111111−i−iii−i−iii−i−iii−i−iii00000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000-2-222-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i00000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000-2-222-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii00000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000022-2-2-1-1-1-1-1-1111111ii−i−iii−i−iii−i−iii−i−i00000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000002-22-211-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i00000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000-22-221111-1-111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii00000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000-22-221111-1-111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i00000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000002-22-211-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii00000000000000000000
χ49222-2-22-2-22i−2i2i2i−2i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000022-2-200002i2i−2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ50222-2-22-2-22i−2i2i2i−2i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000-2-2220000−2i−2i2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ51222-2-22-2-22i−2i2i2i−2i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000022-2-200002i2i−2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ52222-2-22-2-22i−2i2i2i−2i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000-2-2220000−2i−2i2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ53222-2-22-2-2−2i2i−2i−2i2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000022-2-20000−2i−2i2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ54222-2-22-2-2−2i2i−2i−2i2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000-2-22200002i2i−2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ55222-2-22-2-2−2i2i−2i−2i2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000022-2-20000−2i−2i2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ56222-2-22-2-2−2i2i−2i−2i2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000-2-22200002i2i−2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ5722-22-2-2-22222-22-2-2-222-22-2-2-22222-22-2-2-200000000000000002i−2i2i−2i22-2-2000022-2-2000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i0000
χ5822-22-2-2-22222-22-2-2-222-22-2-2-22222-22-2-2-200000000000000002i−2i2i−2i-2-2220000-2-222000000000000000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i0000
χ5922-22-2-2-22222-22-2-2-222-22-2-2-22222-22-2-2-20000000000000000−2i2i−2i2i22-2-2000022-2-200000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i0000
χ6022-22-2-2-22222-22-2-2-222-22-2-2-22222-22-2-2-20000000000000000−2i2i−2i2i-2-2220000-2-22200000000000000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000
χ6122-22-2-2-22-2-2-22-222222-22-2-2-22-2-2-22-222200000000000000002-2-2222-2-20000-2-222000000000000000000000000000000002-2-220000000000002-2-220000
χ6222-22-2-2-22-2-2-22-222222-22-2-2-22-2-2-22-222200000000000000002-2-22-2-222000022-2-2000000000000000000000000000000002-2-22000000000000-222-20000
χ6322-22-2-2-22-2-2-22-222222-22-2-2-22-2-2-22-22220000000000000000-222-222-2-20000-2-22200000000000000000000000000000000-222-2000000000000-222-20000
χ6422-22-2-2-22-2-2-22-222222-22-2-2-22-2-2-22-22220000000000000000-222-2-2-222000022-2-200000000000000000000000000000000-222-20000000000002-2-220000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.