Finite Group Databasebeta

← Group #13173371

Character table — Group #13173371

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222224444444444444444444444444444448888888888888888888888888888888888889999181818181818181818182727272727272727363636363636545454545454545454545454
order12442346888812123333336666666121212121212121212121212122424242466666612121212121224242424242424242424242424242424242424242424242422442466888812128888888861224242424444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ711111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-11111−i−i−i−iiiiiii−i−i
χ811111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-11111iiii−i−i−i−i−i−iii
χ91111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1
χ101111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111
χ111111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i11-1-111ii−i−i−i−iii−i−iii
χ121111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii11-1-111−i−iiiii−i−iii−i−i
χ131111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111111111-1-1-1-111-1-111-1-111-1-1-1-1
χ141111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111
χ151111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i1111-1-1−i−iiiii−i−i−i−iii
χ161111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiii1111-1-1ii−i−i−i−iiiii−i−i
χ1711-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-11-111i−ii−i-1-1ii−i−iii−i−i1-1i−ii−i1-11-11-11-1i−ii−i
χ1811-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-11-111i−ii−i-1-1−i−iii−i−iii1-1i−ii−i-11-11-11-11−ii−ii
χ1911-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-1-111-11-1-1−ii−ii1111-1-1-1-111-11−ii−ii−ii−iii−ii−i1-1-11
χ2011-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-1-111-11-1-1−ii−ii11-1-11111-1-1-11−ii−iii−ii−i−ii−ii-111-1
χ2111-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-11-111−ii−ii-1-1ii−i−iii−i−i1-1−ii−ii-11-11-11-11i−ii−i
χ2211-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii11-1-11-111−ii−ii-1-1−i−iii−i−iii1-1−ii−ii1-11-11-11-1−ii−ii
χ2311-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-1-111-11-1-1i−ii−i1111-1-1-1-111-11i−ii−ii−ii−i−ii−ii1-1-11
χ2411-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-1-111-11-1-1i−ii−i11-1-11111-1-1-11i−ii−i−ii−iii−ii−i-111-1
χ2511-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii11-1-1-1111i−i−ii-1-1ii−i−iii−i−i-11i−i−ii1-1-111-1-11−ii−ii
χ2611-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii11-1-1-1111i−i−ii-1-1−i−iii−i−iii-11i−i−ii-111-1-111-1i−ii−i
χ2711-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1111-1-1-1−iii−i1111-1-1-1-1111-1−iii−i−iii−ii−i−ii-111-1
χ2811-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1111-1-1-1−iii−i11-1-11111-1-11-1−iii−ii−i−ii−iii−i1-1-11
χ2911-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i11-1-1-1111−iii−i-1-1ii−i−iii−i−i-11−iii−i-111-1-111-1−ii−ii
χ3011-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i11-1-1-1111−iii−i-1-1−i−iii−i−iii-11−iii−i1-1-111-1-11i−ii−i
χ3111-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1111-1-1-1i−i−ii1111-1-1-1-1111-1i−i−iii−i−ii−iii−i-111-1
χ3211-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-1111-1-1-1i−i−ii11-1-11111-1-11-1i−i−ii−iii−ii−i−ii1-1-11
χ3322222-12-12222-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1222222-1-12222-1-100000000-1-1-1-1-1-1000000000000
χ3422222-12-12222-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-211-2-2-2-21100000000111111000000000000
χ3522222-12-1-2-2-2-2-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-21111222222-1-1-2-2-2-2-1-100000000-1-11111000000000000
χ3622222-12-1-2-2-2-2-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-21111-2-2-2-2-2-2112222110000000011-1-1-1-1000000000000
χ372222-2-1-2-122-2-2-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-1-1-111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-211112222-2-2-1-122-2-2-1-10000000011-1-111000000000000
χ382222-2-1-2-122-2-2-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-1-1-111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-22211-2-2221100000000-1-111-1-1000000000000
χ392222-2-1-2-1-2-222-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-12222-2-2-1-1-2-222-1-1000000001111-1-1000000000000
χ402222-2-1-2-1-2-222-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-2221122-2-21100000000-1-1-1-111000000000000
χ4122-2-22-1-2-12i−2i2i−2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111−ii−ii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii22-2-22-2-1-12i−2i2i−2i1100000000-11−ii−ii000000000000
χ4222-2-22-1-2-12i−2i2i−2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111−ii−ii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii-2-222-2211−2i2i−2i2i-1-1000000001-1i−ii−i000000000000
χ4322-2-22-1-2-1−2i2i−2i2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111i−ii−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i22-2-22-2-1-1−2i2i−2i2i1100000000-11i−ii−i000000000000
χ4422-2-22-1-2-1−2i2i−2i2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111i−ii−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i-2-222-22112i−2i2i−2i-1-1000000001-1−ii−ii000000000000
χ4522-2-2-2-12-12i−2i−2i2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111−iii−i-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i22-2-2-22-1-12i−2i−2i2i11000000001-1−iii−i000000000000
χ4622-2-2-2-12-12i−2i−2i2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111−iii−i-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-2-2222-211−2i2i2i−2i-1-100000000-11i−i−ii000000000000
χ4722-2-2-2-12-1−2i2i2i−2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111i−i−ii-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii22-2-2-22-1-1−2i2i2i−2i11000000001-1i−i−ii000000000000
χ4822-2-2-2-12-1−2i2i2i−2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111i−i−ii-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-2-2222-2112i−2i−2i2i-1-100000000-11−iii−i000000000000
χ492-22i−2i020-200002i−2i2222220-2-2-2-2-2-202i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002-22i−2i002-200002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ502-22i−2i020-200002i−2i2222220-2-2-2-2-2-202i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002-22i−2i002-200002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ512-22i−2i020-200002i−2i2222220-2-2-2-2-2-202i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000-22−2i2i00-220000−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ522-22i−2i020-200002i−2i2222220-2-2-2-2-2-202i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000-22−2i2i00-220000−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ532-2−2i2i020-20000−2i2i2222220-2-2-2-2-2-20−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002-2−2i2i002-20000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ542-2−2i2i020-20000−2i2i2222220-2-2-2-2-2-20−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002-2−2i2i002-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ552-2−2i2i020-20000−2i2i2222220-2-2-2-2-2-20−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000-222i−2i00-2200002i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ562-2−2i2i020-20000−2i2i2222220-2-2-2-2-2-20−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000-222i−2i00-2200002i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ57444444444444441-211-2-241-211-2-241-21-211-2-211-2-244441-211-2-21-211-2-21-211-2-21-211-2-21-211-2-21-211-2-20000000000000000000000000000000000000000
χ5844444444444444-21-2-2114-21-2-2114-21-21-2-211-2-2114444-21-2-211-21-2-211-21-2-211-21-2-211-21-2-211-21-2-2110000000000000000000000000000000000000000
χ5944444444-4-4-4-4441-211-2-241-211-2-241-21-211-2-211-2-2-4-4-4-41-211-2-21-211-2-2-12-1-122-12-1-122-12-1-122-12-1-1220000000000000000000000000000000000000000
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χ1138-88i−8i0-4040000−4i4i-4222−1−3i3−1+3i304-2-2-21+3i31−3i30−4i2i4i−2i2i2i−2ζ14+4ζ224ζ14−2ζ22−2i−2i2ζ14−4ζ22−4ζ14+2ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-88i−8i0-4040000−4i4i-4222−1+3i3−1−3i304-2-2-21−3i31+3i30−4i2i4i−2i2i2i4ζ14−2ζ22−2ζ14+4ζ22−2i−2i−4ζ14+2ζ222ζ14−4ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-8−8i8i080-80000−8i8i2-422-4-40-24-2-2440−2i4i2i−4i−2i−2i4i4i2i2i−4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8−8i8i080-80000−8i8i-42-4-42204-244-2-204i−2i−4i2i4i4i−2i−2i−4i−4i2i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-8−8i8i0-40400004i−4i2-4−1−3i3−1+3i3220-241+3i31−3i3-2-20−2i4i2i−4i2ζ14−4ζ22−4ζ14+2ζ22−2i−2i−2ζ14+4ζ224ζ14−2ζ222i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1188-8−8i8i0-40400004i−4i2-4−1+3i3−1−3i3220-241−3i31+3i3-2-20−2i4i2i−4i−4ζ14+2ζ222ζ14−4ζ22−2i−2i4ζ14−2ζ22−2ζ14+4ζ222i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-8−8i8i0-40400004i−4i-4222−1−3i3−1+3i304-2-2-21+3i31−3i304i−2i−4i2i−2i−2i2ζ14−4ζ22−4ζ14+2ζ222i2i−2ζ14+4ζ224ζ14−2ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1208-8−8i8i0-40400004i−4i-4222−1+3i3−1−3i304-2-2-21−3i31+3i304i−2i−4i2i−2i−2i−4ζ14+2ζ222ζ14−4ζ222i2i4ζ14−2ζ22−2ζ14+4ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.