Finite Group Databasebeta

← Group #13155543

Character table — Group #13155543

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444488888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12224444333666666666121212121212121212121212333666666666121212121212121212121212366612121212246666666688881212121212121212242424242424242424242424242424242424242424242424242424242424242444448888888812121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111111111i−ii−i-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111111111i−i−ii-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-11
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111111111−iii−i-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i-11
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111111111−ii−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1-1
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1i−ii−i11111111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii-11
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1i−i−ii11111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i1-1
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1−iii−i11111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii1-1
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1−ii−ii11111111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i-11
χ172222222222-122-1-122-122222222-1-122-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1002222-1-1-1-1-1-10000000022-1-122-1-100000000-1-1-1-1-1-1-1-100000000222200000000-1-1-1-100
χ182222222222-122-1-122-122222222-1-122-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-100-2-222-1-1-1-1-1-100000000-2-211-2-211000000001111111100000000-2-2-2-200000000111100
χ192222222222-122-1-122-122222222-1-122-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111110022-2-21111110000000022-1-122-1-100000000-1-1-1-1-1-1-1-100000000-2-2-2-200000000111100
χ202222222222-122-1-122-122222222-1-122-1-12-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111100-2-2-2-211111100000000-2-211-2-211000000001111111100000000222200000000-1-1-1-100
χ21222222222-12-1-1222-12222222-1-122-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122-1-1-1-12200-1-122-1-1-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1000000000000222200000000-1-1-1-1000000
χ22222222222-12-1-1222-12222222-1-122-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-2-200-1-122-1-1-1-1-2-211-2-2110000000011111111000000000000-2-2-2-2000000001111000000
χ23222222222-12-1-1222-12222222-1-122-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-21111220011-2-2111122-1-122-1-100000000-1-1-1-1-1-1-1-1000000000000-2-2-2-2000000001111000000
χ24222222222-12-1-1222-12222222-1-122-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-21111-2-20011-2-21111-2-211-2-2110000000011111111000000000000222200000000-1-1-1-1000000
χ2522222222-1222222-122-1-1-1-1-1-122222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000222200000000-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000000000
χ2622222222-1222222-122-1-1-1-1-1-122222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000022-2-200000000-1-122-1-12211-2-211-2-2-1-1-1-1-1-1-1-111111111-2-2-2-20000000011110000000000
χ2722222222-1222222-122-1-1-1-1-1-122222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2220000000011-2-211-2-2-1-122-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-20000000011110000000000
χ2822222222-1222222-122-1-1-1-1-1-122222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2-2-20000000011-2-211-2-211-2-211-2-21111111111111111222200000000-1-1-1-10000000000
χ292222-2-2-2-222-122-1-122-122-2-2-2-2-2-211-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-211-1-1-1-111112-222-1-1-1-1-1-1002i−2i-2-2111111000000002i2i−i−i−2i−2iii00000000−i−i−i−iiiii000000002i2i−2i−2i00000000−i−iii00
χ302222-2-2-2-222-122-1-122-122-2-2-2-2-2-211-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-211-1-1-1-111112-222-1-1-1-1-1-100−2i2i-2-211111100000000−2i−2iii2i2i−i−i00000000iiii−i−i−i−i00000000−2i−2i2i2i00000000ii−i−i00
χ312222-2-2-2-222-122-1-122-122-2-2-2-2-2-211-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-211-1-1-1-11111-22-2-2111111002i−2i22-1-1-1-1-1-1000000002i2i−i−i−2i−2iii00000000−i−i−i−iiiii00000000−2i−2i2i2i00000000ii−i−i00
χ322222-2-2-2-222-122-1-122-122-2-2-2-2-2-211-2-2112-1-122-1-1-1-12-1-1-2-2111111-2-211-1-1-1-11111-22-2-211111100−2i2i22-1-1-1-1-1-100000000−2i−2iii2i2i−i−i00000000iiii−i−i−i−i000000002i2i−2i−2i00000000−i−iii00
χ332222-2-2-2-22-12-1-1222-1222-2-2-2-211-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2-1-1-1-111112-2-1-122-1-1-1-12i−2i0011-2-211112i2i−i−i−2i−2iii00000000−i−i−i−iiiii0000000000002i2i−2i−2i00000000−i−iii000000
χ342222-2-2-2-22-12-1-1222-1222-2-2-2-211-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2-1-1-1-111112-2-1-122-1-1-1-1−2i2i0011-2-21111−2i−2iii2i2i−i−i00000000iiii−i−i−i−i000000000000−2i−2i2i2i00000000ii−i−i000000
χ352222-2-2-2-22-12-1-1222-1222-2-2-2-211-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2-1-1-1-11111-2211-2-211112i−2i00-1-122-1-1-1-12i2i−i−i−2i−2iii00000000−i−i−i−iiiii000000000000−2i−2i2i2i00000000ii−i−i000000
χ362222-2-2-2-22-12-1-1222-1222-2-2-2-211-2-211-2-2-12-1-1-122-1-1-12-111-2-2111111-2-2-1-1-1-11111-2211-2-21111−2i2i00-1-122-1-1-1-1−2i−2iii2i2i−i−i00000000iiii−i−i−i−i0000000000002i2i−2i−2i00000000−i−iii000000
χ372222-2-2-2-2-1222222-122-1-11111-2-2-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111-1-1-1-1111100000000002i−2i2i−2i00000000−i−i2i2iii−2i−2i−i−i2i2iii−2i−2i−i−i−i−iiiii−i−i−i−iiiii22-2-200000000-1-1110000000000
χ382222-2-2-2-2-1222222-122-1-11111-2-2-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111-1-1-1-1111100000000002i−2i−2i2i00000000−i−i2i2iii−2i−2iii−2i−2i−i−i2i2i−i−i−i−iiiiiiiii−i−i−i−i-2-2220000000011-1-10000000000
χ392222-2-2-2-2-1222222-122-1-11111-2-2-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111-1-1-1-111110000000000−2i2i2i−2i00000000ii−2i−2i−i−i2i2i−i−i2i2iii−2i−2iiiii−i−i−i−i−i−i−i−iiiii-2-2220000000011-1-10000000000
χ402222-2-2-2-2-1222222-122-1-11111-2-2-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111-1-1-1-111110000000000−2i2i−2i2i00000000ii−2i−2i−i−i2i2iii−2i−2i−i−i2i2iiiii−i−i−i−iiiii−i−i−i−i22-2-200000000-1-1110000000000
χ4122-2-222-2-2222-2-2-2-2222-2-222-2-222-2-2-2-222222-2-2-2-2-2-2222-2-22222-2-222-2-22-2-2222-2-20000000000000000000000000000000000000000000000000000002i−2i2i−2i000000002i−2i2i−2i0000000000
χ4222-2-222-2-2222-2-2-2-2222-2-222-2-222-2-2-2-222222-2-2-2-2-2-2222-2-22222-2-222-2-22-2-2222-2-2000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000
χ4322-2-222-2-2-122-2-2-2-2-12211-1-11122-2-2-2-222-1-121111-2-2-1-1211-1-122-2-2-1-111-111-1-1-1110000000000000000000000−i3i300−i3i3003−3003−300−i3−i3i3i3−i3−i3i3i333−3−333−3−32i−2i2i−2i00000000−ii−ii0000000000
χ4422-2-222-2-2-122-2-2-2-2-12211-1-11122-2-2-2-222-1-121111-2-2-1-1211-1-122-2-2-1-111-111-1-1-1110000000000000000000000−i3i300−i3i300−3300−3300−i3−i3i3i3−i3−i3i3i3−3−333−3−333−2i2i−2i2i00000000i−ii−i0000000000
χ4522-2-222-2-2-122-2-2-2-2-12211-1-11122-2-2-2-222-1-121111-2-2-1-1211-1-122-2-2-1-111-111-1-1-1110000000000000000000000i3−i300i3−i3003−3003−300i3i3−i3−i3i3i3−i3−i333−3−333−3−3−2i2i−2i2i00000000i−ii−i0000000000
χ4622-2-222-2-2-122-2-2-2-2-12211-1-11122-2-2-2-222-1-121111-2-2-1-1211-1-122-2-2-1-111-111-1-1-1110000000000000000000000i3−i300i3−i300−3300−3300i3i3−i3−i3i3i3−i3−i3−3−333−3−3332i−2i2i−2i00000000−ii−ii0000000000
χ4722-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2222-2-2-2-2-2-222222-2-2-2-222-2-2222-2-22-2-2220000000000000000000000000000000000000000000000000000002i−2i−2i2i000000002i−2i−2i2i0000000000
χ4822-2-2-2-222222-2-2-2-2222-2-2-2-222-2-22222-2-2222-2-2-2-2-2-222222-2-2-2-222-2-2222-2-22-2-222000000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i0000000000
χ4922-2-2-2-222-122-2-2-2-2-1221111-1-1-2-22222-2-2-1-121111-2-2-1-12-1-111-2-22211-1-1-111-111-1-100000000000000000000003−300−3300−i3i300i3−i30033−3−3−3−333−i3−i3i3i3i3i3−i3−i3−2i2i2i−2i00000000i−i−ii0000000000
χ5022-2-2-2-222-122-2-2-2-2-1221111-1-1-2-22222-2-2-1-121111-2-2-1-12-1-111-2-22211-1-1-111-111-1-100000000000000000000003−300−3300i3−i300−i3i30033−3−3−3−333i3i3−i3−i3−i3−i3i3i32i−2i−2i2i00000000−iii−i0000000000
χ5122-2-2-2-222-122-2-2-2-2-1221111-1-1-2-22222-2-2-1-121111-2-2-1-12-1-111-2-22211-1-1-111-111-1-10000000000000000000000−33003−300−i3i300i3−i300−3−33333−3−3−i3−i3i3i3i3i3−i3−i32i−2i−2i2i00000000−iii−i0000000000
χ5222-2-2-2-222-122-2-2-2-2-1221111-1-1-2-22222-2-2-1-121111-2-2-1-12-1-111-2-22211-1-1-111-111-1-10000000000000000000000−33003−300i3−i300−i3i300−3−33333−3−3i3i3−i3−i3−i3−i3i3i3−2i2i2i−2i00000000i−i−ii0000000000
χ532-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.