Finite Group Databasebeta

← Group #13155457

Character table — Group #13155457

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12224444333666666666121212121212121212121212333666666666121212121212121212121212888836661212121288882424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242244444466121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1i−ii−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-11-11111-1-111-1-1-1-1ii−i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1i−i−iiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1111-1-11-1-111-1-1-1-11111−i−iii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1−iii−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-111-1-1-1-1-11111-1-111−i−iii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1−ii−iiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-1111-1-111-1-111-1-1ii−i−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1i−ii−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-1111-1-111-1-111-1-1−i−iii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1i−i−ii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-111-1-1-1-1-11111-1-111ii−i−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1−iii−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-11-1-111-1-1-1-11111ii−i−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1−ii−ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-11111-1-111-1-1-1-1−i−iii
χ172222222222-1-1-1222222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-1-1-1-1-1-1-1-122220000000022-1-122-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-100000000-1-10000
χ182222222222-1-1-1222222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-1-1-1-1-1-1-1-122-2-20000000022-1-122-1-1-2-211-2-21100000000-1-1-1-1-1-1-1-111111111-2-2-2-200001100000000110000
χ192222222222-1-1-1222222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-1-1-1-1-1-1-1-1-2-22200000000-2-211-2-21122-1-122-1-10000000011111111-1-1-1-1-1-1-1-1-2-2-2-200001100000000110000
χ202222222222-1-1-1222222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211-2-211-2-211-2-21100000000111111111111111122220000-1-100000000-1-10000
χ21222222222-12222-122-1-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1002222-1-122-1-100000000-1-122-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000022000000-1-1-1-1000000
χ22222222222-12222-122-1-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-100-2-222-1-122-1-10000000011-2-211-2-2-1-1-1-1-1-1-1-10000000011111111000000-2-20000001111000000
χ23222222222-12222-122-1-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-10022-2-211-2-21100000000-1-122-1-1221111111100000000-1-1-1-1-1-1-1-1000000-2-20000001111000000
χ24222222222-12222-122-1-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-100-2-2-2-211-2-2110000000011-2-211-2-211111111000000001111111100000022000000-1-1-1-1000000
χ2522222222-12222-12-1-1222-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12200-1-122-1-122-1-122-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000220000-1-1-1-10000000000
χ2622222222-12222-12-1-1222-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-2-200-1-122-1-12211-2-211-2-200000000-1-1-1-1-1-1-1-111111111000000000000-2-2000011110000000000
χ2722222222-12222-12-1-1222-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1220011-2-211-2-2-1-122-1-1220000000011111111-1-1-1-1-1-1-1-1000000000000-2-2000011110000000000
χ2822222222-12222-12-1-1222-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-20011-2-211-2-211-2-211-2-2000000001111111111111111000000000000220000-1-1-1-10000000000
χ292222-2-2-2-222-1-1-1222222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211110000-1-1-1-111112i−2i2i−2i000000002i2i−i−i−2i−2iii2i2i−i−i−2i−2iii00000000−i−i−i−iiiii−i−i−i−iiiii22-2-20000-1-100000000110000
χ302222-2-2-2-222-1-1-1222222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211110000-1-1-1-111112i−2i−2i2i000000002i2i−i−i−2i−2iii−2i−2iii2i2i−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i-2-22200001100000000-1-10000
χ312222-2-2-2-222-1-1-1222222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211110000-1-1-1-11111−2i2i2i−2i00000000−2i−2iii2i2i−i−i2i2i−i−i−2i−2iii00000000iiii−i−i−i−i−i−i−i−iiiii-2-22200001100000000-1-10000
χ322222-2-2-2-222-1-1-1222222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211110000-1-1-1-11111−2i2i−2i2i00000000−2i−2iii2i2i−i−i−2i−2iii2i2i−i−i00000000iiii−i−i−i−iiiii−i−i−i−i22-2-20000-1-100000000110000
χ332222-2-2-2-22-12222-122-1-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i-1-1-1-11111002i−2i2i2i−i−i−2i−2iii00000000−i−i2i2iii−2i−2i−i−i−i−iiiii00000000−i−i−i−iiiii0000002-2000000-1-111000000
χ342222-2-2-2-22-12222-122-1-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i-1-1-1-1111100−2i2i2i2i−i−i−2i−2iii00000000ii−2i−2i−i−i2i2i−i−i−i−iiiii00000000iiii−i−i−i−i000000-2200000011-1-1000000
χ352222-2-2-2-22-12222-122-1-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i-1-1-1-11111002i−2i−2i−2iii2i2i−i−i00000000−i−i2i2iii−2i−2iiiii−i−i−i−i00000000−i−i−i−iiiii000000-2200000011-1-1000000
χ362222-2-2-2-22-12222-122-1-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i-1-1-1-1111100−2i2i−2i−2iii2i2i−i−i00000000ii−2i−2i−i−i2i2iiiii−i−i−i−i00000000iiii−i−i−i−i0000002-2000000-1-111000000
χ372222-2-2-2-2-12222-12-1-122211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-22i2i−2i−2i-1-1-1-111112i−2i00−i−i2i2iii−2i−2i−i−i2i2iii−2i−2i00000000−i−i−i−iiiii−i−i−i−iiiii0000000000002-20000-1-1110000000000
χ382222-2-2-2-2-12222-12-1-122211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-22i2i−2i−2i-1-1-1-11111−2i2i00−i−i2i2iii−2i−2iii−2i−2i−i−i2i2i00000000−i−i−i−iiiiiiiii−i−i−i−i000000000000-22000011-1-10000000000
χ392222-2-2-2-2-12222-12-1-122211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-2−2i−2i2i2i-1-1-1-111112i−2i00ii−2i−2i−i−i2i2i−i−i2i2iii−2i−2i00000000iiii−i−i−i−i−i−i−i−iiiii000000000000-22000011-1-10000000000
χ402222-2-2-2-2-12222-12-1-122211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-2−2i−2i2i2i-1-1-1-11111−2i2i00ii−2i−2i−i−i2i2iii−2i−2i−i−i2i2i00000000iiii−i−i−i−iiiii−i−i−i−i0000000000002-20000-1-1110000000000
χ4122-2-222-2-2222-2-222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-200002-2-2222-2-200000000000000000000000000000000000000000000000000002-22-200002-2000000002-20000
χ4222-2-222-2-2222-2-222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-200002-2-2222-2-20000000000000000000000000000000000000000000000000000-22-220000-2200000000-220000
χ4322-2-222-2-222-11122-2-2-2-2-12222-1-1-2-2-2-2112-1-1-2-211112-1-122-1-1-1-1-2-211110000-111-1-1-111000000000000003−3003−3003−3003−30000000033−3−333−3−333−3−333−3−32-22-20000-1100000000-110000
χ4422-2-222-2-222-11122-2-2-2-2-12222-1-1-2-2-2-2112-1-1-2-211112-1-122-1-1-1-1-2-211110000-111-1-1-111000000000000003−3003−300−3300−330000000033−3−333−3−3−3−333−3−333-22-2200001-1000000001-10000
χ4522-2-222-2-222-11122-2-2-2-2-12222-1-1-2-2-2-2112-1-1-2-211112-1-122-1-1-1-1-2-211110000-111-1-1-11100000000000000−3300−33003−3003−300000000−3−333−3−33333−3−333−3−3-22-2200001-1000000001-10000
χ4622-2-222-2-222-11122-2-2-2-2-12222-1-1-2-2-2-2112-1-1-2-211112-1-122-1-1-1-1-2-211110000-111-1-1-11100000000000000−3300−3300−3300−3300000000−3−333−3−333−3−333−3−3332-22-20000-1100000000-110000
χ4722-2-2-2-222222-2-222-2-2-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222222200002-2-22-2-22200000000000000000000000000000000000000000000000000002-2-2200002-200000000-220000
χ4822-2-2-2-222222-2-222-2-2-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222222200002-2-22-2-2220000000000000000000000000000000000000000000000000000-222-20000-22000000002-20000
χ4922-2-2-2-22222-11122-2-2-2-2-1-2-2-2-2112222-1-12-1-1-2-211112-1-1-2-2111122-1-1-1-10000-111-111-1-100000000000000−i3i300i3−i300−i3i300i3−i300000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-220000-11000000001-10000
χ5022-2-2-2-22222-11122-2-2-2-2-1-2-2-2-2112222-1-12-1-1-2-211112-1-1-2-2111122-1-1-1-10000-111-111-1-100000000000000−i3i300i3−i300i3−i300−i3i300000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-222-200001-100000000-110000
χ5122-2-2-2-22222-11122-2-2-2-2-1-2-2-2-2112222-1-12-1-1-2-211112-1-1-2-2111122-1-1-1-10000-111-111-1-100000000000000i3−i300−i3i300−i3i300i3−i300000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-222-200001-100000000-110000
χ5222-2-2-2-22222-11122-2-2-2-2-1-2-2-2-2112222-1-12-1-1-2-211112-1-1-2-2111122-1-1-1-10000-111-111-1-100000000000000i3−i300−i3i300i3−i300−i3i300000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-220000-11000000001-10000
χ532-22-22i−2i2i−2i2222-2-2-22-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ542-22-22i−2i2i−2i2222-2-2-22-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.