Finite Group Databasebeta

← Group #13155599

Character table — Group #13155599

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order122244443336666666661212121212121212121212123336666666661212121212121212121212128888366612121212888824242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242444442244666612121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111-1-1-1-1-1-111-1-11111
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−i11-1-111-1-1111111-1-1-1-1-1-1ii−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-1-1111-1-1111-1-1-1-111-1-111−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-1-111-111-1-1-111-1-11111-1-1−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−iiiii11-1-1-1-111-1-1-1-111-1-11111ii−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−i11-1-1-1-111-1-1-1-111-1-11111−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-1-111-111-1-1-111-1-11111-1-1ii−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-1-1111-1-1111-1-1-1-111-1-111ii−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−iiiii11-1-111-1-1111111-1-1-1-1-1-1−i−iii
χ172222222222-122-1-12222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1002222-1-122-1-10000000022-1-122-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000020200-1-1000000-1-10000
χ182222222222-122-1-12222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-100-2-222-1-122-1-100000000-2-211-2-211-1-1-1-1-1-1-1-1000000001111111100000-20-20011000000110000
χ192222222222-122-1-12222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-10022-2-211-2-2110000000022-1-122-1-11111111100000000-1-1-1-1-1-1-1-100000-20-20011000000110000
χ202222222222-122-1-12222-12222-1-12222-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-100-2-2-2-211-2-21100000000-2-211-2-2111111111100000000111111110000020200-1-1000000-1-10000
χ21222222222-12-1-122222-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-12200-1-122-1-12222-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002020-1-1000000-1-1000000
χ22222222222-12-1-122222-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-2-200-1-122-1-122-2-211-2-21100000000-1-1-1-1-1-1-1-111111111000000000000-20-201100000011000000
χ23222222222-12-1-122222-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1220011-2-211-2-222-1-122-1-10000000011111111-1-1-1-1-1-1-1-1000000000000-20-201100000011000000
χ24222222222-12-1-122222-1222-1-12222-1-122-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-20011-2-211-2-2-2-211-2-2110000000011111111111111110000000000002020-1-1000000-1-1000000
χ2522222222-1222222-1-1-122-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-1222200000000-1-122-1-122-1-122-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-100000000
χ2622222222-1222222-1-1-122-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-122-2-200000000-1-122-1-12211-2-211-2-200000000-1-1-1-1-1-1-1-111111111-2-2-2-200000000111100000000
χ2722222222-1222222-1-1-122-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-1-2-2220000000011-2-211-2-2-1-122-1-1220000000011111111-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000
χ2822222222-1222222-1-1-122-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-1-2-2-2-20000000011-2-211-2-211-2-211-2-2000000001111111111111111222200000000-1-1-1-100000000
χ292222-2-2-2-222-122-1-12222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211112i2i−2i−2i-1-1-1-11111002i−2i2i2i−i−i−2i−2iii000000002i2i−i−i−2i−2iii−i−i−i−iiiii00000000−i−i−i−iiiii0000020-200-1-1000000110000
χ302222-2-2-2-222-122-1-12222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-211112i2i−2i−2i-1-1-1-1111100−2i2i2i2i−i−i−2i−2iii00000000−2i−2iii2i2i−i−i−i−i−i−iiiii00000000iiii−i−i−i−i00000-2020011000000-1-10000
χ312222-2-2-2-222-122-1-12222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-21111−2i−2i2i2i-1-1-1-11111002i−2i−2i−2iii2i2i−i−i000000002i2i−i−i−2i−2iiiiiii−i−i−i−i00000000−i−i−i−iiiii00000-2020011000000-1-10000
χ322222-2-2-2-222-122-1-12222-1-2-2-2-211-2-2-2-2112-1-122-1-1-1-12-1-1-2-21111-2-21111−2i−2i2i2i-1-1-1-1111100−2i2i−2i−2iii2i2i−i−i00000000−2i−2iii2i2i−i−iiiii−i−i−i−i00000000iiii−i−i−i−i0000020-200-1-1000000110000
χ332222-2-2-2-22-12-1-122222-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i-1-1-1-111112i−2i00−i−i2i2iii−2i−2i2i2i−i−i−2i−2iii00000000−i−i−i−iiiii−i−i−i−iiiii00000000000020-20-1-100000011000000
χ342222-2-2-2-22-12-1-122222-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i-1-1-1-11111−2i2i00−i−i2i2iii−2i−2i−2i−2iii2i2i−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i000000000000-202011000000-1-1000000
χ352222-2-2-2-22-12-1-122222-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i-1-1-1-111112i−2i00ii−2i−2i−i−i2i2i2i2i−i−i−2i−2iii00000000iiii−i−i−i−i−i−i−i−iiiii000000000000-202011000000-1-1000000
χ362222-2-2-2-22-12-1-122222-12-2-211-2-2-2-211-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i-1-1-1-11111−2i2i00ii−2i−2i−i−i2i2i−2i−2iii2i2i−i−i00000000iiii−i−i−i−iiiii−i−i−i−i00000000000020-20-1-100000011000000
χ372222-2-2-2-2-1222222-1-1-12211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-20000-1-1-1-111112i−2i2i−2i00000000−i−i2i2iii−2i−2i−i−i2i2iii−2i−2i00000000−i−i−i−iiiii−i−i−i−iiiii22-2-200000000-1-11100000000
χ382222-2-2-2-2-1222222-1-1-12211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-20000-1-1-1-111112i−2i−2i2i00000000−i−i2i2iii−2i−2iii−2i−2i−i−i2i2i00000000−i−i−i−iiiiiiiii−i−i−i−i-2-2220000000011-1-100000000
χ392222-2-2-2-2-1222222-1-1-12211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-20000-1-1-1-11111−2i2i2i−2i00000000ii−2i−2i−i−i2i2i−i−i2i2iii−2i−2i00000000iiii−i−i−i−i−i−i−i−iiiii-2-2220000000011-1-100000000
χ402222-2-2-2-2-1222222-1-1-12211-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-21111-2-20000-1-1-1-11111−2i2i−2i2i00000000ii−2i−2i−i−i2i2iii−2i−2i−i−i2i2i00000000iiii−i−i−i−iiiii−i−i−i−i22-2-200000000-1-11100000000
χ4122-2-22i−2i2i−2i2222-22-2-22-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i2i−2i−2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ4222-2-22i−2i2i−2i2222-22-2-22-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ4322-2-2−2i2i−2i2i2222-22-2-22-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ4422-2-2−2i2i−2i2i2222-22-2-22-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ452-22-22i−2i−2i2i222-22-22-2-22-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i222-22-22-22-2-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000000000000000000000002-22i−2i000000002-22i−2i00000000
χ462-22-22i−2i−2i2i222-22-22-2-22-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i222-22-22-22-2-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000-22−2i2i00000000-22−2i2i00000000
χ472-22-22i−2i−2i2i-122-22-2211-1-2-2i−i−2i2i−2i2i−ii2i−2i2i−2i-1-121-11-1-2211-2i−ii−i−2i2i−ii−ii2i−2i0000-11-11−ii−ii000000000000ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ230000000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ232-22i−2i00000000-11−ii00000000
χ482-22-22i−2i−2i2i-122-22-2211-1-2-2i−i−2i2i−2i2i−ii2i−2i2i−2i-1-121-11-1-2211-2i−ii−i−2i2i−ii−ii2i−2i0000-11-11−ii−ii000000000000ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ230000000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23-22−2i2i000000001-1i−i00000000
χ492-22-22i−2i−2i2i-122-22-2211-1-2-2i−i−2i2i−2i2i−ii2i−2i2i−2i-1-121-11-1-2211-2i−ii−i−2i2i−ii−ii2i−2i0000-11-11−ii−ii000000000000−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ1300−ζ7+ζ23ζ7−ζ230000000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23-22−2i2i000000001-1i−i00000000
χ502-22-22i−2i−2i2i-122-22-2211-1-2-2i−i−2i2i−2i2i−ii2i−2i2i−2i-1-121-11-1-2211-2i−ii−i−2i2i−ii−ii2i−2i0000-11-11−ii−ii000000000000−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ1300ζ7−ζ23−ζ7+ζ230000000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ232-22i−2i00000000-11−ii00000000
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χ1448-8-88-8-888-4-4-44444-444-4-4-4-4-4-4-4-4444444222-2-2-2-2-2-2222222222-2-2-2-2-2-20000-111-11-1-110000000000000000000000000000000000000000000000000000000000000000000000000000

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