Finite Group Databasebeta

← Group #13155527

Character table — Group #13155527

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12224444333666666666121212121212121212121212333666666666121212121212121212121212444436661212121288881212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424242244668888121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−ii−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1i−i−ii1111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1i−i−ii11ii−i−i−i−iii-1-111
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−iii−i1111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1−iii−i11−i−iiiii−i−i-1-111
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−ii−ii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii-1-1−i−iii−i−iii11-1-1
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1i−ii−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111−ii−ii-1-1−i−iii−i−iii-1-111
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1i−i−ii-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1−iii−i11−i−iiiii−i−i11-1-1
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−iii−i-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1i−i−ii11ii−i−i−i−iii11-1-1
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−ii−ii-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111i−ii−i-1-1ii−i−iii−i−i-1-111
χ172222222222-1-1-1222222-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-10000-1-1000000000000
χ182222222222-1-1-1222222-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-122-2-20000000000000000-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-211000011000000000000
χ192222222222-1-1-1222222-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-2-22200000000000000001111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-2-2-2-211000011000000000000
χ202222222222-1-1-1222222-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-2-2-2-2000000000000000011111111-2-2-2-2-2-2-2-211111111111111112222-1-10000-1-1000000000000
χ21222222222-12222-122-1-1222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-12222-1-1-1-1-1-1-1-1002222-1-122-1-1-1-1-1-1-1-1-1-1000022220000-1-1-1-100000000-1-1-1-1-1-1-1-10000000022000000-1-1-1-10000
χ22222222222-12222-122-1-1222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-12222-1-1-1-1-1-1-1-100-2-222-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200001111000000001111111100000000-2-200000011110000
χ23222222222-12222-122-1-1222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-10022-2-211-2-21111111111000022220000-1-1-1-100000000-1-1-1-1-1-1-1-100000000-2-200000011110000
χ24222222222-12222-122-1-1222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-100-2-2-2-211-2-211111111110000-2-2-2-20000111100000000111111110000000022000000-1-1-1-10000
χ2522222222-12222-12-1-1222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-12200-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-10000-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100000000
χ2622222222-12222-12-1-1222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-2-200-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000111100001111111100000000000000-2-20000111100000000
χ2722222222-12222-12-1-1222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1220011-2-211-2-21111111122220000-1-1-1-10000-1-1-1-1-1-1-1-100000000000000-2-20000111100000000
χ2822222222-12222-12-1-1222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-20011-2-211-2-211111111-2-2-2-20000111100001111111100000000000000220000-1-1-1-100000000
χ292222-2-2-2-222-1-1-1222222-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-2111111110000-1-1-1-111112i−2i2i−2i0000000000000000−i−iii−i−iii2i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii22-2-2-1-1000011000000000000
χ302222-2-2-2-222-1-1-1222222-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-2111111110000-1-1-1-111112i−2i−2i2i0000000000000000−i−iiiii−i−i2i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-2-222110000-1-1000000000000
χ312222-2-2-2-222-1-1-1222222-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-2111111110000-1-1-1-11111−2i2i2i−2i0000000000000000ii−i−i−i−iii−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-2-222110000-1-1000000000000
χ322222-2-2-2-222-1-1-1222222-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-2111111110000-1-1-1-11111−2i2i−2i2i0000000000000000ii−i−iii−i−i−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i22-2-2-1-1000011000000000000
χ332222-2-2-2-22-12222-122-1-12-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-21122-2-2-1-1-1-11111002i−2i22-1-1-2-211-1-1-1-1111100002i2i−2i−2i0000−i−iii00000000−i−i−i−iiiii000000002i−2i000000−i−iii0000
χ342222-2-2-2-22-12222-122-1-12-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-21122-2-2-1-1-1-1111100−2i2i22-1-1-2-211-1-1-1-111110000−2i−2i2i2i0000ii−i−i00000000iiii−i−i−i−i00000000−2i2i000000ii−i−i0000
χ352222-2-2-2-22-12222-122-1-12-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-2-222-1-1-1-11111002i−2i-2-21122-1-11111-1-1-1-100002i2i−2i−2i0000−i−iii00000000−i−i−i−iiiii00000000−2i2i000000ii−i−i0000
χ362222-2-2-2-22-12222-122-1-12-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-2-222-1-1-1-1111100−2i2i-2-21122-1-11111-1-1-1-10000−2i−2i2i2i0000ii−i−i00000000iiii−i−i−i−i000000002i−2i000000−i−iii0000
χ372222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-222-2-2-1-1-1-111112i−2i00-1-12211-2-2-1-1-1-111112i2i−2i−2i0000−i−iii0000−i−i−i−iiiii000000000000002i−2i0000−i−iii00000000
χ382222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-222-2-2-1-1-1-11111−2i2i00-1-12211-2-2-1-1-1-11111−2i−2i2i2i0000ii−i−i0000iiii−i−i−i−i00000000000000−2i2i0000ii−i−i00000000
χ392222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-2-222-1-1-1-111112i−2i0011-2-2-1-1221111-1-1-1-12i2i−2i−2i0000−i−iii0000−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00000000
χ402222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-2-222-1-1-1-11111−2i2i0011-2-2-1-1221111-1-1-1-1−2i−2i2i2i0000ii−i−i0000iiii−i−i−i−i000000000000002i−2i0000−i−iii00000000
χ4122-2-222-2-2222-2-222-2-2-2-2222-2-222-2-2-2-222222-2-2-2-2222-2-222-2-222-2-2-2-22200002-2-2222-2-20000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4222-2-222-2-2222-2-222-2-2-2-2222-2-222-2-2-2-222222-2-2-2-2222-2-222-2-222-2-2-2-22200002-2-2222-2-2000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4322-2-2-2-222222-2-222-2-2-2-22-2-222-2-22222-2-2222-2-2-2-2222-2-2-2-222-2-22222-2-200002-2-22-2-2220000000000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-2-2-222222-2-222-2-2-2-22-2-222-2-22222-2-2222-2-2-2-2222-2-2-2-222-2-22222-2-200002-2-22-2-222000000000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-22-22i−2i2i−2i2222-2-2-22-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000002-22i−2i2-200002i−2i000000000000
χ462-22-22i−2i2i−2i2222-2-2-22-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000-22−2i2i-220000−2i2i000000000000
χ472-22-22i−2i2i−2i22-1-11-2-22-22-212i−2i2i−2i−ii−ii2i−2i2i−2i2-1-1-11-11-2112-22i−2i2i−2i−ii−ii−ii−ii0000-1-111−ii−ii00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132-22i−2i-110000−ii000000000000
χ482-22-22i−2i2i−2i22-1-11-2-22-22-212i−2i2i−2i−ii−ii2i−2i2i−2i2-1-1-11-11-2112-22i−2i2i−2i−ii−ii−ii−ii0000-1-111−ii−ii00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-22−2i2i1-10000i−i000000000000
χ492-22-22i−2i2i−2i22-1-11-2-22-22-212i−2i2i−2i−ii−ii2i−2i2i−2i2-1-1-11-11-2112-22i−2i2i−2i−ii−ii−ii−ii0000-1-111−ii−ii00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-22−2i2i1-10000i−i000000000000
χ502-22-22i−2i2i−2i22-1-11-2-22-22-212i−2i2i−2i−ii−ii2i−2i2i−2i2-1-1-11-11-2112-22i−2i2i−2i−ii−ii−ii−ii0000-1-111−ii−ii00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ132-22i−2i-110000−ii000000000000
χ512-22-2−2i2i−2i2i2222-2-2-22-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-2-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i2i−2i2i00000000000000000000000000000000000000000000000000002-2−2i2i2-20000−2i2i000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.