Finite Group Databasebeta

← Group #13155536

Character table — Group #13155536

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order12224444333666666666121212121212121212121212333666666666121212121212121212121212444436661212121244881212121212121212121212121212121212121212121212121212121212121212242424242424242424242424242424248888246688121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1i−i11-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-111i−i-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1−ii11-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-111−ii-1-1−i−iii−i−iii−i−iii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11i−i11-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii-11-1-1i−i11ii−i−i−i−iii−i−iii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11−ii11-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i-11-1-1−ii11−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1i−i-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-11-1-1−ii11−i−iiiii−i−i−i−iii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1−ii-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-11-1-1i−i11ii−i−i−i−iiiii−i−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11i−i-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii1-111−ii-1-1−i−iii−i−iiiii−i−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11−ii-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i1-111i−i-1-1ii−i−iii−i−i−i−iii
χ172222222222-1222222-1-1-122-1-1-1-12222222-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1220022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000022-1-100-1-1000000000000
χ182222222222-1222222-1-1-122-1-1-1-12222222-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2002222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000-2-2110011000000000000
χ192222222222-1222222-1-1-122-1-1-1-12222222-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12200-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000-2-2110011000000000000
χ202222222222-1222222-1-1-122-1-1-1-12222222-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-200-2-2-2-2-2-2-2-21111111111111111111111110000000000000000000022-1-100-1-1000000000000
χ21222222222-122-122-1-1222222222-1-1-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000-1-1-1-12222-1-1-1-1-1-1-1-1000000002200-1-1-1-100000000
χ22222222222-122-122-1-1222222222-1-1-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-2-1-1-1-1000022220000-1-1-1-1-1-1-1-1000000001111-2-2-2-21111111100000000-2-200111100000000
χ23222222222-122-122-1-1222222222-1-1-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1002211110000-2-2-2-200001111111100000000-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-200111100000000
χ24222222222-122-122-1-1222222222-1-1-1-122-12-1-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-100-2-211110000-2-2-2-2000011111111000000001111-2-2-2-211111111000000002200-1-1-1-100000000
χ2522222222-122-12-1-122222-1-122222222-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-122220000-1-1-1-10000222200000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000-1-1-1-10000
χ2622222222-122-12-1-122222-1-122222222-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-122-2-20000-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-200000000000011110000
χ2722222222-122-12-1-122222-1-122222222-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-1-2-222000011110000-2-2-2-200000000111111112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000011110000
χ2822222222-122-12-1-122222-1-122222222-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-1-2-2-2-2000011110000-2-2-2-20000000011111111-2-2-2-21111111111112222000000000000-1-1-1-10000
χ292222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-1222-1-1-1-1-1-1-2-211111111-2-222-2-2-1-1-1-111112-20022-2-222-2-2-1-111-1-111-1-1-1-11111-1-1-1-11111000000000000000000002-2-1-10011000000000000
χ302222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-1222-1-1-1-1-1-1-2-211111111-2-222-2-2-1-1-1-11111-220022-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-100000000000000000000-221100-1-1000000000000
χ312222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-1222-1-1-1-1-1-1-2-211111111-2-2-2-222-1-1-1-111112-200-2-22222-2-211-1-1-1-1111111-1-1-1-1-1-1-1-1111100000000000000000000-221100-1-1000000000000
χ322222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-1222-1-1-1-1-1-1-2-211111111-2-2-2-222-1-1-1-11111-2200-2-222-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-1000000000000000000002-2-1-10011000000000000
χ332222-2-2-2-22-122-122-1-1222-2-2-2-2-2-21111-2-2-12-1-1-1-12-122-1-111-2-2-2-211111122-2-2-1-1-1-11111002i−2i-1-111000022-2-20000-1-1-1-1111100000000−i−iii2i2i−2i−2i−i−i−i−iiiii000000002i−2i00−i−iii00000000
χ342222-2-2-2-22-122-122-1-1222-2-2-2-2-2-21111-2-2-12-1-1-1-12-122-1-111-2-2-2-211111122-2-2-1-1-1-1111100−2i2i-1-111000022-2-20000-1-1-1-1111100000000ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−2i2i00ii−i−i00000000
χ352222-2-2-2-22-122-122-1-1222-2-2-2-2-2-21111-2-2-12-1-1-1-12-122-1-111-2-2-2-2111111-2-222-1-1-1-11111002i−2i11-1-10000-2-22200001111-1-1-1-100000000−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−2i2i00ii−i−i00000000
χ362222-2-2-2-22-122-122-1-1222-2-2-2-2-2-21111-2-2-12-1-1-1-12-122-1-111-2-2-2-2111111-2-222-1-1-1-1111100−2i2i11-1-10000-2-22200001111-1-1-1-100000000ii−i−i−2i−2i2i2iiiii−i−i−i−i000000002i−2i00−i−iii00000000
χ372222-2-2-2-2-122-12-1-12222211-2-2-2-2-2-2-2-211-1-12-1-1-1-12-1-122111111-2-2-2-2110000-1-1-1-111112-22i−2i0000-1-111000022-2-200000000-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii2i2i−2i−2i000000000000−i−iii0000
χ382222-2-2-2-2-122-12-1-12222211-2-2-2-2-2-2-2-211-1-12-1-1-1-12-1-122111111-2-2-2-2110000-1-1-1-111112-2−2i2i0000-1-111000022-2-200000000-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i−2i−2i2i2i000000000000ii−i−i0000
χ392222-2-2-2-2-122-12-1-12222211-2-2-2-2-2-2-2-211-1-12-1-1-1-12-1-122111111-2-2-2-2110000-1-1-1-11111-222i−2i000011-1-10000-2-222000000001111-1-1-1-12i2i−2i−2i−i−iii−i−i−i−iiiii−2i−2i2i2i000000000000ii−i−i0000
χ402222-2-2-2-2-122-12-1-12222211-2-2-2-2-2-2-2-211-1-12-1-1-1-12-1-122111111-2-2-2-2110000-1-1-1-11111-22−2i2i000011-1-10000-2-222000000001111-1-1-1-1−2i−2i2i2iii−i−iiiii−i−i−i−i2i2i−2i−2i000000000000−i−iii0000
χ4122-2-22i−2i2i−2i222-2-22-22-22-2-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-2-2-2-22-22-22i−2i2i2i−2i−2i2i2i−2i−2i2i−2i000022-2-22i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ4222-2-22i−2i2i−2i222-2-22-22-22-2-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-2-2-2-22-22-22i−2i2i2i−2i−2i2i2i−2i−2i2i−2i000022-2-22i2i−2i−2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ4322-2-2−2i2i−2i2i222-2-22-22-22-2-2−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i2222-2-2-2-22-22-2−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i000022-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ4422-2-2−2i2i−2i2i222-2-22-22-22-2-2−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i2222-2-2-2-22-22-2−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i000022-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ452-22-22i−2i−2i2i222-2-2-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i222-22-2-2-2-22-22−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ462-22-22i−2i−2i2i222-2-2-22-22-22-2−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i222-22-2-2-2-22-22−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i00002-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ472-22-22i−2i−2i2i-1221-21-1-22-22-2i−i2i−2i2i−2i2i−2i−2i2i−ii-1-121-111-21-1-22i−i−ii−ii2i−2i2i−2i−ii0000-11-11−ii−ii00000000−i3i33−30000000000000000−i3−i3i3i333−3−30000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ482-22-22i−2i−2i2i-1221-21-1-22-22-2i−i2i−2i2i−2i2i−2i−2i2i−ii-1-121-111-21-1-22i−i−ii−ii2i−2i2i−2i−ii0000-11-11−ii−ii00000000−i3i33−30000000000000000−i3−i3i3i333−3−30000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ492-22-22i−2i−2i2i-1221-21-1-22-22-2i−i2i−2i2i−2i2i−2i−2i2i−ii-1-121-111-21-1-22i−i−ii−ii2i−2i2i−2i−ii0000-11-11−ii−ii00000000i3−i3−330000000000000000i3i3−i3−i3−3−3330000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ502-22-22i−2i−2i2i-1221-21-1-22-22-2i−i2i−2i2i−2i2i−2i−2i2i−ii-1-121-111-21-1-22i−i−ii−ii2i−2i2i−2i−ii0000-11-11−ii−ii00000000i3−i3−330000000000000000i3i3−i3−i3−3−3330000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.