Finite Group Databasebeta

← Group #13155600

Character table — Group #13155600

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12224444333666666666121212121212121212121212333666666666121212121212121212121212888888882424242424242424242424242424242436661212121224666666661212121212121212242424242424242424242424242424242424242424242424444412121212121212128888242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−ii−iii−i−iii−i−i1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1−ii−ii−i−iii−i−iii-11
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111i−i−iiii−i−i−i−iii-11
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111−iii−i−i−iiiii−i−i1-1
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−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111−iii−i−i−iiiii−i−i-11
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111i−i−iiii−i−i−i−iii1-1
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−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii−i−iii−i−iii1-1
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1i−ii−iii−i−iii−i−i-11
χ172222222222-122-1-122-122222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222200002222222200000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000000000002200-1-1-1-1000000
χ182222222222-122-1-122-122222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222200002222222200000000-1-1-1-1-1-1-1-1-2-2-2-2111111-2-2111111-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000-2-2001111000000
χ192222222222-122-1-122-122222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1111100001111111100000000000000000000-2-2001111000000
χ202222222222-122-1-122-122222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-2-2-2-2111111-2-21111111111000011111111000000000000000000002200-1-1-1-1000000
χ21222222222-12-1-1222-1222-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122000022220000000022222222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-10000-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100
χ22222222222-12-1-1222-1222-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122000022220000000022222222-1-1-1-1-1-1-1-1-2-211-2-2111111-2-211110000-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000-2-20000111100
χ23222222222-12-1-1222-1222-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1220000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-100001111000000001111111100000000000000-2-20000111100
χ24222222222-12-1-1222-1222-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1220000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-211-2-2111111-2-2111100001111000000001111111100000000000000220000-1-1-1-100
χ2522222222-1222222-122-1-122-1-1-1-1222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ2622222222-1222222-122-1-122-1-1-1-1222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000002222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-21111111100000000000000
χ2722222222-1222222-122-1-122-1-1-1-1222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2222211111111-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ2822222222-1222222-122-1-122-1-1-1-1222222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-100000000000000
χ292222-2-2-2-222-122-1-122-122-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-2111111-2-2112i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1-1-1-111112-222-1-1-1-1-1-1-2-2111111−i−iii0000−i−i−i−iiiii000000000000000000002i−2i00−i−iii000000
χ302222-2-2-2-222-122-1-122-122-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-2111111-2-2112i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1-1-1-11111-22-2-211111122-1-1-1-1-1-1−i−iii0000−i−i−i−iiiii00000000000000000000−2i2i00ii−i−i000000
χ312222-2-2-2-222-122-1-122-122-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1-1-1-111112-222-1-1-1-1-1-1-2-2111111ii−i−i0000iiii−i−i−i−i00000000000000000000−2i2i00ii−i−i000000
χ322222-2-2-2-222-122-1-122-122-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1-1-1-11111-22-2-211111122-1-1-1-1-1-1ii−i−i0000iiii−i−i−i−i000000000000000000002i−2i00−i−iii000000
χ332222-2-2-2-22-12-1-1222-122211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-200002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-111112-2-1-122-1-1-1-111-2-211110000−i−iii00000000−i−i−i−iiiii000000000000002i−2i0000−i−iii00
χ342222-2-2-2-22-12-1-1222-122211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-200002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-11111-2211-2-21111-1-122-1-1-1-10000−i−iii00000000−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00
χ352222-2-2-2-22-12-1-1222-122211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-20000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112-2-1-122-1-1-1-111-2-211110000ii−i−i00000000iiii−i−i−i−i00000000000000−2i2i0000ii−i−i00
χ362222-2-2-2-22-12-1-1222-122211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-20000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-2211-2-21111-1-122-1-1-1-10000ii−i−i00000000iiii−i−i−i−i000000000000002i−2i0000−i−iii00
χ372222-2-2-2-2-1222222-122-1-1-2-21111-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-211112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111110000000000000000002i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii22-2-2-1-1-1-1111100000000000000
χ382222-2-2-2-2-1222222-122-1-1-2-21111-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-211112i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111110000000000000000002i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-2-2221111-1-1-1-100000000000000
χ392222-2-2-2-2-1222222-122-1-1-2-21111-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111000000000000000000−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-2-2221111-1-1-1-100000000000000
χ402222-2-2-2-2-1222222-122-1-1-2-21111-2-2-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111000000000000000000−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i22-2-2-1-1-1-1111100000000000000
χ4122-2-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i00000000000000000000000022-2-22i2i−2i−2i0000000000000000000000000000000000000000002-22i−2i22-2-22i2i−2i−2i00000000000000
χ4222-2-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i00000000000000000000000022-2-22i2i−2i−2i000000000000000000000000000000000000000000-22−2i2i-2-222−2i−2i2i2i00000000000000
χ4322-2-22i−2i2i−2i-1222-22-21-2-2-112i−2i−i−iii2i−2i2i−2i2i−2i-1-12-11-112-211-2−ii−ii2i2i−2i−2i−ii−ii00000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−i−iii00000000000000000000000000−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-1-111−i−iii00000000000000
χ4422-2-22i−2i2i−2i-1222-22-21-2-2-112i−2i−i−iii2i−2i2i−2i2i−2i-1-12-11-112-211-2−ii−ii2i2i−2i−2i−ii−ii00000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-1-111−i−iii00000000000000000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-22−2i2i11-1-1ii−i−i00000000000000
χ4522-2-22i−2i2i−2i-1222-22-21-2-2-112i−2i−i−iii2i−2i2i−2i2i−2i-1-12-11-112-211-2−ii−ii2i2i−2i−2i−ii−ii00000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−i−iii00000000000000000000000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-22−2i2i11-1-1ii−i−i00000000000000
χ4622-2-22i−2i2i−2i-1222-22-21-2-2-112i−2i−i−iii2i−2i2i−2i2i−2i-1-12-11-112-211-2−ii−ii2i2i−2i−2i−ii−ii00000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-1-111−i−iii00000000000000000000000000ζ7−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-1-111−i−iii00000000000000
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χ1568-8-88-8-888-4-4-44444-4-4-444444-4-4444-4-4-4-4222-2-2-2-2-2-2222-2-222-222-222-2-2000000000000000000000000-111-11-1-1100000000000000000000000000000000000000000000000000000000000000000000

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