Finite Group Databasebeta

← Group #13155597

Character table — Group #13155597

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order122244443336666666661212121212121212121212123336666666661212121212121212121212128888366612121212224466666666666666661212121212121212121212121212121224242424242424242424242424242424444488881212121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1111111111-11-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-11-11-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i11-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-11-1-1111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111i−i−ii-1-111ii−i−i−i−iii−i−iii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1-111-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−iii−i-1-111−i−iiiii−i−i−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−i1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii11-1-1−i−iii−i−iiiii−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−iii1111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii11-1-1−i−iii−i−iii−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−iii1111-1-1-1-11-1-1111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111−iii−i-1-111−i−iiiii−i−iii−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−iii1111-1-1-1-1-111-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111i−i−ii-1-111ii−i−i−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−i−iii1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−i11-1-1ii−i−iii−i−i−i−iii
χ172222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022220000-1-1-1-1000000000000
χ182222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-12-22-222-2-2-1-111-1-1-1-1111122-2-2-1-111-1-1-1-111110000000000000000-2-2-2-200001111000000000000
χ192222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-1-22-22-2-22211-1-11111-1-1-1-1-2-22211-1-11111-1-1-1-10000000000000000-2-2-2-200001111000000000000
χ202222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111-2-2-2-2111111111111000000000000000022220000-1-1-1-1000000000000
χ21222222222-1222-1-12-1222222222-1-122-1-1-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1020200-1-100220000-1-1-1-100-1-100220000-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000002200000000-1-1-1-10000
χ22222222222-1222-1-12-1222222222-1-122-1-1-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-10-20-2001100-2-200001111001100-2-20000111122-1-122-1-1-1-1-1-1-1-1-1-1000000-2-20000000011110000
χ23222222222-1222-1-12-1222222222-1-122-1-1-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1020200-1-100220000-1-1-1-100-1-100220000-1-1-1-1-2-211-2-21111111111000000-2-20000000011110000
χ24222222222-1222-1-12-1222222222-1-122-1-1-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-10-20-2001100-2-200001111001100-2-200001111-2-211-2-211111111110000002200000000-1-1-1-10000
χ2522222222-122-1-122-122222222-1-122-1-122-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-12020-1-1002200-1-1-1-10000-1-1002200-1-1-1-10000-1-122-1-122-1-1-1-1-1-1-1-1000022000000-1-1-1-100000000
χ2622222222-122-1-122-122222222-1-122-1-122-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-20-201100-2-200111100001100-2-20011110000-1-122-1-122-1-1-1-1-1-1-1-10000-2-2000000111100000000
χ2722222222-122-1-122-122222222-1-122-1-122-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-12020-1-1002200-1-1-1-10000-1-1002200-1-1-1-1000011-2-211-2-2111111110000-2-2000000111100000000
χ2822222222-122-1-122-122222222-1-122-1-122-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-20-201100-2-200111100001100-2-2001111000011-2-211-2-211111111000022000000-1-1-1-100000000
χ292222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-20000-1-1-1-1111122-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000022-2-20000-1-111000000000000
χ302222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-20000-1-1-1-111112-2-2222-2-2-1-111-1-1-1-11111-2-22211-1-11111-1-1-1-10000000000000000-2-222000011-1-1000000000000
χ312222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-20000-1-1-1-11111-222-2-2-22211-1-11111-1-1-1-122-2-2-1-111-1-1-1-111110000000000000000-2-222000011-1-1000000000000
χ322222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-20000-1-1-1-11111-2-222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-2-20000-1-111000000000000
χ332222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-211-2-211-12-1-1-122-1-1-12-111-2-2-2-21111112i2i−2i−2i-1-1-1-11111020-200-1-100220000-1-1-1-1001100-2-2000011112i2i−i−i−2i−2iii−i−i−i−iiiii0000002i−2i00000000−i−iii0000
χ342222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-211-2-211-12-1-1-122-1-1-12-111-2-2-2-21111112i2i−2i−2i-1-1-1-111110-202001100-2-20000111100-1-100220000-1-1-1-12i2i−i−i−2i−2iii−i−i−i−iiiii000000−2i2i00000000ii−i−i0000
χ352222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-211-2-211-12-1-1-122-1-1-12-111-2-2-2-2111111−2i−2i2i2i-1-1-1-11111020-200-1-100220000-1-1-1-1001100-2-200001111−2i−2iii2i2i−i−iiiii−i−i−i−i000000−2i2i00000000ii−i−i0000
χ362222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-211-2-211-12-1-1-122-1-1-12-111-2-2-2-2111111−2i−2i2i2i-1-1-1-111110-202001100-2-20000111100-1-100220000-1-1-1-1−2i−2iii2i2i−i−iiiii−i−i−i−i0000002i−2i00000000−i−iii0000
χ372222-2-2-2-2-122-1-122-12222-2-2-2-211-2-211-2-2-1-12-1-1-1-122-1-12111111-2-2-2-2112i2i−2i−2i-1-1-1-1111120-20-1-1002200-1-1-1-100001100-2-20011110000−i−i2i2iii−2i−2i−i−i−i−iiiii00002i−2i000000−i−iii00000000
χ382222-2-2-2-2-122-1-122-12222-2-2-2-211-2-211-2-2-1-12-1-1-1-122-1-12111111-2-2-2-2112i2i−2i−2i-1-1-1-11111-20201100-2-20011110000-1-1002200-1-1-1-10000−i−i2i2iii−2i−2i−i−i−i−iiiii0000−2i2i000000ii−i−i00000000
χ392222-2-2-2-2-122-1-122-12222-2-2-2-211-2-211-2-2-1-12-1-1-1-122-1-12111111-2-2-2-211−2i−2i2i2i-1-1-1-1111120-20-1-1002200-1-1-1-100001100-2-20011110000ii−2i−2i−i−i2i2iiiii−i−i−i−i0000−2i2i000000ii−i−i00000000
χ402222-2-2-2-2-122-1-122-12222-2-2-2-211-2-211-2-2-1-12-1-1-1-122-1-12111111-2-2-2-211−2i−2i2i2i-1-1-1-11111-20201100-2-20011110000-1-1002200-1-1-1-10000ii−2i−2i−i−i2i2iiiii−i−i−i−i00002i−2i000000−i−iii00000000
χ4122-2-222-2-2222-2-2-2-2222-2-222-2-22222-2-2-2-2222-2-2-2-2-2-2222-2-222-2-222-2-22200002-2-2222-2-20000000000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4222-2-222-2-2222-2-2-2-2222-2-222-2-22222-2-2-2-2222-2-2-2-2-2-2222-2-222-2-222-2-22200002-2-2222-2-2000000000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4322-2-2-2-222222-2-2-2-2222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-222222-2-222-2-222-2-200002-2-22-2-2220000000000000000000000000000000000000000000000000000000000000000000000002-2-22
χ4422-2-2-2-222222-2-2-2-2222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-222222-2-222-2-222-2-200002-2-22-2-222000000000000000000000000000000000000000000000000000000000000000000000000-222-2
χ452-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000002-22i−2i00002-22i−2i000000000000
χ462-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000-22−2i2i0000-22−2i2i000000000000
χ472-22-22i−2i2i−2i22-12-22-2-2-21-11−ii−ii2i−2i2i−2i2i−2i2i−2i2-1-12-2-11-11-2112i−2i−ii−ii−ii−ii2i−2i0000-1-111−ii−ii00000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300003−33−333−3−333−3−300000000000000002-22i−2i0000-11−ii000000000000
χ482-22-22i−2i2i−2i22-12-22-2-2-21-11−ii−ii2i−2i2i−2i2i−2i2i−2i2-1-12-2-11-11-2112i−2i−ii−ii−ii−ii2i−2i0000-1-111−ii−ii00000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i300003−3−3333−3−3−3−3330000000000000000-22−2i2i00001-1i−i000000000000
χ492-22-22i−2i2i−2i22-12-22-2-2-21-11−ii−ii2i−2i2i−2i2i−2i2i−2i2-1-12-2-11-11-2112i−2i−ii−ii−ii−ii2i−2i0000-1-111−ii−ii00000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i30000−333−3−3−33333−3−30000000000000000-22−2i2i00001-1i−i000000000000
χ502-22-22i−2i2i−2i22-12-22-2-2-21-11−ii−ii2i−2i2i−2i2i−2i2i−2i2-1-12-2-11-11-2112i−2i−ii−ii−ii−ii2i−2i0000-1-111−ii−ii00000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000−33−33−3−333−3−33300000000000000002-22i−2i0000-11−ii000000000000
χ512-22-2−2i2i−2i2i2222-22-2-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i2i−2i2i00000000000000000000000000000000000000000000000000002-2−2i2i00002-2−2i2i000000000000
χ522-22-2−2i2i−2i2i2222-22-2-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000-222i−2i0000-222i−2i000000000000
χ532-22-2−2i2i−2i2i22-12-22-2-2-21-11i−ii−i−2i2i−2i2i−2i2i−2i2i2-1-12-2-11-11-211−2i2ii−ii−ii−ii−i−2i2i0000-1-111i−ii−i00000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000−33−33−3−333−3−33300000000000000002-2−2i2i0000-11i−i000000000000
χ542-22-2−2i2i−2i2i22-12-22-2-2-21-11i−ii−i−2i2i−2i2i−2i2i−2i2i2-1-12-2-11-11-211−2i2ii−ii−ii−ii−i−2i2i0000-1-111i−ii−i00000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i30000−333−3−3−33333−3−30000000000000000-222i−2i00001-1−ii000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.