Finite Group Databasebeta

← Group #13155534

Character table — Group #13155534

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444488888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12224444333666666666121212121212121212121212333666666666121212121212121212121212366612121212244466666666881212121212121212121212121212121212121212121212122424242424242424242424242424242444448888888812121212242424242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111111111i−i11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111111111−ii11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−ii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111111111i−i-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111−i−iiiii−i−i-1-111ii−i−i−i−iii−ii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111111111−ii-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111ii−i−i−i−iii-1-111−i−iiiii−i−ii−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1i−i11-1-1111111-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i-1-111ii−i−i−i−iii-1-111−i−iiiii−i−i−ii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1−ii11-1-1111111-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii-1-111−i−iiiii−i−i-1-111ii−i−i−i−iiii−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-1-1i−i-1-1111111-1-111-1-1-1-111111111ii−i−iii−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii11-1-1−i−iii−i−iiii−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-1-1−ii-1-1111111-1-111-1-1-1-111111111−i−iii−i−iii−i−i−i−iiiii11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i−ii
χ172222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-100222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000222200000000-1-1-1-10000000000
χ182222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-1-1-1-1-1-100-2-2-2-222-1-1111111111111-1-1-1-10000000000000000-2-2-2-20000000011110000000000
χ192222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2111111002222-2-211-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000-2-2-2-20000000011110000000000
χ202222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-211111100-2-2-2-2-2-21111111111111111110000000000000000222200000000-1-1-1-10000000000
χ21222222222-12-1-1222-1222222222-1-1-1-122-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-122-1-1-1-1220000-1-122000000000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000-1-1-1-1000000
χ22222222222-12-1-1222-1222222222-1-1-1-122-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-122-1-1-1-1-2-20000-1-122000000000000-1-1-1-11111-2-2-2-21111111100000000-2-2-2-200001111000000
χ23222222222-12-1-1222-1222222222-1-1-1-122-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20011-2-2111122000011-2-20000000000001111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-200001111000000
χ24222222222-12-1-1222-1222222222-1-1-1-122-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20011-2-21111-2-2000011-2-200000000000011111111-2-2-2-2111111110000000022220000-1-1-1-1000000
χ2522222222-12222-1-1-12222-1-122222222-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100220000000022-1-1-1-100002222-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000-1-1-1-100
χ2622222222-12222-1-1-12222-1-122222222-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1002200000000-2-2-1-1-1-100002222-1-1-1-1-1-1-1-10000-2-2-2-21111111111110000-2-2-2-2000000000000111100
χ2722222222-12222-1-1-12222-1-122222222-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100-2-2000000002211110000-2-2-2-21111111100002222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000000000111100
χ2822222222-12222-1-1-12222-1-122222222-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100-2-200000000-2-211110000-2-2-2-2111111110000-2-2-2-211111111111100002222000000000000-1-1-1-100
χ292222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-1-1-1-111112-22-222-1-1-1-1-1-10022-2-2-2-211-1-111-1-1-1-111111111000000000000000022-2-200000000-1-1110000000000
χ302222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-1-1-1-111112-2-2222-1-1-1-1-1-100-2-222-2-21111-1-11111-1-1-1-111110000000000000000-2-2220000000011-1-10000000000
χ312222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-1-1-1-11111-222-2-2-21111110022-2-222-1-1-1-111-1-1-1-11111-1-1-1-10000000000000000-2-2220000000011-1-10000000000
χ322222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-1-1-1-11111-22-22-2-211111100-2-22222-1-111-1-11111-1-1-1-1-1-1-1-1000000000000000022-2-200000000-1-1110000000000
χ332222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-21111-2-2-12-1-1-1-1-1-1222-111-2-2-2-2111111-1-1-1-111112-200-1-122-1-1-1-12i−2i000011-2-20000000000001111−i−iii2i2i−2i−2i−i−i−i−iiiii000000002i2i−2i−2i0000−i−iii000000
χ342222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-21111-2-2-12-1-1-1-1-1-1222-111-2-2-2-2111111-1-1-1-111112-200-1-122-1-1-1-1−2i2i000011-2-20000000000001111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−2i−2i2i2i0000ii−i−i000000
χ352222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-21111-2-2-12-1-1-1-1-1-1222-111-2-2-2-2111111-1-1-1-11111-220011-2-211112i−2i0000-1-122000000000000-1-1-1-1−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−2i−2i2i2i0000ii−i−i000000
χ362222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-21111-2-2-12-1-1-1-1-1-1222-111-2-2-2-2111111-1-1-1-11111-220011-2-21111−2i2i0000-1-122000000000000-1-1-1-1ii−i−i−2i−2i2i2iiiii−i−i−i−i000000002i2i−2i−2i0000−i−iii000000
χ372222-2-2-2-2-12222-1-1-1222211-2-2-2-2-2-2-2-211-1-12-1-122-1-1-1-12111111-2-2-2-211-1-1-1-11111002-2000000002i−2i-1-111000022-2-2-1-1-1-1111100002i2i−2i−2i−i−iii−i−i−i−iiiii00002i2i−2i−2i000000000000−i−iii00
χ382222-2-2-2-2-12222-1-1-1222211-2-2-2-2-2-2-2-211-1-12-1-122-1-1-1-12111111-2-2-2-211-1-1-1-11111002-200000000−2i2i-1-111000022-2-2-1-1-1-111110000−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i−2i2i2i000000000000ii−i−i00
χ392222-2-2-2-2-12222-1-1-1222211-2-2-2-2-2-2-2-211-1-12-1-122-1-1-1-12111111-2-2-2-211-1-1-1-1111100-22000000002i−2i11-1-10000-2-2221111-1-1-1-100002i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i−2i2i2i000000000000ii−i−i00
χ402222-2-2-2-2-12222-1-1-1222211-2-2-2-2-2-2-2-211-1-12-1-122-1-1-1-12111111-2-2-2-211-1-1-1-1111100-2200000000−2i2i11-1-10000-2-2221111-1-1-1-10000−2i−2i2i2iii−i−iiiii−i−i−i−i00002i2i−2i−2i000000000000−i−iii00
χ4122-2-222-2-2222-2-22-2-222-2-2-2-222-2-222-2-222222-2-2-2-222-2-22-2-222-2-222-2-2222-2-2222-2-20000000000000000000000000000000000000000000000000000002i−2i2i−2i000000002i−2i2i−2i0000000000
χ4222-2-222-2-2222-2-22-2-222-2-2-2-222-2-222-2-222222-2-2-2-222-2-22-2-222-2-222-2-2222-2-2222-2-2000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000
χ4322-2-222-2-222-1-2-22-2-22-111-2-2-1-11122-2-2222-1-1-2-2112-111-1-2-2-1-111-1-11122-111-1-1-111000000−i3i3−i3−i3i3i300000000−i3i33−33−333−3−333−3−3−i3−i3i3i300000000000000002i−2i2i−2i00000000−ii−ii0000000000
χ4422-2-222-2-222-1-2-22-2-22-111-2-2-1-11122-2-2222-1-1-2-2112-111-1-2-2-1-111-1-11122-111-1-1-111000000−i3i3−i3−i3i3i300000000−i3i3−33−33−3−333−3−333−i3−i3i3i30000000000000000−2i2i−2i2i00000000i−ii−i0000000000
χ4522-2-222-2-222-1-2-22-2-22-111-2-2-1-11122-2-2222-1-1-2-2112-111-1-2-2-1-111-1-11122-111-1-1-111000000i3−i3i3i3−i3−i300000000i3−i33−33−333−3−333−3−3i3i3−i3−i30000000000000000−2i2i−2i2i00000000i−ii−i0000000000
χ4622-2-222-2-222-1-2-22-2-22-111-2-2-1-11122-2-2222-1-1-2-2112-111-1-2-2-1-111-1-11122-111-1-1-111000000i3−i3i3i3−i3−i300000000i3−i3−33−33−3−333−3−333i3i3−i3−i300000000000000002i−2i2i−2i00000000−ii−ii0000000000
χ4722-2-2-2-222222-2-22-2-222-2-222-2-222-2-222-2-2222-2-2-2-222-2-2222-2-222-2-222-2-22-2-22-2-2220000000000000000000000000000000000000000000000000000002i−2i−2i2i000000002i−2i−2i2i0000000000
χ4822-2-2-2-222222-2-22-2-222-2-222-2-222-2-222-2-2222-2-2-2-222-2-2222-2-222-2-222-2-22-2-22-2-222000000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i0000000000
χ4922-2-2-2-22222-1-2-22-2-22-1112211-1-1-2-222-2-22-1-1-2-2112-111-12211-1-111-1-1-2-2-111-111-1-1000000−i3i3−i3−i3i3i300000000i3−i33−3−3333−3−3−3−333i3i3−i3−i300000000000000002i−2i−2i2i00000000−iii−i0000000000
χ5022-2-2-2-22222-1-2-22-2-22-1112211-1-1-2-222-2-22-1-1-2-2112-111-12211-1-111-1-1-2-2-111-111-1-1000000−i3i3−i3−i3i3i300000000i3−i3−333−3−3−33333−3−3i3i3−i3−i30000000000000000−2i2i2i−2i00000000i−i−ii0000000000
χ5122-2-2-2-22222-1-2-22-2-22-1112211-1-1-2-222-2-22-1-1-2-2112-111-12211-1-111-1-1-2-2-111-111-1-1000000i3−i3i3i3−i3−i300000000−i3i33−3−3333−3−3−3−333−i3−i3i3i30000000000000000−2i2i2i−2i00000000i−i−ii0000000000
χ5222-2-2-2-22222-1-2-22-2-22-1112211-1-1-2-222-2-22-1-1-2-2112-111-12211-1-111-1-1-2-2-111-111-1-1000000i3−i3i3i3−i3−i300000000−i3i3−333−3−3−33333−3−3−i3−i3i3i300000000000000002i−2i−2i2i00000000−iii−i0000000000
χ532-22-22i−2i2i−2i2222-2-22-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-2-2-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ542-22-22i−2i2i−2i2222-2-22-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-2-2-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.