Finite Group Databasebeta

← Group #13155544

Character table — Group #13155544

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444488888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order1222444433366666666612121212121212121212121233366666666612121212121212121212121236661212121244888812121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242444448888888812121212242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1i−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−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1i−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-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-11
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1−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−i−iiiii−i−i-1-111−i−iiiii−i−i-11
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1−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−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1-1
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11i−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−i11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii-11
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11i−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−i−iiiii−i−i-1-111−i−iiiii−i−i1-1
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11−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-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii1-1
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11−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−iiiii11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i-11
χ172222222222-122-12222-1-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000000000000-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000000000
χ182222222222-122-12222-1-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-2-20000000000000000-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-20000000011110000000000
χ192222222222-122-12222-1-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-22200000000000000001111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-2-2-2-20000000011110000000000
χ202222222222-122-12222-1-12222-1-1-1-122222-1-1-1-1-1-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2000000000000000011111111-2-2-2-2-2-2-2-21111111111111111222200000000-1-1-1-10000000000
χ21222222222-122-1222-1-12222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-122002222-1-122-1-1-1-1-1-1-1-1-1-1000022220000-1-1-1-100000000-1-1-1-1-1-1-1-100000000222200000000-1-1-1-100
χ22222222222-122-1222-1-12222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-12200-2-222-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200001111000000001111111100000000-2-2-2-200000000111100
χ23222222222-122-1222-1-12222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-20022-2-211-2-21111111111000022220000-1-1-1-100000000-1-1-1-1-1-1-1-100000000-2-2-2-200000000111100
χ24222222222-122-1222-1-12222-1-1222222-1-1-12-122-1-1-12-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-211-2-211111111110000-2-2-2-200001111000000001111111100000000222200000000-1-1-1-100
χ2522222222-122-122-1-12222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222200-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-10000-1-1-1-1-1-1-1-1000000000000222200000000-1-1-1-1000000
χ2622222222-122-122-1-12222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-2-200-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111000011111111000000000000-2-2-2-2000000001111000000
χ2722222222-122-122-1-12222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2220011-2-211-2-21111111122220000-1-1-1-10000-1-1-1-1-1-1-1-1000000000000-2-2-2-2000000001111000000
χ2822222222-122-122-1-12222-1-1222222-1-122-1-12-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20011-2-211-2-211111111-2-2-2-200001111000011111111000000000000222200000000-1-1-1-1000000
χ292222-2-2-2-222-122-12222-1-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-211111111-1-1-1-11111002i−2i2i−2i0000000000000000−i−iii−i−iii2i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii22-2-200000000-1-1110000000000
χ302222-2-2-2-222-122-12222-1-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-211111111-1-1-1-11111002i−2i−2i2i0000000000000000−i−iiiii−i−i2i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-2-2220000000011-1-10000000000
χ312222-2-2-2-222-122-12222-1-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-211111111-1-1-1-1111100−2i2i2i−2i0000000000000000ii−i−i−i−iii−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-2-2220000000011-1-10000000000
χ322222-2-2-2-222-122-12222-1-1-2-2-2-21111-2-2-2-22-1-1-1-1-1-12-1-122-2-2-2-211111111-1-1-1-1111100−2i2i−2i2i0000000000000000ii−i−iii−i−i−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i22-2-200000000-1-1110000000000
χ332222-2-2-2-22-122-1222-1-122-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-1-1-1-111112-2002i−2i22-1-1-2-211-1-1-1-1111100002i2i−2i−2i0000−i−iii00000000−i−i−i−iiiii000000002i2i−2i−2i00000000−i−iii00
χ342222-2-2-2-22-122-1222-1-122-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-1-1-1-111112-200−2i2i22-1-1-2-211-1-1-1-111110000−2i−2i2i2i0000ii−i−i00000000iiii−i−i−i−i00000000−2i−2i2i2i00000000ii−i−i00
χ352222-2-2-2-22-122-1222-1-122-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-1-1-1-11111-22002i−2i-2-21122-1-11111-1-1-1-100002i2i−2i−2i0000−i−iii00000000−i−i−i−iiiii00000000−2i−2i2i2i00000000ii−i−i00
χ362222-2-2-2-22-122-1222-1-122-2-211-2-2-2-2-2-211-12-122-1-1-12-1-1-11111-2-211-2-211-1-1-1-11111-2200−2i2i-2-21122-1-11111-1-1-1-10000−2i−2i2i2i0000ii−i−i00000000iiii−i−i−i−i000000002i2i−2i−2i00000000−i−iii00
χ372222-2-2-2-2-122-122-1-1222211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-1-1-1-111112-22i−2i00-1-12211-2-2-1-1-1-111112i2i−2i−2i0000−i−iii0000−i−i−i−iiiii0000000000002i2i−2i−2i00000000−i−iii000000
χ382222-2-2-2-2-122-122-1-1222211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-1-1-1-111112-2−2i2i00-1-12211-2-2-1-1-1-11111−2i−2i2i2i0000ii−i−i0000iiii−i−i−i−i000000000000−2i−2i2i2i00000000ii−i−i000000
χ392222-2-2-2-2-122-122-1-1222211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-1-1-1-11111-222i−2i0011-2-2-1-1221111-1-1-1-12i2i−2i−2i0000−i−iii0000−i−i−i−iiiii000000000000−2i−2i2i2i00000000ii−i−i000000
χ402222-2-2-2-2-122-122-1-1222211-2-2-2-2-2-211-2-2-1-12-1-122-1-12-1-1111111-2-211-2-2-1-1-1-11111-22−2i2i0011-2-2-1-1221111-1-1-1-1−2i−2i2i2i0000ii−i−i0000iiii−i−i−i−i0000000000002i2i−2i−2i00000000−i−iii000000
χ4122-2-22i2i−2i−2i222-2-2-22-22-22-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2222-22-2-2-2-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ4222-2-22i2i−2i−2i222-2-2-22-22-22-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2222-22-2-2-2-22-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ4322-2-22i2i−2i−2i2-12-21-22-2-112-22i−2i−ii2i2i−2i−2i2i−2i−ii-12-12-2-111-21-11−i−iii2i−2i−ii2i−2i−ii-1-111−i−iii00000000−i3i3003−3−i3−i3i3i333−3−3000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300
χ4422-2-22i2i−2i−2i2-12-21-22-2-112-22i−2i−ii2i2i−2i−2i2i−2i−ii-12-12-2-111-21-11−i−iii2i−2i−ii2i−2i−ii-1-111−i−iii00000000−i3i3003−3−i3−i3i3i333−3−3000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300
χ4522-2-22i2i−2i−2i2-12-21-22-2-112-22i−2i−ii2i2i−2i−2i2i−2i−ii-12-12-2-111-21-11−i−iii2i−2i−ii2i−2i−ii-1-111−i−iii00000000i3−i300−33i3i3−i3−i3−3−333000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300
χ4622-2-22i2i−2i−2i2-12-21-22-2-112-22i−2i−ii2i2i−2i−2i2i−2i−ii-12-12-2-111-21-11−i−iii2i−2i−ii2i−2i−ii-1-111−i−iii00000000i3−i300−33i3i3−i3−i3−3−333000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300
χ4722-2-2−2i−2i2i2i222-2-2-22-22-22-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i2222-22-2-2-2-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ4822-2-2−2i−2i2i2i222-2-2-22-22-22-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i2222-22-2-2-2-22-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.