Finite Group Databasebeta

← Group #13138929

Character table — Group #13138929

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444436668888121212122424242433666666121212121212121224242424242424243666121212122424242424242424242424244444888812121212121212122424242424242424224466668888121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ7111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ91111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-1−ii−ii1111−i−iii−i−iii
χ111111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ121111-1-1-1-11111ii−i−i-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-111-1-1-111−iii−i11-1-1−i−iiiii−i−i
χ131111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11111−ii−ii-1-1-1-1−i−iii−i−iii
χ141111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i
χ151111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ161111-1-1-1-11111−i−iii-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-111-1-1-111i−i−ii11-1-1ii−i−i−i−iii
χ172222222222222222222222222-1-1-1222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-1002200-1-10000-1-1-1-1
χ182222222222222222222222222-1-1-1222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-2001100-2-2001100001111
χ19222222222222222222222222-1222-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-1222-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ21222222222222-2-2-2-22222-2-2-2-22-1-1-1222-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111000000000000000000000000020200-1-100-2-200-1-100001111
χ22222222222222-2-2-2-22222-2-2-2-22-1-1-1222-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000000000000-20-20011002200110000-1-1-1-1
χ23222222222222-2-2-2-22222-2-2-2-2-1222-1-1-1222-1-1-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ24222222222222-2-2-2-22222-2-2-2-2-1222-1-1-1222-1-1-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ252222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-1-1-1222-111-2-2-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii000000000000000000000000020-200-1-1002i−2i00110000−i−iii
χ262222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-1-1-1222-111-2-2-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii0000000000000000000000000-202001100−2i2i00-1-10000ii−i−i
χ272222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-1222-1-1-12-2-21111-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ282222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-1222-1-1-12-2-21111-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ292222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-1-1-1222-111-2-2-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i000000000000000000000000020-200-1-100−2i2i00110000ii−i−i
χ302222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-1-1-1222-111-2-2-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i0000000000000000000000000-2020011002i−2i00-1-10000−i−iii
χ312222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-1222-1-1-12-2-21111-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ322222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-1222-1-1-12-2-21111-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ3322-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000222-2-22-2-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ3422-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000222-2-22-2-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ3522-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000-122-21-11-22i−2i−ii−ii2i−2i−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−ii−ii0000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ130000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2333−3−3−i3−i3i3i3ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000000000
χ3622-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000-122-21-11-22i−2i−ii−ii2i−2i−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−ii−ii0000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−3−333i3i3−i3−i3−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000000000
χ3722-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000-122-21-11-22i−2i−ii−ii2i−2iζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-1-111−ii−ii0000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ130000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−3−333i3i3−i3−i3ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000000000
χ3822-2-22i−2i2i−2i22-2-200002i−2i2i−2i0000-122-21-11-22i−2i−ii−ii2i−2iζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-1-111−ii−ii0000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2333−3−3−i3−i3i3i3−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000000000
χ3922-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ4022-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000222-2-22-2-2−2i2i−2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ4122-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000-122-21-11-2−2i2ii−ii−i−2i2iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23-1-111i−ii−i0000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1333−3−3i3i3−i3−i3−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000000000
χ4222-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000-122-21-11-2−2i2ii−ii−i−2i2iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23-1-111i−ii−i0000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−3−333−i3−i3i3i3ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
χ4322-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000-122-21-11-2−2i2ii−ii−i−2i2i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23-1-111i−ii−i0000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−3−333−i3−i3i3i3−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000000000
χ4422-2-2−2i2i−2i2i22-2-20000−2i2i−2i2i0000-122-21-11-2−2i2ii−ii−i−2i2i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23-1-111i−ii−i0000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ230000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1333−3−3i3i3−i3−i3ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
χ452-22-22i−2i−2i2i2-22-200002i−2i−2i2i000022-22-2-22-22i−2i−2i2i2i−2i−2i2i000000002-22-22i−2i−2i2i0000000000002-22i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000
χ462-22-22i−2i−2i2i2-22-200002i−2i−2i2i000022-22-2-22-22i−2i−2i2i2i−2i−2i2i000000002-22-22i−2i−2i2i000000000000-22−2i2i0000-22-22−2i2i−2i2i00000000000000000000000000000000
χ472-22-22i−2i−2i2i2-22-200002i−2i−2i2i0000-12-2211-1-22i−2ii−i−ii−2i2iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ232-22i−2i0000-11-11−ii−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ482-22-22i−2i−2i2i2-22-200002i−2i−2i2i0000-12-2211-1-22i−2ii−i−ii−2i2iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-11-11−iii−i0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23-22−2i2i00001-11-1i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ492-22-22i−2i−2i2i2-22-200002i−2i−2i2i0000-12-2211-1-22i−2ii−i−ii−2i2i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232-22i−2i0000-11-11−ii−ii−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ502-22-22i−2i−2i2i2-22-200002i−2i−2i2i0000-12-2211-1-22i−2ii−i−ii−2i2i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-11-11−iii−i0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23-22−2i2i00001-11-1i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ512-22-2−2i2i2i−2i2-22-20000−2i2i2i−2i000022-22-2-22-2−2i2i2i−2i−2i2i2i−2i000000002-22-2−2i2i2i−2i0000000000002-2−2i2i00002-22-2−2i2i−2i2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.