Finite Group Databasebeta

← Group #13138796

Character table — Group #13138796

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444366688881212121224242424336666661212121212121212242424242424242436661212121224242424242424242424242422446666888812121212242424242424242424446688881212121212122424242424242424
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-11111-1-1-1-1
χ5111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ7111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111111-1-1-1-1-1-1111111-1-1-1-1
χ8111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-1-1111111-1-1-1-1-1-11111
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−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-111i−ii−i11-1-1-1-1ii−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−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-111-1-1−ii−ii-1-11111−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-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii1-11-111−iii−i-1-111-1-1−i−iiiii−i−i
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-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii
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−iiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11-1-111−ii−ii11-1-1-1-1−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−iiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-111-1-1i−ii−i-1-11111ii−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-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i1-11-111i−i−ii-1-111-1-1ii−i−i−i−iii
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-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-11-11-1-1−iii−i11-1-111−i−iiiii−i−i
χ172222222222222222222222222-122-1-12-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002002-1-100220000-1-10000-1-1-1-1
χ182222222222222222222222222-122-1-12-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-200-21100-2-200001100001111
χ19222222222222222222222222-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000000000000000
χ21222222222222-2-2-2-22222-2-2-2-22-122-1-12-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000000000002002-1-100-2-20000-1-100001111
χ22222222222222-2-2-2-22222-2-2-2-22-122-1-12-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111000000000000000000000000-200-21100220000110000-1-1-1-1
χ23222222222222-2-2-2-22222-2-2-2-2-12-1-122-12-1-122-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000000000
χ24222222222222-2-2-2-22222-2-2-2-2-12-1-122-12-1-122-1-12211111111-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000000000000000
χ252222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-122-1-12-1-2-211-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii000000000000000000000000200-2-1-1002i−2i0000110000−i−iii
χ262222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i2-122-1-12-1-2-211-2-2112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−iii−i−i−i−iiiii000000000000000000000000-20021100−2i2i0000-1-10000ii−i−i
χ272222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-1-122-1211-2-211-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii000000000000000000000000
χ282222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i−2i−2i-12-1-122-1211-2-211-2-2−i−i−i−iiiii-1-1-1-111112i2i−2i−2i−i−i−i−iiiii-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ292222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-122-1-12-1-2-211-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i000000000000000000000000200-2-1-100−2i2i0000110000ii−i−i
χ302222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i2-122-1-12-1-2-211-2-211−2i−2i−2i−2i2i2i2i2i-1-1-1-11111ii−i−iiiii−i−i−i−i000000000000000000000000-200211002i−2i0000-1-10000−i−iii
χ312222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-1-122-1211-2-211-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i000000000000000000000000
χ322222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i2i2i-12-1-122-1211-2-211-2-2iiii−i−i−i−i-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ3322-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000222-22-2-2-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ3422-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000222-22-2-2-22i−2i2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ3522-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000-12-112-21-2−ii2i−2i−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−i3−i3i3i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1333−3−3−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000000000
χ3622-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000-12-112-21-2−ii2i−2i−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+ζ130000i3i3−i3−i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−3−333ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
χ3722-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000-12-112-21-2−ii2i−2i−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−i3−i3i3i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1333−3−3ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000000000
χ3822-2-22i−2i2i−2i2-22-200002i−2i2i−2i0000-12-112-21-2−ii2i−2i−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−ζ130000i3i3−i3−i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−3−333−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000000000
χ3922-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000222-22-2-2-2−2i2i−2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ4022-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000222-22-2-2-2−2i2i−2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ4122-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000-12-112-21-2i−i−2i2ii−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−i3−i3i3i32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−3−333−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000000000
χ4222-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000-12-112-21-2i−i−2i2ii−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−ζ230000i3i3−i3−i3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2333−3−3ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000000000
χ4322-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000-12-112-21-2i−i−2i2ii−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−i3−i3i3i3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−3−333ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000000000
χ4422-2-2−2i2i−2i2i2-22-20000−2i2i−2i2i0000-12-112-21-2i−i−2i2ii−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+ζ230000i3i3−i3−i32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2333−3−3−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000000000
χ452-22-22i−2i−2i2i2-2-220000−2i2i2i−2i000022-22-22-2-22i−2i2i−2i−2i2i−2i2i000000002-22-22i−2i−2i2i0000000000002-22i−2i2-22-200002i−2i2i−2i00000000000000000000000000000000
χ462-22-22i−2i−2i2i2-2-220000−2i2i2i−2i000022-22-22-2-22i−2i2i−2i−2i2i−2i2i000000002-22-22i−2i−2i2i000000000000-22−2i2i-22-220000−2i2i−2i2i00000000000000000000000000000000
χ472-22-22i−2i−2i2i2-2-220000−2i2i2i−2i0000-121-1-221-2−ii2i−2ii−i−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−2i-11-110000−ii−iiζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ482-22-22i−2i−2i2i2-2-220000−2i2i2i−2i0000-121-1-221-2−ii2i−2ii−i−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−ζ23-22−2i2i1-11-10000i−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ492-22-22i−2i−2i2i2-2-220000−2i2i2i−2i0000-121-1-221-2−ii2i−2ii−i−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−2i-11-110000−ii−ii−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ502-22-22i−2i−2i2i2-2-220000−2i2i2i−2i0000-121-1-221-2−ii2i−2ii−i−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+ζ23-22−2i2i1-11-10000i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ512-22-2−2i2i2i−2i2-2-2200002i−2i−2i2i000022-22-22-2-2−2i2i−2i2i2i−2i2i−2i000000002-22-2−2i2i2i−2i0000000000002-2−2i2i2-22-20000−2i2i−2i2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.