Finite Group Databasebeta

← Group #13139950

Character table — Group #13139950

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444422344666121212126612123366666666661212121212121212121212123666666666121212121212121212128888888824242424242424242424242424242424224444446666121212121212121212121212
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ81111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ91-1-1111-1-11-111-11-1-111-1-11-11-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-111-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-1ii−i−iii−i−i11-1-1
χ101-1-1111-1-11-111-11-1-111-1-11-11-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-111-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11−ii−ii-11-1-111−i−iii−i−iii-1-111
χ111-1-1111-1-11-111-11-1-111-1-11-11-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-111-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii1-111-1-1−i−iii−i−iii11-1-1
χ121-1-1111-1-11-111-11-1-111-1-11-11-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-111-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11i−ii−i-11-1-111ii−i−iii−i−i-1-111
χ131-1-11-1-111-1111-11-1-1-1-111-111-111-1-1-1-111-1-11111-1-111-1-111-1-11-11-1-1-1-11111-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1i−i−ii-1111-1-1ii−i−i−i−iii-1-111
χ141-1-11-1-111-1111-11-1-1-1-111-111-111-1-1-1-111-1-11111-1-111-1-111-1-11-11-1-1-1-11111-111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11−iii−i1-1-1-111−i−iiiii−i−i11-1-1
χ151-1-11-1-111-1111-11-1-1-1-111-111-111-1-1-1-111-1-11111-1-111-1-111-1-11-11-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i-1111-1-1−i−iiiii−i−i-1-111
χ161-1-11-1-111-1111-11-1-1-1-111-111-111-1-1-1-111-1-11111-1-111-1-111-1-11-11-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11i−i−ii1-1-1-111ii−i−i−i−iii11-1-1
χ172222222222222222222222222-1222222-1-12-1222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022000022-1-1-1-100000000-1-1-1-1
χ182222222222222222222222222-1222222-1-12-1222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-20000-2-21111000000001111
χ19222222222222222222222222-12-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2122222222-2-22-2-22222222-2-2-2-22222-2-2-2-22222-2-222222222-2-22-2-222-2-2-2-22-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2222222222-2-22-2-22222222-2-2-2-22-122-2-2-2-2-1-12-1-2-22222-1-1-1-1-2-2-111-1-11111-1111111-1-1-1-100000000000000000000000000000000−i3i3−i3i300000000−i3i3−i3i3
χ2322222222-2-22-2-22222222-2-2-2-22-122-2-2-2-2-1-12-1-2-22222-1-1-1-1-2-2-111-1-11111-1111111-1-1-1-100000000000000000000000000000000i3−i3i3−i300000000i3−i3i3−i3
χ2422222222-2-22-2-22222222-2-2-2-2-12-1-1111122-1211-1-1-1-1222211-1-2-2-1-11111-1-2-21111-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ2522222222-2-22-2-22222222-2-2-2-2-12-1-1111122-1211-1-1-1-1222211-1-2-2-1-11111-1-2-21111-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-22-1222222-1-12-1-2-2-2-2-2-21111-2-2-1-1-1-1-1-1-1-1-1-1111111111100000000000000000000000000000000−i3i3−i3i300000000i3−i3i3−i3
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-22-1222222-1-12-1-2-2-2-2-2-21111-2-2-1-1-1-1-1-1-1-1-1-1111111111100000000000000000000000000000000i3−i3i3−i300000000−i3i3−i3i3
χ292222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-122-12111111-2-2-2-211-122-1-1-1-1-1-1-1-2-2111111110000000033−3−333−3−3−3−333−3−333000000000000000000000000
χ302222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-122-12111111-2-2-2-211-122-1-1-1-1-1-1-1-2-21111111100000000−3−333−3−33333−3−333−3−3000000000000000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-2-1-12-122-2-2-2-2111122-111-1-11111-1-1-1-1-1-1-11111000000000000000000000000220000-2-2-1-1-1-1000000001111
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-2-1-12-122-2-2-2-2111122-111-1-11111-1-1-1-1-1-1-11111000000000000000000000000-2-2000022111100000000-1-1-1-1
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-1111122-12-1-11111-2-2-2-2-1-1-1-2-2-1-11111-122-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-1111122-12-1-11111-2-2-2-2-1-1-1-2-2-1-11111-122-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ3522-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-200002-2-2-2002i−2i2i−2i2i−2i2i−2i002002-20000-20000002i−2i2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ3622-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-200002-2-2-2002i−2i2i−2i2i−2i2i−2i002002-20000-20000002i−2i2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ3722-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11−i3i3−i3i32-21-23−3−ii−ii2i−2i2i−2i3−3-100-11−i3i3−i3i31003−33−3−ii−ii2−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000000000
χ3822-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11−i3i3−i3i32-21-23−3−ii−ii2i−2i2i−2i3−3-100-11−i3i3−i3i31003−33−3−ii−ii−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000000000
χ3922-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11i3−i3i3−i32-21-2−33−ii−ii2i−2i2i−2i−33-100-11i3−i3i3−i3100−33−33−ii−ii2−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000000000
χ4022-2-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11i3−i3i3−i32-21-2−33−ii−ii2i−2i2i−2i−33-100-11i3−i3i3−i3100−33−33−ii−ii−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000000000
χ4122-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-200002-2-2-200−2i2i−2i2i−2i2i−2i2i002002-20000-2000000−2i2i−2i2i2−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ4222-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-200002-2-2-200−2i2i−2i2i−2i2i−2i2i002002-20000-2000000−2i2i−2i2i−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ4322-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11−i3i3−i3i32-21-2−33i−ii−i−2i2i−2i2i−33-100-11−i3i3−i3i3100−33−33i−ii−i2−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000000000
χ4422-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11−i3i3−i3i32-21-2−33i−ii−i−2i2i−2i2i−33-100-11−i3i3−i3i3100−33−33i−ii−i−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000000000
χ4522-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11i3−i3i3−i32-21-23−3i−ii−i−2i2i−2i2i3−3-100-11i3−i3i3−i31003−33−3i−ii−i2−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000000000
χ4622-2-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11i3−i3i3−i32-21-23−3i−ii−i−2i2i−2i2i3−3-100-11i3−i3i3−i31003−33−3i−ii−i−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000000000
χ472-22-22i−2i−2i2i00200-2-222i−2i−2i2i000022-220000-22-2-2002i−2i−2i2i2i−2i−2i2i00200-220000-20000002i−2i−2i2i−i2i2i2−i2−222−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000000000000000
χ482-22-22i−2i−2i2i00200-2-222i−2i−2i2i000022-220000-22-2-2002i−2i−2i2i2i−2i−2i2i00200-220000-20000002i−2i−2i2ii2−i2−i2i22−2−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000000000000000
χ492-22-22i−2i−2i2i00200-2-222i−2i−2i2i0000-121-1−i3i3i3−i3-221-23−3−iii−i2i−2i−2i2i−33-1001-1−i3i3i3−i31003−3−33−iii−i−i2i2i2−i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000000000000000
χ502-22-22i−2i−2i2i00200-2-222i−2i−2i2i0000-121-1−i3i3i3−i3-221-23−3−iii−i2i−2i−2i2i−33-1001-1−i3i3i3−i31003−3−33−iii−ii2−i2−i2i22−2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000000000000000
χ512-22-22i−2i−2i2i00200-2-222i−2i−2i2i0000-121-1i3−i3−i3i3-221-2−33−iii−i2i−2i−2i2i3−3-1001-1i3−i3−i3i3100−333−3−iii−i−i2i2i2−i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000
χ522-22-22i−2i−2i2i00200-2-222i−2i−2i2i0000-121-1i3−i3−i3i3-221-2−33−iii−i2i−2i−2i2i3−3-1001-1i3−i3−i3i3100−333−3−iii−ii2−i2−i2i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000
χ532-22-2−2i2i2i−2i00200-2-22−2i2i2i−2i000022-220000-22-2-200−2i2i2i−2i−2i2i2i−2i00200-220000-2000000−2i2i2i−2i−i2i2i2−i22−2−22−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000000000000000
χ542-22-2−2i2i2i−2i00200-2-22−2i2i2i−2i000022-220000-22-2-200−2i2i2i−2i−2i2i2i−2i00200-220000-2000000−2i2i2i−2ii2−i2−i2i2−222−2i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000000000000000
χ552-22-2−2i2i2i−2i00200-2-22−2i2i2i−2i0000-121-1−i3i3i3−i3-221-2−33i−i−ii−2i2i2i−2i3−3-1001-1−i3i3i3−i3100−333−3i−i−ii−i2i2i2−i22−2−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000
χ562-22-2−2i2i2i−2i00200-2-22−2i2i2i−2i0000-121-1−i3i3i3−i3-221-2−33i−i−ii−2i2i2i−2i3−3-1001-1−i3i3i3−i3100−333−3i−i−iii2−i2−i2i2−222−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.