Finite Group Databasebeta

← Group #13139934

Character table — Group #13139934

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444223446661212121266121233666666666612121212121212121212121236666666661212121212121212121288888888242424242424242424242424242424244444444412121212121212121212121212121212
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-11-111-1-111-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1-111-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-11-11-111-1-111-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1-111-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-11-11-111-1-111-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1-111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-11-11-111-1-111-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1-111-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-1-111-111-111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ1411-1-1-1-111-111-111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-1-1-111-111-111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ1611-1-1-1-111-111-111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222222-12222222-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ182222222222222222222222222-12222222-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ19222222222222222222222222-12-1-1-1-1-1-1-1222-1-1-1-122-1-122-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-1-1-1-1-1-1222-1-1-1-122-1-122-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
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
χ2222222222-2-22-2-22222222-2-2-2-22-122-2-2-2-22-1-1-1-2-222-1-122-1-1-2-2-111-1-11111-1111111-1-1-1-10000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ2322222222-2-22-2-22222222-2-2-2-22-122-2-2-2-22-1-1-1-2-222-1-122-1-1-2-2-111-1-11111-1111111-1-1-1-10000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ2422222222-2-22-2-22222222-2-2-2-2-12-1-11111-122211-1-122-1-12211-1-2-2-1-11111-1-2-21111-1-1-1-10000000033−3−333−3−333−3−333−3−3000000000000000000000000
χ2522222222-2-22-2-22222222-2-2-2-2-12-1-11111-122211-1-122-1-12211-1-2-2-1-11111-1-2-21111-1-1-1-100000000−3−333−3−333−3−333−3−333000000000000000000000000
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
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-22-12222222-1-1-1-2-2-2-211-2-211-2-2-1-1-1-1-1-1-1-1-1-111111111110000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-22-12222222-1-1-1-2-2-2-211-2-211-2-2-1-1-1-1-1-1-1-1-1-111111111110000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ292222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-1-12221111-2-211-2-211-122-1-1-1-1-1-1-1-2-2111111110000000033−3−333−3−3−3−333−3−333000000000000000000000000
χ302222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-1-12221111-2-211-2-211-122-1-1-1-1-1-1-1-2-21111111100000000−3−333−3−33333−3−333−3−3000000000000000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-22-1-1-122-2-211-2-21122-111-1-11111-1-1-1-1-1-1-11111000000000000000000000000000022-2-200000000-1-1-1-11111
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-22-1-1-122-2-211-2-21122-111-1-11111-1-1-1-1-1-1-111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-11111-1222-1-111-2-211-2-2-1-1-1-2-2-1-11111-122-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-11111-1222-1-111-2-211-2-2-1-1-1-2-2-1-11111-122-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ3522-2-222-2-22-22-222-2-222-2-22-22-22-1-2-222-2-22-111-2-222-1-1-2-21122-1-1111-1-111-1-11-1-111-1-11100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ3622-2-222-2-22-22-222-2-222-2-22-22-22-1-2-222-2-22-111-2-222-1-1-2-21122-1-1111-1-111-1-11-1-111-1-1110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ3722-2-222-2-22-22-222-2-222-2-22-22-2-1211-1-111-12-2-211-1-12211-2-2-1-1-12-211-1-111-12-2-1-111-1-11122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ3822-2-222-2-22-22-222-2-222-2-22-22-2-1211-1-111-12-2-211-1-12211-2-2-1-1-12-211-1-111-12-2-1-111-1-111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ3922-2-222-2-2-2222-22-2-222-2-2-22-2222-2-2-2-22222-2-2222222-2-2-2-2-2-22-22-2-2-2-2222-22-2-22222-2-2000000000000000000000000000000000000000000000000
χ4022-2-222-2-2-2222-22-2-222-2-2-22-222-1-2-2-2-2222-1112222-1-1-2-211-2-2-11-11111-1-1-11-111-1-1-1-11100000000000000000000000000000000000000003−3−333−3−33
χ4122-2-222-2-2-2222-22-2-222-2-2-22-222-1-2-2-2-2222-1112222-1-1-2-211-2-2-11-11111-1-1-11-111-1-1-1-1110000000000000000000000000000000000000000−333−3−333−3
χ4222-2-222-2-2-2222-22-2-222-2-2-22-22-121111-1-1-12-2-2-1-1-1-12211-2-211-1-221111-1-1-1-2211-1-1-1-1110000000033−3−3−3−33333−3−3−3−333000000000000000000000000
χ4322-2-222-2-2-2222-22-2-222-2-2-22-22-121111-1-1-12-2-2-1-1-1-12211-2-211-1-221111-1-1-1-2211-1-1-1-11100000000−3−33333−3−3−3−33333−3−3000000000000000000000000
χ4422-2-2-2-2222-222-22-2-2-2-2222-2-2222-2-222-2-222-2-222-2-2-2-22222-2-222-2-2-222-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4522-2-2-2-2222-222-22-2-2-2-2222-2-222-1-2-222-2-22-11122-2-21122-1-1-2-2-1-1111-1-111-11-111-1-111-1-100000000000000000000000000000000000000003−3−33−333−3
χ4622-2-2-2-2222-222-22-2-2-2-2222-2-222-1-2-222-2-22-11122-2-21122-1-1-2-2-1-1111-1-111-11-111-1-111-1-10000000000000000000000000000000000000000−333−33−3−33
χ4722-2-2-2-2222-222-22-2-2-2-2222-2-22-1211-1-111-12-2-2-1-111-2-2-1-12211-12-211-1-111-1-2211-1-111-1-10000000033−3−3−3−333−3−33333−3−3000000000000000000000000
χ4822-2-2-2-2222-222-22-2-2-2-2222-2-22-1211-1-111-12-2-2-1-111-2-2-1-12211-12-211-1-111-1-2211-1-111-1-100000000−3−33333−3−333−3−3−3−333000000000000000000000000
χ4922-2-2-2-222-222-222-2-2-2-222-222-22-1-2-2-2-2222-111-2-2-2-21122-1-122-11-11111-1-1-1-11-1-11111-1-100000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ5022-2-2-2-222-222-222-2-2-2-222-222-22-1-2-2-2-2222-111-2-2-2-21122-1-122-11-11111-1-1-1-11-1-11111-1-10000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ5122-2-2-2-222-222-222-2-2-2-222-222-2-121111-1-1-12-2-21111-2-2-1-122-1-1-1-221111-1-1-12-2-1-11111-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ5222-2-2-2-222-222-222-2-2-2-222-222-2-121111-1-1-12-2-21111-2-2-1-122-1-1-1-221111-1-1-12-2-1-11111-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ532-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-20000-2-22-2002i−2i2i−2i2i−2i2i−2i002002-20000-20000002i−2i2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ542-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000222-20000-2-22-2002i−2i2i−2i2i−2i2i−2i002002-20000-20000002i−2i2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ552-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11−i3i3−i3i31-22-23−3−ii2i−2i−ii2i−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
χ562-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11−i3i3−i3i31-22-23−3−ii2i−2i−ii2i−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
χ572-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11i3−i3i3−i31-22-2−33−ii2i−2i−ii2i−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
χ582-22-22i−2i2i−2i00200-22-22i−2i2i−2i0000-12-11i3−i3i3−i31-22-2−33−ii2i−2i−ii2i−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
χ592-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-20000-2-22-200−2i2i−2i2i−2i2i−2i2i002002-20000-2000000−2i2i−2i2i2−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ602-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000222-20000-2-22-200−2i2i−2i2i−2i2i−2i2i002002-20000-2000000−2i2i−2i2i−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ612-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11−i3i3−i3i31-22-2−33i−i−2i2ii−i−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
χ622-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11−i3i3−i3i31-22-2−33i−i−2i2ii−i−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
χ632-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11i3−i3i3−i31-22-23−3i−i−2i2ii−i−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
χ642-22-2−2i2i−2i2i00200-22-2−2i2i−2i2i0000-12-11i3−i3i3−i31-22-23−3i−i−2i2ii−i−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
χ652-2-222i−2i−2i2i00200-2-222i−2i−2i2i000022-220000-2-2-22002i−2i2i−2i−2i2i−2i2i00200-220000-20000002i−2i−2i2i2−2−22−i2i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.