Finite Group Databasebeta

← Group #13139964

Character table — Group #13139964

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12224444223446666666121212121212121233666666121212121212121236666666666612121212121212121212121288888888242424242424242424242424242424244444888812121212121212122424242424242424
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
χ511111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222222-1222-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222222222-1222-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-200001111111100000000
χ192222222222222222222222222222-12-1-1-1222-1-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ202222222222222222222222222222-12-1-1-1222-1-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ2122222222-2-22-2-222-2-2-2-2222-2-2-2-2222-1222-1-1-122-1-1-1-122-1-2-211-1-11111-1-2-211-1-1-1-1111100000000000000000000000022-2-20000-1-1-1-1111100000000
χ2222222222-2-22-2-222-2-2-2-2222-2-2-2-2222-1222-1-1-122-1-1-1-122-1-2-211-1-11111-1-2-211-1-1-1-11111000000000000000000000000-2-22200001111-1-1-1-100000000
χ2322222222-2-22-2-222-2-2-2-2222-2-2-2-222-12-1-1-1222-1-12222-1-1-111-2-2-1-11111-111-2-2-1-1-1-11111000000000000000000000000000022-2-200000000-1-1-1-11111
χ2422222222-2-22-2-222-2-2-2-2222-2-2-2-222-12-1-1-1222-1-12222-1-1-111-2-2-1-11111-111-2-2-1-1-1-111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ252222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-1-2-21111-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111110000000000000000000000002-22-20000-1-111-1-11100000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-1-2-21111-2-2-122-1-1-1-1-1-1-1-1-1-2-21111111111000000000000000000000000-22-22000011-1-111-1-100000000
χ272222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-122211-2-2-2-211-1-1-122-1-1-1-1-1-1-111-2-21111111100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ282222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-122211-2-2-2-211-1-1-122-1-1-1-1-1-1-111-2-2111111110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ292222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-22-1222-1-1-1-2-21111-2-2-1-2-211-1-11111-122-1-11111-1-1-1-10000000000000000000000002-2-220000-1-11111-1-100000000
χ302222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-22-1222-1-1-1-2-21111-2-2-1-2-211-1-11111-122-1-11111-1-1-1-1000000000000000000000000-222-2000011-1-1-1-11100000000
χ312222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-2-12-1-1-122211-2-2-2-211-111-2-2-1-11111-1-1-1221111-1-1-1-100000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ322222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-2-12-1-1-122211-2-2-2-211-111-2-2-1-11111-1-1-1221111-1-1-1-10000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ3322-2-222-2-22-222-2-2-222-2-222222-2-2-2-222-2-222-2-22222-2-2-2-222-22-2-2-222-2-222-22-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3422-2-222-2-22-222-2-2-222-2-222222-2-2-2-22-1-2-22-11122-1-111-2-2-12-2-1111-1-111-12-2-11-1-111-1-111000000000000000000000000000000003−33−33−33−300000000
χ3522-2-222-2-22-222-2-2-222-2-222222-2-2-2-22-1-2-22-11122-1-111-2-2-12-2-1111-1-111-12-2-11-1-111-1-11100000000000000000000000000000000−33−33−33−3300000000
χ3622-2-222-2-22-222-2-2-222-2-222222-2-2-2-2-1211-12-2-2-1-122-2-211-1-112-211-1-111-1-112-2-1-111-1-11100000000000000000000000000000000000000003−33−33−33−3
χ3722-2-222-2-22-222-2-2-222-2-222222-2-2-2-2-1211-12-2-2-1-122-2-211-1-112-211-1-111-1-112-2-1-111-1-1110000000000000000000000000000000000000000−33−33−33−33
χ3822-2-222-2-2-222-22-2-2-2-222222-2-222-2-222-2-222-2-22222-2-2-2-22-22-22-2-2-2-2222-22-2222-2-2-2-222000000000000000000000000000000000000000000000000
χ3922-2-222-2-2-222-22-2-2-2-222222-2-222-2-22-1-2-22-11122-1-111-2-2-1-221-11111-1-1-1-221-1-1-11111-1-1000000000000000000000000000000003−33−3−33−3300000000
χ4022-2-222-2-2-222-22-2-2-2-222222-2-222-2-22-1-2-22-11122-1-111-2-2-1-221-11111-1-1-1-221-1-1-11111-1-100000000000000000000000000000000−33−333−33−300000000
χ4122-2-222-2-2-222-22-2-2-2-222222-2-222-2-2-1211-12-2-2-1-122-2-211-11-1-221111-1-1-11-1-22-1-11111-1-100000000000000000000000000000000000000003−33−3−33−33
χ4222-2-222-2-2-222-22-2-2-2-222222-2-222-2-2-1211-12-2-2-1-122-2-211-11-1-221111-1-1-11-1-22-1-11111-1-10000000000000000000000000000000000000000−33−333−33−3
χ4322-2-2-2-2222-22-22-2-222-2-22-2-2-2-2222222-2-222-2-2-2-2-2-2222222-22-2-2-222-2-22-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4422-2-2-2-2222-22-22-2-222-2-22-2-2-2-222222-1-2-22-111-2-211-1-122-12-2-1111-1-111-1-221-111-1-111-1-1000000000000000000000000000000003−3−333−3−3300000000
χ4522-2-2-2-2222-22-22-2-222-2-22-2-2-2-222222-1-2-22-111-2-211-1-122-12-2-1111-1-111-1-221-111-1-111-1-100000000000000000000000000000000−333−3−333−300000000
χ4622-2-2-2-2222-22-22-2-222-2-22-2-2-2-22222-1211-12-2-211-2-222-1-1-1-112-211-1-111-11-1-2211-1-111-1-10000000000000000000000000000000000000000−i3i3i3−i3−i3i3i3−i3
χ4722-2-2-2-2222-22-22-2-222-2-22-2-2-2-22222-1211-12-2-211-2-222-1-1-1-112-211-1-111-11-1-2211-1-111-1-10000000000000000000000000000000000000000i3−i3−i3i3i3−i3−i3i3
χ4822-2-2-2-222-2222-2-2-2-2-2222-2-222-2-22222-2-222-2-2-2-2-2-222222-22-22-2-2-2-22222-22-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ4922-2-2-2-222-2222-2-2-2-2-2222-2-222-2-2222-1-2-22-111-2-211-1-122-1-221-11111-1-1-12-2-1111-1-1-1-111000000000000000000000000000000003−3−33−333−300000000
χ5022-2-2-2-222-2222-2-2-2-2-2222-2-222-2-2222-1-2-22-111-2-211-1-122-1-221-11111-1-1-12-2-1111-1-1-1-11100000000000000000000000000000000−333−33−3−3300000000
χ5122-2-2-2-222-2222-2-2-2-2-2222-2-222-2-222-1211-12-2-211-2-222-1-1-11-1-221111-1-1-1-112-211-1-1-1-1110000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ5222-2-2-2-222-2222-2-2-2-2-2222-2-222-2-222-1211-12-2-211-2-222-1-1-11-1-221111-1-1-1-112-211-1-1-1-1110000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ532-22-22i−2i2i−2i002002-20000-22i−2i00002i−2i222-2-2-22-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ542-22-22i−2i2i−2i002002-20000-22i−2i00002i−2i222-2-2-22-22i−2i2i−2i2i−2i2i−2i200002-20000-200002i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ552-22-2−2i2i−2i2i002002-20000-2−2i2i0000−2i2i222-2-2-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ562-22-2−2i2i−2i2i002002-20000-2−2i2i0000−2i2i222-2-2-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-20000−2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ572-2-222i−2i−2i2i00200-220000-22i−2i0000−2i2i22-22-2-2-222i−2i2i−2i−2i2i−2i2i20000-220000-200002i−2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ582-2-222i−2i−2i2i00200-220000-22i−2i0000−2i2i22-22-2-2-222i−2i2i−2i−2i2i−2i2i20000-220000-200002i−2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ592-2-22−2i2i2i−2i00200-220000-2−2i2i00002i−2i22-22-2-2-22−2i2i−2i2i2i−2i2i−2i20000-220000-20000−2i2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000
χ602-2-22−2i2i2i−2i00200-220000-2−2i2i00002i−2i22-22-2-2-22−2i2i−2i2i2i−2i2i−2i20000-220000-20000−2i2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ614444444444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000000000000000
χ6244444444-4-44-4-444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122221111-1-1-1-1000000000000000000000000000000000000000000000000
χ634444-4-4-4-4444-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-444444-4-4-4-44-4-44444-4-4-2-2-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000000000
χ6544-4-444-4-44-444-4-4-444-4-444444-4-4-4-4-2-222-2-222-2-2-2-222221-22-22-1-111-1-11-22-2211-1-111-1-1000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-444-44-4-4-4-444444-4-444-4-4-2-222-2-222-2-2-2-2222212-22-2-1-1-1-11112-22-211-1-1-1-111000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444-44-44-4-444-4-44-4-4-4-44444-2-222-2-2222222-2-2-2-21-22-22-1-111-1-112-22-2-1-111-1-111000000000000000000000000000000000000000000000000
χ6844-4-4-4-444-4444-4-4-4-4-4444-4-444-4-444-2-222-2-2222222-2-2-2-212-22-2-1-1-1-1111-22-22-1-11111-1-1000000000000000000000000000000000000000000000000
χ694-44-44i−4i4i−4i004004-40000-44i−4i00004i−4i4-24-4-42-224i−4i−2i2i−2i2i4i−4i-20000-22000020000−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i004004-40000-44i−4i00004i−4i-24-222-44-4−2i2i4i−4i4i−4i−2i2i-20000-22000020000−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ714-44-44i−4i4i−4i004004-40000-44i−4i00004i−4i-2-2-2222-22−2i2i−2i2i−2i2i−2i2i100001-13-33-3-10000i−ii−i3i−3i3i−3i000000000000000000000000000000000000000000000000
χ724-44-44i−4i4i−4i004004-40000-44i−4i00004i−4i-2-2-2222-22−2i2i−2i2i−2i2i−2i2i100001-1-33-33-10000i−ii−i−3i3i−3i3i000000000000000000000000000000000000000000000000
χ734-44-4−4i4i−4i4i004004-40000-4−4i4i0000−4i4i4-24-4-42-22−4i4i2i−2i2i−2i−4i4i-20000-220000200002i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ744-44-4−4i4i−4i4i004004-40000-4−4i4i0000−4i4i-24-222-44-42i−2i−4i4i−4i4i2i−2i-20000-220000200002i−2i2i−2i0000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.