Finite Group Databasebeta

← Group #68614

Character table — Group #68614

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111111111111222222222222222244444444444444444444444444444444444412121212121212121212121212121212
order12222222444444443666666612121212121212124444888888881212121212121212242424242424242424242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ2222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ2322222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ2422222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ252222-2-2-2-22222-2-2-2-2222-2-22-2-222-2-222-2-2000000002-22-2000000000000000022-2-222-2-20000000000000000
χ262222-2-2-2-22222-2-2-2-2222-2-22-2-222-2-222-2-200000000-22-220000000000000000-2-222-2-2220000000000000000
χ272222-2-2-2-22222-2-2-2-2-1-1-111-111-1-111-1-111000000002-22-233−3−333−3−333−3−333−3−3-1-111-1-1110000000000000000
χ282222-2-2-2-22222-2-2-2-2-1-1-111-111-1-111-1-111000000002-22-2−3−333−3−333−3−333−3−333-1-111-1-1110000000000000000
χ292222-2-2-2-22222-2-2-2-2-1-1-111-111-1-111-1-11100000000-22-2233−3−333−3−3−3−333−3−33311-1-111-1-10000000000000000
χ302222-2-2-2-22222-2-2-2-2-1-1-111-111-1-111-1-11100000000-22-22−3−333−3−33333−3−333−3−311-1-111-1-10000000000000000
χ312222-2-2-2-2-2-2-2-22222222-2-22-2-2-2-222-2-222000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2-2-2-2-22222222-2-22-2-2-2-222-2-22200000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2-2-2-2-22222-1-1-111-11111-1-111-1-1000000002i−2i−2i2i33−3−3−3−333i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i0000000000000000
χ342222-2-2-2-2-2-2-2-22222-1-1-111-11111-1-111-1-1000000002i−2i−2i2i−3−33333−3−3−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000000000
χ352222-2-2-2-2-2-2-2-22222-1-1-111-11111-1-111-1-100000000−2i2i2i−2i33−3−3−3−333−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii0000000000000000
χ362222-2-2-2-2-2-2-2-22222-1-1-111-11111-1-111-1-100000000−2i2i2i−2i−3−33333−3−3i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000000000
χ3722-2-22-22-22i−2i2i−2i2i−2i2i−2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ3822-2-22-22-22i−2i2i−2i2i−2i2i−2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ3922-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ4022-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ4122-2-2-22-222i−2i2i−2i−2i2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002i−2i2-2000000000000
χ4222-2-2-22-222i−2i2i−2i−2i2i−2i2i22-2-22-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000−2i2i-22000000000000
χ4322-2-2-22-22−2i2i−2i2i2i−2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002i−2i-22000000000000
χ4422-2-2-22-22−2i2i−2i2i2i−2i2i−2i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000−2i2i2-2000000000000
χ452-22-22-2-222i−2i−2i2i−2i2i2i−2i2-222-2-2-222i−2i2i−2i−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ462-22-22-2-222i−2i−2i2i−2i2i2i−2i2-222-2-2-222i−2i2i−2i−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ472-22-22-2-222i−2i−2i2i−2i2i2i−2i-11-1-1111-1−ii−iii−ii−i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300003−33−3−i3i3−i3i3ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ482-22-22-2-222i−2i−2i2i−2i2i2i−2i-11-1-1111-1−ii−iii−ii−i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−33−33i3−i3i3−i3ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ492-22-22-2-222i−2i−2i2i−2i2i2i−2i-11-1-1111-1−ii−iii−ii−i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300003−33−3−i3i3−i3i3−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ502-22-22-2-222i−2i−2i2i−2i2i2i−2i-11-1-1111-1−ii−iii−ii−i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−33−33i3−i3i3−i3−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ512-22-22-2-22−2i2i2i−2i2i−2i−2i2i2-222-2-2-22−2i2i−2i2i2i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ522-22-22-2-22−2i2i2i−2i2i−2i−2i2i2-222-2-2-22−2i2i−2i2i2i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ532-22-22-2-22−2i2i2i−2i2i−2i−2i2i-11-1-1111-1i−ii−i−ii−ii00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300003−33−3i3−i3i3−i3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ542-22-22-2-22−2i2i2i−2i2i−2i−2i2i-11-1-1111-1i−ii−i−ii−ii00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−33−33−i3i3−i3i3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ552-22-22-2-22−2i2i2i−2i2i−2i−2i2i-11-1-1111-1i−ii−i−ii−ii0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300003−33−3i3−i3i3−i3ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ562-22-22-2-22−2i2i2i−2i2i−2i−2i2i-11-1-1111-1i−ii−i−ii−ii0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−33−33−i3i3−i3i3ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ572-22-2-222-22i−2i−2i2i2i−2i−2i2i2-22-22-22-22i−2i−2i2i−2i2i2i−2i2-22i−2i000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ582-22-2-222-22i−2i−2i2i2i−2i−2i2i2-22-22-22-22i−2i−2i2i−2i2i2i−2i-22−2i2i00000000-222-22i−2i−2i2i00000000000000000000000000000000
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χ602-22-2-222-22i−2i−2i2i2i−2i−2i2i-11-11-11-11−iii−ii−i−ii2-22i−2i00000000-111-1i−i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ612-22-2-222-22i−2i−2i2i2i−2i−2i2i-11-11-11-11−iii−ii−i−ii-22−2i2i000000001-1-11−iii−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
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χ632-22-2-222-2−2i2i2i−2i−2i2i2i−2i2-22-22-22-2−2i2i2i−2i2i−2i−2i2i2-2−2i2i000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ642-22-2-222-2−2i2i2i−2i−2i2i2i−2i2-22-22-22-2−2i2i2i−2i2i−2i−2i2i-222i−2i00000000-222-2−2i2i2i−2i00000000000000000000000000000000
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χ662-22-2-222-2−2i2i2i−2i−2i2i2i−2i-11-11-11-11i−i−ii−iii−i2-2−2i2i00000000-111-1−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ672-22-2-222-2−2i2i2i−2i−2i2i2i−2i-11-11-11-11i−i−ii−iii−i-222i−2i000000001-1-11i−i−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
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χ814-4-4444-4-444-4-4-4-444-222-2-2-222-2-2-2-222220000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-4-44444-4-4-222-2-2-2222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-4-44444-4-444-4-4-22222-2-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-4-444-4-444-22222-2-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.