Finite Group Databasebeta

← Group #69859

Character table — Group #69859

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444434444444466612121212121212121212121224668888888812121212121224242424242424242424242424242424888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1-11-1
χ6111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-11-11
χ7111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-11-11
χ8111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1-11-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-222-2-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ2122222222-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2222222222-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2322222222-1-2-222-2-222-1-1-1-1-1-1-111111111-2-2110000000011-1-1-1-133−3−333−3−3−3−333−3−333000000000000
χ2422222222-1-2-222-2-222-1-1-1-1-1-1-111111111-2-2110000000011-1-1-1-1−3−333−3−33333−3−333−3−3000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-1-12i2i2i2i−2i−2i−2i−2i-1-11111−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-1-1−2i−2i−2i−2i2i2i2i2i-1-11111iiiiiiii−i−i−i−i−i−i−i−i000000000000
χ272222-2-2-2-2222-2-2-2-222222-2-2-2-22222-2-2-2-22-22200000000-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-222222-22200000000-2-222-2-20000000000000000000000000000
χ292222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-22112i2i−2i−2i2i2i−2i−2i-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ302222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-2211−2i−2i2i2i−2i−2i2i2i-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ312222-2-2-2-2-122-2-2-2-222-1-1-11111-1-1-1-111112-2-1-1000000001111-1-133−3−3−3−33333−3−3−3−333000000000000
χ322222-2-2-2-2-122-2-2-2-222-1-1-11111-1-1-1-111112-2-1-1000000001111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ332222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-10000000011-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ342222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-10000000011-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ352222-2-2-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-1-221122-2-2-2-222-1-111-1-1-1-1-1-111111111-1-1-1-1000000000000
χ362222-2-2-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-1-2211-2-22222-2-2-1-111-1-11111-1-1-1-1-1-1-1-11111000000000000
χ3722-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i002-22i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-2-22i2i−2i−2i2002-2002i−2i2-2-22i2i−2i−2i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i002-22i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-2-22i2i−2i−2i200-2200−2i2i2-2-22i2i−2i−2i0000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00-22−2i2i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000
χ4022-2-22i2i−2i−2i200-2200−2i2i2-2-22i2i−2i−2i000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00-22−2i2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000
χ4122-2-22i2i−2i−2i-1002-2002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i31+i−1−i1−i−1+i1+i−1−i1−i−1+i3−3-11−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ4222-2-22i2i−2i−2i-1002-2002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i3−1−i1+i−1+i1−i−1−i1+i−1+i1−i3−3-11−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ4322-2-22i2i−2i−2i-1002-2002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i31+i−1−i1−i−1+i1+i−1−i1−i−1+i−33-11−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ4422-2-22i2i−2i−2i-1002-2002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i3−1−i1+i−1+i1−i−1−i1+i−1+i1−i−33-11−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ4522-2-22i2i−2i−2i-100-2200−2i2i-111−i−iii33−3−3−i3−i3i3i300i3−i31−i−1+i−1−i1+i−1+i1−i1+i−1−i−331-1i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ4622-2-22i2i−2i−2i-100-2200−2i2i-111−i−iii33−3−3−i3−i3i3i300i3−i3−1+i1−i1+i−1−i1−i−1+i−1−i1+i−331-1i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ4722-2-22i2i−2i−2i-100-2200−2i2i-111−i−iii−3−333i3i3−i3−i300−i3i31−i−1+i−1−i1+i−1+i1−i1+i−1−i3−31-1i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ4822-2-22i2i−2i−2i-100-2200−2i2i-111−i−iii−3−333i3i3−i3−i300−i3i3−1+i1−i1+i−1−i1−i−1+i−1−i1+i3−31-1i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ4922-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i002-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ5022-2-2−2i−2i2i2i2002-200−2i2i2-2-2−2i−2i2i2i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i002-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ5122-2-2−2i−2i2i2i200-22002i−2i2-2-2−2i−2i2i2i0000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00-222i−2i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000
χ5222-2-2−2i−2i2i2i200-22002i−2i2-2-2−2i−2i2i2i000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00-222i−2i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000
χ5322-2-2−2i−2i2i2i-1002-200−2i2i-111ii−i−i33−3−3i3i3−i3−i300i3−i31−i−1+i1+i−1−i1−i−1+i1+i−1−i3−3-11i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ5422-2-2−2i−2i2i2i-1002-200−2i2i-111ii−i−i33−3−3i3i3−i3−i300i3−i3−1+i1−i−1−i1+i−1+i1−i−1−i1+i3−3-11i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ5522-2-2−2i−2i2i2i-1002-200−2i2i-111ii−i−i−3−333−i3−i3i3i300−i3i31−i−1+i1+i−1−i1−i−1+i1+i−1−i−33-11i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ5622-2-2−2i−2i2i2i-1002-200−2i2i-111ii−i−i−3−333−i3−i3i3i300−i3i3−1+i1−i−1−i1+i−1+i1−i−1−i1+i−33-11i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ5722-2-2−2i−2i2i2i-100-22002i−2i-111ii−i−i33−3−3i3i3−i3−i300−i3i31+i−1−i−1+i1−i−1−i1+i1−i−1+i−331-1−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ5822-2-2−2i−2i2i2i-100-22002i−2i-111ii−i−i33−3−3i3i3−i3−i300−i3i3−1−i1+i1−i−1+i1+i−1−i−1+i1−i−331-1−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ5922-2-2−2i−2i2i2i-100-22002i−2i-111ii−i−i−3−333−i3−i3i3i300i3−i31+i−1−i−1+i1−i−1−i1+i1−i−1+i3−31-1−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ6022-2-2−2i−2i2i2i-100-22002i−2i-111ii−i−i−3−333−i3−i3i3i300i3−i3−1−i1+i1−i−1+i1+i−1−i−1+i1−i3−31-1−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ612-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ622-22-22i−2i2i−2i22-2002i−2i00-22-22i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ632-22-22i−2i2i−2i2-2200−2i2i00-22-22i−2i2i−2i-22-22−2i2i−2i2i00000000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ642-22-22i−2i2i−2i2-2200−2i2i00-22-22i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ652-22-2−2i2i−2i2i22-200−2i2i00-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-2−2i2i−2i2i22-200−2i2i00-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ672-22-2−2i2i−2i2i2-22002i−2i00-22-2−2i2i−2i2i-22-222i−2i2i−2i00000000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ682-22-2−2i2i−2i2i2-22002i−2i00-22-2−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ694-44-44i−4i4i−4i-24-4004i−4i002-22−2i2i−2i2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i-2-4400−4i4i002-22−2i2i−2i2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i-24-400−4i4i002-222i−2i2i−2i-22-222i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-2-44004i−4i002-222i−2i2i−2i2-22-2−2i2i−2i2i0000000000000000000000000000000000000000000000
χ734-4-444-4-44400000000-4-444-4-44000000000000000000000000000000000000000000000000000000
χ744-4-444-4-44-20000000022-2-222-223−23−2323−232323−230000000000000000000000000000000000000000000000
χ754-4-444-4-44-20000000022-2-222-2−232323−2323−23−23230000000000000000000000000000000000000000000000
χ764-4-44-444-4400000000-4-44-444-4000000000000000000000000000000000000000000000000000000
χ774-4-44-444-4-20000000022-22-2-2223−23−232323−23−23230000000000000000000000000000000000000000000000
χ784-4-44-444-4-20000000022-22-2-22−232323−23−232323−230000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.