Finite Group Databasebeta

← Group #10705711

Character table — Group #10705711

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888888888888888888888888888824242424484848484848
order1222223446661212121222444444466666612121212121244888888881212121212121212242424242424242424242424242424244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ61111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ71111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ81111111111111111-1-1111-1-1-1-111-1-1-1-111-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ91111111-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−ii−i
χ101111111-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-11−ii−ii
χ111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii−ii
χ121111111-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-11i−ii−i
χ131111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111-1-11
χ141111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-111-1
χ151111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-11-111-1
χ161111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-11-1-11
χ172222222222222222222-2-222-2-2222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000
χ182222222222222222-2-22-2-2-2-22222-2-2-2-222-2-2-2-2-2200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2222-2-2-2-222-222-2-222222222-2-2-2-2-2-2-2-200000000-2-222-2-22200000000000000000000000000
χ202222222-2-2222-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-2200000000-2-22222-2-200000000000000000000000000
χ21222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ22222222-122-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ23222222-122-1-1-1-1-1-1-1222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000
χ24222222-122-1-1-1-1-1-1-1222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000
χ25222222-122-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-11111-1-111112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000
χ26222222-122-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-11111-1-111112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000
χ27222222-122-1-1-1-1-1-1-1-2-22-2-2-2-222-1-11111-1-11111-22000000001111-1-1-1-133−3−333−3−3−3−333−3−3330000000000
χ28222222-122-1-1-1-1-1-1-1-2-22-2-2-2-222-1-11111-1-11111-22000000001111-1-1-1-1−3−333−3−33333−3−333−3−30000000000
χ29222222-1-2-2-1-1-1111122-222-2-222-1-1-1-1-1-1111111-2-20000000011-1-111-1-133−3−3−3−33333−3−3−3−3330000000000
χ30222222-1-2-2-1-1-1111122-222-2-222-1-1-1-1-1-1111111-2-20000000011-1-111-1-1−3−33333−3−3−3−33333−3−30000000000
χ31222222-1-2-2-1-1-1111122-2-2-2-2-2-2-2-1-1-1-1-1-1111111222i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000
χ32222222-1-2-2-1-1-1111122-2-2-2-2-2-2-2-1-1-1-1-1-111111122−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000
χ33222222-1-2-2-1-1-11111-2-2-22222-2-2-1-1111111-1-1-1-1-220000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000
χ34222222-1-2-2-1-1-11111-2-2-22222-2-2-1-1111111-1-1-1-1-220000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000
χ35222222-1-2-2-1-1-11111-2-2-2-2-22222-1-1111111-1-1-1-12-222-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-10000000000
χ36222222-1-2-2-1-1-11111-2-2-2-2-22222-1-1111111-1-1-1-12-2-2-22222-2-2-1-11111-1-11111-1-1-1-1-1-1-1-111110000000000
χ372-22-22-22002-2-200002-202i−2i002i−2i2-222-2-2000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i002i−2i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ382-22-22-22002-2-200002-202i−2i002i−2i2-222-2-200000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i002i−2i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ392-22-22-22002-2-200002-20−2i2i00−2i2i2-222-2-2000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00−2i2i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ402-22-22-22002-2-200002-20−2i2i00−2i2i2-222-2-200000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00−2i2i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ412-22-22-22002-2-20000-2202i−2i00−2i2i2-2-2-222000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i002i−2i00−2i2i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000000000
χ422-22-22-22002-2-20000-2202i−2i00−2i2i2-2-2-22200000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i002i−2i00−2i2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000000000
χ432-22-22-22002-2-20000-220−2i2i002i−2i2-2-2-222000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00−2i2i002i−2i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000
χ442-22-22-22002-2-20000-220−2i2i002i−2i2-2-2-22200000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00−2i2i002i−2i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000
χ452-22-22-2-100-111−i3−i3i3i32-202i−2i002i−2i-11-1-111−i3i3−i3i3−i3i3001+i−1−i1−i−1+i1+i−1−i1−i−1+i3−3−ii3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ110000000000
χ462-22-22-2-100-111−i3−i3i3i32-202i−2i002i−2i-11-1-111−i3i3−i3i3−i3i300−1−i1+i−1+i1−i−1−i1+i−1+i1−i3−3−ii3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ110000000000
χ472-22-22-2-100-111−i3−i3i3i32-20−2i2i00−2i2i-11-1-111−i3i3−i3i3−i3i3001−i−1+i1+i−1−i1−i−1+i1+i−1−i−33i−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110000000000
χ482-22-22-2-100-111−i3−i3i3i32-20−2i2i00−2i2i-11-1-111−i3i3−i3i3−i3i300−1+i1−i−1−i1+i−1+i1−i−1−i1+i−33i−i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110000000000
χ492-22-22-2-100-111−i3−i3i3i3-2202i−2i00−2i2i-1111-1-1−i3i3i3−i3i3−i3001−i−1+i−1−i1+i−1+i1−i1+i−1−i3−3−ii−33i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ70000000000
χ502-22-22-2-100-111−i3−i3i3i3-2202i−2i00−2i2i-1111-1-1−i3i3i3−i3i3−i300−1+i1−i1+i−1−i1−i−1+i−1−i1+i3−3−ii−33i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ70000000000
χ512-22-22-2-100-111−i3−i3i3i3-220−2i2i002i−2i-1111-1-1−i3i3i3−i3i3−i3001+i−1−i−1+i1−i−1−i1+i1−i−1+i−33i−i3−3−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70000000000
χ522-22-22-2-100-111−i3−i3i3i3-220−2i2i002i−2i-1111-1-1−i3i3i3−i3i3−i300−1−i1+i1−i−1+i1+i−1−i−1+i1−i−33i−i3−3−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70000000000
χ532-22-22-2-100-111i3i3−i3−i32-202i−2i002i−2i-11-1-111i3−i3i3−i3i3−i3001+i−1−i1−i−1+i1+i−1−i1−i−1+i−33−ii−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70000000000
χ542-22-22-2-100-111i3i3−i3−i32-202i−2i002i−2i-11-1-111i3−i3i3−i3i3−i300−1−i1+i−1+i1−i−1−i1+i−1+i1−i−33−ii−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70000000000
χ552-22-22-2-100-111i3i3−i3−i32-20−2i2i00−2i2i-11-1-111i3−i3i3−i3i3−i3001−i−1+i1+i−1−i1−i−1+i1+i−1−i3−3i−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ70000000000
χ562-22-22-2-100-111i3i3−i3−i32-20−2i2i00−2i2i-11-1-111i3−i3i3−i3i3−i300−1+i1−i−1−i1+i−1+i1−i−1−i1+i3−3i−i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ70000000000
χ572-22-22-2-100-111i3i3−i3−i3-2202i−2i00−2i2i-1111-1-1i3−i3−i3i3−i3i3001−i−1+i−1−i1+i−1+i1−i1+i−1−i−33−ii3−3i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110000000000
χ582-22-22-2-100-111i3i3−i3−i3-2202i−2i00−2i2i-1111-1-1i3−i3−i3i3−i3i300−1+i1−i1+i−1−i1−i−1+i−1−i1+i−33−ii3−3i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110000000000
χ592-22-22-2-100-111i3i3−i3−i3-220−2i2i002i−2i-1111-1-1i3−i3−i3i3−i3i3001+i−1−i−1+i1−i−1−i1+i1−i−1+i3−3i−i−33−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ110000000000
χ602-22-22-2-100-111i3i3−i3−i3-220−2i2i002i−2i-1111-1-1i3−i3−i3i3−i3i300−1−i1+i1−i−1+i1+i−1−i−1+i1−i3−3i−i−33−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ110000000000
χ614444-4-4444444444400-4000000-4-40000-4-4000000000000000000000000000000000000000000000000
χ624444-4-44-4-4444-4-4-4-4004000000-4-4000044000000000000000000000000000000000000000000000000
χ634444-4-4-244-2-2-2-2-2-2-200-400000022−2i32i3−2i32i322−2i32i32i3−2i300000000000000000000000000000000000000000000
χ644444-4-4-244-2-2-2-2-2-2-200-4000000222i3−2i32i3−2i3222i3−2i3−2i32i300000000000000000000000000000000000000000000
χ654444-4-4-2-4-4-2-2-2222200400000022−2i32i3−2i32i3-2-22i3−2i3−2i32i300000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-2-2-22222004000000222i3−2i32i3−2i3-2-2−2i32i32i3−2i300000000000000000000000000000000000000000000
χ674-44-4-444004-4-40000000004-400-4400000044-4-400000000000000000000000000000000000000000000
χ684-44-4-444004-4-4000000000-4400-44000000-4-44400000000000000000000000000000000000000000000
χ694-44-4-44-200-222−2i3−2i32i32i3000004-4002-2−2i32i32i3−2i32i3−2i3-2-22200000000000000000000000000000000000000000000
χ704-44-4-44-200-222−2i3−2i32i32i300000-44002-22i3−2i3−2i32i32i3−2i322-2-200000000000000000000000000000000000000000000
χ714-44-4-44-200-2222i32i3−2i3−2i3000004-4002-22i3−2i3−2i32i3−2i32i3-2-22200000000000000000000000000000000000000000000
χ724-44-4-44-200-2222i32i3−2i3−2i300000-44002-2−2i32i32i3−2i3−2i32i322-2-200000000000000000000000000000000000000000000
χ734-4-440044i−4i-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000000002i−2i2-2000000
χ744-4-440044i−4i-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000−2i2i-22000000
χ754-4-44004−4i4i-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000002i−2i-22000000
χ764-4-44004−4i4i-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000−2i2i2-2000000
χ7788-8-800800-8-88000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-40044-443−43−434300000000000000000000000000000000000000000000000000000000000000000
χ7988-8-800-40044-4−434343−4300000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-48i−8i4-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-4−8i8i4-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000

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