Finite Group Databasebeta

← Group #10690023

Character table — Group #10690023

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212124444448888888812121212121212122424242424242424242424242424242422666688881212121224242424242424244444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ6111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ91-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-1111-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−iii−i−ii−iii−i−i11-1-11-1
χ101-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-1111-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−i−i−iii−ii−i−iii-1-111-11
χ111-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-1111-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiiiii−i−ii−iii−i−i-1-111-11
χ121-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-1111-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiii−i−iii−ii−i−iii11-1-11-1
χ131-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-11-1-111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiiiii−i−ii−i−i−iii11-1-1-11
χ141-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-11-1-111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii−i−iii−iiii−i−i-1-1111-1
χ151-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-11-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−iii−i−ii−i−i−iii-1-1111-1
χ161-111-1-1-11111-11-1-1-11-1-1-1-11111111-1-1-1-11-1-111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i−i−iii−iiii−i−i11-1-1-11
χ17222222222222-2-2-22-2222222222222222-20000-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002222-2-20000000000
χ18222222222222-2-2-22-2222222222222222-20000-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-22222-20000000022-2-222-2-20000000000000000-2-2-2-2-2-200002222000000000000000000000000
χ20222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-200000000000000002222220000-2-2-2-2000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-220000200000000-2-222-2-222000000000000000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-220000200000000-2-222-2-22200000000000000000000000000000000000000000000-22-22000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-21111111111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-22-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-22222-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−3-2-211110000-1-1-1-133−3−333−3−30000000000000000
χ2822222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-22222-200000000-1-111-1-111−3−3−3−33333−3−3−3−33333-2-211110000-1-1-1-1−3−333−3−3330000000000000000
χ2922222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−322-1-1-1-100001111−3−333−3−3330000000000000000
χ3022222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-111-1-111−3−3−3−33333−3−3−3−3333322-1-1-1-10000111133−3−333−3−30000000000000000
χ3122-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-22200000022−2−222−2−20000000022−2−222−2−222−2−222−2−200000000000000000000002i−2i2i−2i000000−i2i2−i2i200
χ3222-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-22200000022−2−222−2−20000000022−2−222−2−222−2−222−2−20000000000000000000000−2i2i−2i2i000000i2−i2i2−i200
χ3322-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-222000000−2−222−2−22200000000−2−222−2−222−2−222−2−22200000000000000000000002i−2i2i−2i000000i2−i2i2−i200
χ3422-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-222000000−2−222−2−22200000000−2−222−2−222−2−222−2−2220000000000000000000000−2i2i−2i2i000000−i2i2−i2i200
χ3522-2-2-2-222200022-20-22-22-22-2-20000000002i−2i2i−2i02−22−22−22−22-2002-2002−22−22−22−22−22−22−22−2000000−i2i2−i2i22i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3622-2-2-2-222200022-20-22-22-22-2-20000000002i−2i2i−2i0−22−22−22−222-2002-200−22−22−22−22−22−22−22−22000000i2−i2i2−i22i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3722-2-2-2-222200022-20-22-22-22-2-2000000000−2i2i−2i2i02−22−22−22−22-2002-2002−22−22−22−22−22−22−22−2000000i2−i2i2−i2−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-2-2-2-222200022-20-22-22-22-2-2000000000−2i2i−2i2i0−22−22−22−222-2002-200−22−22−22−22−22−22−22−22000000−i2i2−i2i2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-2-2-2-222-100022-20-2-11-11-1113−33−33−33−302i−2i2i−2i02−22−22−22−2-113−3-113−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300−i3i3−i3i3−i2i2−i2i2−ii−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4022-2-2-2-222-100022-20-2-11-11-1113−33−33−33−302i−2i2i−2i0−22−22−22−22-113−3-113−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300−i3i3−i3i3i2−i2i2−i2−ii−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ4122-2-2-2-222-100022-20-2-11-11-1113−33−33−33−30−2i2i−2i2i02−22−22−22−2-113−3-113−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300i3−i3i3−i3i2−i2i2−i2i−ii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ4222-2-2-2-222-100022-20-2-11-11-1113−33−33−33−30−2i2i−2i2i0−22−22−22−22-113−3-113−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300i3−i3i3−i3−i2i2−i2i2i−ii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4322-2-2-2-222-100022-20-2-11-11-111−33−33−33−3302i−2i2i−2i02−22−22−22−2-11−33-11−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700i3−i3i3−i3−i2i2−i2i2−ii−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ4422-2-2-2-222-100022-20-2-11-11-111−33−33−33−3302i−2i2i−2i0−22−22−22−22-11−33-11−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700i3−i3i3−i3i2−i2i2−i2−ii−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ4522-2-2-2-222-100022-20-2-11-11-111−33−33−33−330−2i2i−2i2i02−22−22−22−2-11−33-11−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700−i3i3−i3i3i2−i2i2−i2i−ii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ4622-2-2-2-222-100022-20-2-11-11-111−33−33−33−330−2i2i−2i2i0−22−22−22−22-11−33-11−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700−i3i3−i3i3−i2i2−i2i2i−ii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ472-222-2-2-22222-2-222-2-2-2-2-2-22222222-2-2-2-2-20000200000000-2-2-2-22222000000000000000000000000000000000000002i2i−2i−2i−2i2i0000000000
χ482-222-2-2-22222-2-222-2-2-2-2-2-22222222-2-2-2-2-20000200000000-2-2-2-2222200000000000000000000000000000000000000−2i−2i2i2i2i−2i0000000000
χ492-222-2-2-222-2-222-2-222-2-2-2-2222-2-2-2-22222-222-2-220000000022-2-2-2-2220000000000000000-22-2-222000022-2-2000000000000000000000000
χ502-222-2-2-222-2-222-2-222-2-2-2-2222-2-2-2-22222-2-2-22220000000022-2-2-2-22200000000000000002-222-2-20000-2-222000000000000000000000000
χ512-222-2-2-222-2-22-2222-2-2-2-2-2222-2-2-2-2222220000-200000000-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i000000
χ522-222-2-2-222-2-22-2222-2-2-2-2-2222-2-2-2-2222220000-200000000-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i000000
χ532-222-2-2-22-122-22-2-2-221111-1-1-1-1-1-1-11111222-2-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2-2-1-1112i2i−2i−2i-1-111−i−i−i−iiiii0000000000000000
χ542-222-2-2-22-122-22-2-2-221111-1-1-1-1-1-1-11111222-2-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2-2-1-111−2i−2i2i2i-1-111iiii−i−i−i−i0000000000000000
χ552-222-2-2-22-122-22-2-2-221111-1-1-1-1-1-1-111112-2-222-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2211-1-1−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000000000
χ562-222-2-2-22-122-22-2-2-221111-1-1-1-1-1-1-111112-2-222-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2211-1-12i2i−2i−2i11-1-1−i−i−i−iiiii0000000000000000
χ572-222-2-2-22-1-2-222-2-2221111-1-1-11111-1-1-1-1-222-2-2200000000-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-2211-1-10000-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ582-222-2-2-22-1-2-222-2-2221111-1-1-11111-1-1-1-1-222-2-2200000000-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-2211-1-10000-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ592-222-2-2-22-1-2-222-2-2221111-1-1-11111-1-1-1-1-2-2-222200000000-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-1-111000011-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ602-222-2-2-22-1-2-222-2-2221111-1-1-11111-1-1-1-1-2-2-222200000000-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-1-111000011-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ612-2-22-222-222-22000-20-2-222-2-2222-2-222-2-2000000−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000002-2-22000000−i2i2i2−i200
χ622-2-22-222-222-22000-20-2-222-2-2222-2-222-2-2000000−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000000000-222-2000000i2−i2−i2i200
χ632-2-22-222-222-22000-20-2-222-2-2222-2-222-2-2000000i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000002-2-22000000i2−i2−i2i200
χ642-2-22-222-222-22000-20-2-222-2-2222-2-222-2-2000000i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000000000-222-2000000−i2i2i2−i200
χ652-2-2-222-2220002-220-2-22-222-2-20000000002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i22-200-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000−222−22i−2i−2i2i−22−222−22−20000000000000000
χ662-2-2-222-2220002-220-2-22-222-2-20000000002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i22-200-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002−2−222i−2i−2i2i2−22−2−22−220000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.