Finite Group Databasebeta

← Group #10849225

Character table — Group #10849225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121244444488888888121212121212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-11
χ121111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ131111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-11
χ141111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-11-1
χ151111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ17222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000220000-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-200000000-2-2-2-222220000000000000000-22000022-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000000000002-20000-2-22222-2-2000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2222200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2222200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-220000-1-11111-1-133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-220000-1-11111-1-1−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2000011-1-1-1-111−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ37222-2-2-2-222022-2-200022-2-2-22-200000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002−22−22i−2i002i−2i002−22−22−22−20000000000000000
χ38222-2-2-2-222022-2-200022-2-2-22-200000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−22−222i−2i002i−2i00−22−22−22−220000000000000000
χ39222-2-2-2-222022-2-200022-2-2-22-20000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−22−22−2i2i00−2i2i00−22−22−22−220000000000000000
χ40222-2-2-2-222022-2-200022-2-2-22-20000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002−22−2−2i2i00−2i2i002−22−22−22−20000000000000000
χ41222-2-2-2-2220-2-22200022-2-2-22-200000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002−2−222i−2i00−2i2i002−22−2−22−220000000000000000
χ42222-2-2-2-2220-2-22200022-2-2-22-200000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−222−22i−2i00−2i2i00−22−222−22−20000000000000000
χ43222-2-2-2-2220-2-22200022-2-2-22-20000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−222−2−2i2i002i−2i00−22−222−22−20000000000000000
χ44222-2-2-2-2220-2-22200022-2-2-22-20000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002−2−22−2i2i002i−2i002−22−2−22−220000000000000000
χ45222-2-2-2-22-1022-2-2000-1-1111-113−333−3−33−3002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2-1-11133−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002−22−2−ii−i3i3−ii−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ46222-2-2-2-22-1022-2-2000-1-1111-113−333−3−33−3002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2-1-11133−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−22−22−ii−i3i3−ii−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ47222-2-2-2-22-1022-2-2000-1-1111-113−333−3−33−300−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2-1-11133−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−22−22i−ii3−i3i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ48222-2-2-2-22-1022-2-2000-1-1111-113−333−3−33−300−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2-1-11133−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002−22−2i−ii3−i3i−ii3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ49222-2-2-2-22-1022-2-2000-1-1111-11−33−3−333−33002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2-1-111−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002−22−2−iii3−i3−iii3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ50222-2-2-2-22-1022-2-2000-1-1111-11−33−3−333−33002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2-1-111−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−22−22−iii3−i3−iii3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ51222-2-2-2-22-1022-2-2000-1-1111-11−33−3−333−3300−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2-1-111−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−22−22i−i−i3i3i−i−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ52222-2-2-2-22-1022-2-2000-1-1111-11−33−3−333−3300−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2-1-111−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002−22−2i−i−i3i3i−i−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ53222-2-2-2-22-10-2-222000-1-1111-113−333−3−33−3002i−2i−2i2i−i2−i2i2i2i2i2−i2−i211-1-1−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002−2−22−ii−i3i3i−ii3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ54222-2-2-2-22-10-2-222000-1-1111-113−333−3−33−3002i−2i−2i2ii2i2−i2−i2−i2−i2i2i211-1-1−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−222−2−ii−i3i3i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ55222-2-2-2-22-10-2-222000-1-1111-113−333−3−33−300−2i2i2i−2i−i2−i2i2i2i2i2−i2−i211-1-1−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−222−2i−ii3−i3−ii−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ56222-2-2-2-22-10-2-222000-1-1111-113−333−3−33−300−2i2i2i−2ii2i2−i2−i2−i2−i2i2i211-1-1−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002−2−22i−ii3−i3−ii−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ57222-2-2-2-22-10-2-222000-1-1111-11−33−3−333−33002i−2i−2i2i−i2−i2i2i2i2i2−i2−i211-1-133−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002−2−22−iii3−i3i−i−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ58222-2-2-2-22-10-2-222000-1-1111-11−33−3−333−33002i−2i−2i2ii2i2−i2−i2−i2−i2i2i211-1-133−3−3−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−222−2−iii3−i3i−i−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ59222-2-2-2-22-10-2-222000-1-1111-11−33−3−333−3300−2i2i2i−2i−i2−i2i2i2i2i2−i2−i211-1-133−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−222−2i−i−i3i3−iii3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.