Finite Group Databasebeta

← Group #10855244

Character table — Group #10855244

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121244444488888888121212121212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ91111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1
χ101111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11
χ111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11
χ121111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1
χ131111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-11
χ141111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ151111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1111-1
χ161111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11
χ17222222222-22222-2-2-22222222-2-2-2-2-2-2-2-22222-2-2000000002222-2-2-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
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
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-222220000000000000000-22000022-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2222200000000000000002-20000-2-22222-2-2000000000000000000000000
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
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-22-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
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
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-220000-1-11111-1-1−3−33333−3−30000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-220000-1-11111-1-133−3−3−3−3330000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-2000011-1-1-1-111−3−33333−3−30000000000000000
χ3722-222-2-2-22-200002-22222-2-2-2-2-2-222-2-2220000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000022-2-200002i−2i000000
χ3822-222-2-2-22-200002-22222-2-2-2-2-2-222-2-2220000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2-2220000−2i2i000000
χ3922-222-2-2-22-200002-22222-2-2-2-2-2-222-2-222000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000022-2-20000−2i2i000000
χ4022-222-2-2-22-200002-22222-2-2-2-2-2-222-2-222000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-2-22200002i−2i000000
χ412-222-2-22-22022-2-20002-2-22-22-2000000002-22-200−i2i2−i2i2−i2−i2i2i222-2-20000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200−i2i2−i2i22-2002-200−i2i2−i2i2−i2i2−i2i20000000000000000
χ422-222-2-22-22022-2-20002-2-22-22-2000000002-22-200i2−i2i2−i2i2i2−i2−i222-2-20000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200i2−i2i2−i22-2002-200i2−i2i2−i2i2−i2i2−i20000000000000000
χ432-222-2-22-22022-2-20002-2-22-22-200000000-22-2200−i2i2−i2i2−i2−i2i2i222-2-20000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200i2−i2i2−i2-2200-2200i2−i2i2−i2i2−i2i2−i20000000000000000
χ442-222-2-22-22022-2-20002-2-22-22-200000000-22-2200i2−i2i2−i2i2i2−i2−i222-2-20000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200−i2i2−i2i2-2200-2200−i2i2−i2i2−i2i2−i2i20000000000000000
χ452-222-2-22-220-2-2220002-2-22-22-2000000002-2-2200−i2i2−i2i2i2i2−i2−i2-2-2220000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200i2−i2−i2i22-200-2200i2−i2i2−i2−i2i2−i2i20000000000000000
χ462-222-2-22-220-2-2220002-2-22-22-2000000002-2-2200i2−i2i2−i2−i2−i2i2i2-2-2220000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200−i2i2i2−i22-200-2200−i2i2−i2i2i2−i2i2−i20000000000000000
χ472-222-2-22-220-2-2220002-2-22-22-200000000-222-200−i2i2−i2i2i2i2−i2−i2-2-2220000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200−i2i2i2−i2-22002-200−i2i2−i2i2i2−i2i2−i20000000000000000
χ482-222-2-22-220-2-2220002-2-22-22-200000000-222-200i2−i2i2−i2−i2−i2i2i2-2-2220000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200i2−i2−i2i2-22002-200i2−i2i2−i2−i2i2−i2i20000000000000000
χ492-222-2-22-2-1022-2-2000-111-11-113−33−33−33−32-22-200−i2i2−i2i2−i2−i2i2i2-1-11133−3−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−i2i2−i2i2-113−3-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ502-222-2-22-2-1022-2-2000-111-11-113−33−33−33−32-22-200i2−i2i2−i2i2i2−i2−i2-1-11133−3−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300i2−i2i2−i2-113−3-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ512-222-2-22-2-1022-2-2000-111-11-113−33−33−33−3-22-2200−i2i2−i2i2−i2−i2i2i2-1-11133−3−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300i2−i2i2−i21-1−331-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ522-222-2-22-2-1022-2-2000-111-11-113−33−33−33−3-22-2200i2−i2i2−i2i2i2−i2−i2-1-11133−3−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−i2i2−i2i21-1−331-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ532-222-2-22-2-1022-2-2000-111-11-11−33−33−33−332-22-200−i2i2−i2i2−i2−i2i2i2-1-111−3−333ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−i2i2−i2i2-11−33-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ542-222-2-22-2-1022-2-2000-111-11-11−33−33−33−332-22-200i2−i2i2−i2i2i2−i2−i2-1-111−3−333−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700i2−i2i2−i2-11−33-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ552-222-2-22-2-1022-2-2000-111-11-11−33−33−33−33-22-2200−i2i2−i2i2−i2−i2i2i2-1-111−3−333ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700i2−i2i2−i21-13−31-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ562-222-2-22-2-1022-2-2000-111-11-11−33−33−33−33-22-2200i2−i2i2−i2i2i2−i2−i2-1-111−3−333−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−i2i2−i2i21-13−31-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ572-222-2-22-2-10-2-222000-111-11-113−33−33−33−32-2-2200−i2i2−i2i2i2i2−i2−i211-1-1−3−333ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300i2−i2−i2i2-113−31-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ582-222-2-22-2-10-2-222000-111-11-113−33−33−33−32-2-2200i2−i2i2−i2−i2−i2i2i211-1-1−3−333−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−i2i2i2−i2-113−31-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ592-222-2-22-2-10-2-222000-111-11-113−33−33−33−3-222-200−i2i2−i2i2i2i2−i2−i211-1-1−3−333ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−i2i2i2−i21-1−33-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.