Finite Group Databasebeta

← Group #10858308

Character table — Group #10858308

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121244444488888888121212121212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
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
χ91111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-11
χ101111111111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-1
χ111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11-1
χ121111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ131111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111-1
χ141111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ151111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-11
χ161111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-11-1
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
χ37222-22-2-2-22200002-2-2222-2-2-2-22222-2-2-2-200000022-2-200000000000022-2-222-2-200000000000000000000000000000022-2-22-20000000000
χ38222-22-2-2-22200002-2-2222-2-2-2-22222-2-2-2-200000022-2-200000000000022-2-222-2-2000000000000000000000000000000-2-222-220000000000
χ39222-22-2-2-22200002-2-2222-2-2-2-22222-2-2-2-2000000-2-222000000000000-2-222-2-22200000000000000000000000000000022-2-2-220000000000
χ40222-22-2-2-22200002-2-2222-2-2-2-22222-2-2-2-2000000-2-222000000000000-2-222-2-222000000000000000000000000000000-2-2222-20000000000
χ4122-22-2-2-22202i2i−2i−2i0002-2-22-22-2000000002-22i−2i00−i2i2−i2i222−2−22i2i−2i−2i0000−i2i2−i2i2−i2i2−i2i222−2−222−2−2002−2−i2i22-2002i−2i002−22−2−i2i2−i2i20000000000000000
χ4222-22-2-2-22202i2i−2i−2i0002-2-22-22-2000000002-22i−2i00i2−i2i2−i2−2−2222i2i−2i−2i0000i2−i2i2−i2i2−i2i2−i2−2−222−2−22200−22i2−i22-2002i−2i00−22−22i2−i2i2−i20000000000000000
χ4322-22-2-2-22202i2i−2i−2i0002-2-22-22-200000000-22−2i2i00−i2i2−i2i222−2−22i2i−2i−2i0000−i2i2−i2i2−i2i2−i2i222−2−222−2−200−22i2−i2-2200−2i2i00−22−22i2−i2i2−i20000000000000000
χ4422-22-2-2-22202i2i−2i−2i0002-2-22-22-200000000-22−2i2i00i2−i2i2−i2−2−2222i2i−2i−2i0000i2−i2i2−i2i2−i2i2−i2−2−222−2−222002−2−i2i2-2200−2i2i002−22−2−i2i2−i2i20000000000000000
χ4522-22-2-2-2220−2i−2i2i2i0002-2-22-22-2000000002-2−2i2i00−i2i2−i2i2−2−222−2i−2i2i2i0000−i2i2−i2i2−i2i2−i2i2−2−222−2−22200−22−i2i22-200−2i2i00−22−22−i2i2−i2i20000000000000000
χ4622-22-2-2-2220−2i−2i2i2i0002-2-22-22-2000000002-2−2i2i00i2−i2i2−i222−2−2−2i−2i2i2i0000i2−i2i2−i2i2−i2i2−i222−2−222−2−2002−2i2−i22-200−2i2i002−22−2i2−i2i2−i20000000000000000
χ4722-22-2-2-2220−2i−2i2i2i0002-2-22-22-200000000-222i−2i00−i2i2−i2i2−2−222−2i−2i2i2i0000−i2i2−i2i2−i2i2−i2i2−2−222−2−222002−2i2−i2-22002i−2i002−22−2i2−i2i2−i20000000000000000
χ4822-22-2-2-2220−2i−2i2i2i0002-2-22-22-200000000-222i−2i00i2−i2i2−i222−2−2−2i−2i2i2i0000i2−i2i2−i2i2−i2i2−i222−2−222−2−200−22−i2i2-22002i−2i00−22−22−i2i2−i2i20000000000000000
χ4922-22-2-2-22-102i2i−2i−2i000-111-11-113−33−33−33−32-22i−2i00−i2i2−i2i222−2−2−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7002−2−i2i2-113−3−ii−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5022-22-2-2-22-102i2i−2i−2i000-111-11-113−33−33−33−32-22i−2i00i2−i2i2−i2−2−222−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−22i2−i2-113−3−ii−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5122-22-2-2-22-102i2i−2i−2i000-111-11-113−33−33−33−3-22−2i2i00−i2i2−i2i222−2−2−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−22i2−i21-1−33i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5222-22-2-2-22-102i2i−2i−2i000-111-11-113−33−33−33−3-22−2i2i00i2−i2i2−i2−2−222−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002−2−i2i21-1−33i−ii3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5322-22-2-2-22-102i2i−2i−2i000-111-11-11−33−33−33−332-22i−2i00−i2i2−i2i222−2−2−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23002−2−i2i2-11−33−iii3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5422-22-2-2-22-102i2i−2i−2i000-111-11-11−33−33−33−332-22i−2i00i2−i2i2−i2−2−222−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−22i2−i2-11−33−iii3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5522-22-2-2-22-102i2i−2i−2i000-111-11-11−33−33−33−33-22−2i2i00−i2i2−i2i222−2−2−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−22i2−i21-13−3i−i−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5622-22-2-2-22-102i2i−2i−2i000-111-11-11−33−33−33−33-22−2i2i00i2−i2i2−i2−2−222−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23002−2−i2i21-13−3i−i−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5722-22-2-2-22-10−2i−2i2i2i000-111-11-113−33−33−33−32-2−2i2i00−i2i2−i2i2−2−222ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−22−i2i2-113−3i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5822-22-2-2-22-10−2i−2i2i2i000-111-11-113−33−33−33−32-2−2i2i00i2−i2i2−i222−2−2ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7002−2i2−i2-113−3i−ii3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5922-22-2-2-22-10−2i−2i2i2i000-111-11-113−33−33−33−3-222i−2i00−i2i2−i2i2−2−222ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002−2i2−i21-1−33−ii−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6022-22-2-2-22-10−2i−2i2i2i000-111-11-113−33−33−33−3-222i−2i00i2−i2i2−i222−2−2ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−22−i2i21-1−33−ii−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6122-22-2-2-22-10−2i−2i2i2i000-111-11-11−33−33−33−332-2−2i2i00−i2i2−i2i2−2−222ii−i−i−i3−i3i3i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−22−i2i2-11−33i−i−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.