Finite Group Databasebeta

← Group #10858751

Character table — Group #10858751

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212122244446666888888881212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1
χ1011111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ1111111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-11
χ1211111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1
χ1311111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-11
χ1411111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-11-1
χ1511111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-11-1
χ1611111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ17222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022220000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000220000-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2222200000000-2-2-2-20000000000000000-22000022-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-200000000000000002-20000-2-22222-2-2000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-22-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-2222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-13333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-1−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2111100000000-1-1-1-13333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2111100000000-1-1-1-1−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333-220000-1-11111-1-133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3-220000-1-11111-1-1−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-10000000011113333−3−3−3−3−3−3−3−333332-2000011-1-1-1-111−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1000000001111−3−3−3−333333333−3−3−3−32-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ372222-2-2-2-222222-2-2-2-222-2-2-2-222222-2-2-2-22-2000022-2-20000000022-2-20000000000000000000000000000000000000000002-22-200000000
χ382222-2-2-2-222222-2-2-2-222-2-2-2-222222-2-2-2-22-2000022-2-20000000022-2-2000000000000000000000000000000000000000000-22-2200000000
χ392222-2-2-2-2222-2-222-2-222-2-2-2-222222-2-2-2-2-220000-2-22200000000-2-2220000000000000000000000000000000000000000002-2-2200000000
χ402222-2-2-2-2222-2-222-2-222-2-2-2-222222-2-2-2-2-220000-2-22200000000-2-222000000000000000000000000000000000000000000-222-200000000
χ412222-2-2-2-22-2-222-2-22222-2-2-2-22-2-2-2-22222-220000-2-2220000000022-2-2000000000000000000000000000000000000002i2i−2i−2i00002i−2i000000
χ422222-2-2-2-22-2-222-2-22222-2-2-2-22-2-2-2-22222-220000-2-2220000000022-2-200000000000000000000000000000000000000−2i−2i2i2i0000−2i2i000000
χ432222-2-2-2-22-2-2-2-2222222-2-2-2-22-2-2-2-222222-2000022-2-200000000-2-222000000000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ442222-2-2-2-22-2-2-2-2222222-2-2-2-22-2-2-2-222222-2000022-2-200000000-2-22200000000000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ4522-2-22-22-22002i−2i2i−2i002-222-2-2-200000000002i−2i2-20000−i2−i2i2i222−2−22i−2i2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2002−2−i2i22i−2i002-2002−22−2−i2i2−i2i20000000000000000
χ4622-2-22-22-22002i−2i2i−2i002-222-2-2-200000000002i−2i2-20000i2i2−i2−i2−2−2222i−2i2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200−22i2−i22i−2i002-200−22−22i2−i2i2−i20000000000000000
χ4722-2-22-22-22002i−2i2i−2i002-222-2-2-20000000000−2i2i-220000−i2−i2i2i222−2−22i−2i2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200−22i2−i2−2i2i00-2200−22−22i2−i2i2−i20000000000000000
χ4822-2-22-22-22002i−2i2i−2i002-222-2-2-20000000000−2i2i-220000i2i2−i2−i2−2−2222i−2i2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222002−2−i2i2−2i2i00-22002−22−2−i2i2−i2i20000000000000000
χ4922-2-22-22-2200−2i2i−2i2i002-222-2-2-200000000002i−2i-220000−i2−i2i2i2−2−222−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222002−2i2−i22i−2i00-22002−22−2i2−i2i2−i20000000000000000
χ5022-2-22-22-2200−2i2i−2i2i002-222-2-2-200000000002i−2i-220000i2i2−i2−i222−2−2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200−22−i2i22i−2i00-2200−22−22−i2i2−i2i20000000000000000
χ5122-2-22-22-2200−2i2i−2i2i002-222-2-2-20000000000−2i2i2-20000−i2−i2i2i2−2−222−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−22−i2i2−2i2i002-200−22−22−i2i2−i2i20000000000000000
χ5222-2-22-22-2200−2i2i−2i2i002-222-2-2-20000000000−2i2i2-20000i2i2−i2−i222−2−2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2002−2i2−i2−2i2i002-2002−22−2i2−i2i2−i20000000000000000
χ5322-2-22-22-2-1002i−2i2i−2i00-11-1-111133−3−33−33−3002i−2i2-2−i3i3−i3i3−i2−i2i2i222−2−2−ii−iiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7002−2−i2i2−ii−i3i3-113−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5422-2-22-22-2-1002i−2i2i−2i00-11-1-111133−3−33−33−3002i−2i2-2−i3i3−i3i3i2i2−i2−i2−2−222−ii−ii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−22i2−i2−ii−i3i3-113−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5522-2-22-22-2-1002i−2i2i−2i00-11-1-111133−3−33−33−300−2i2i-22−i3i3−i3i3−i2−i2i2i222−2−2−ii−iiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−22i2−i2i−ii3−i31-1−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5622-2-22-22-2-1002i−2i2i−2i00-11-1-111133−3−33−33−300−2i2i-22−i3i3−i3i3i2i2−i2−i2−2−222−ii−ii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002−2−i2i2i−ii3−i31-1−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5722-2-22-22-2-1002i−2i2i−2i00-11-1-1111−3−333−33−33002i−2i2-2i3−i3i3−i3−i2−i2i2i222−2−2−ii−iiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23002−2−i2i2−iii3−i3-11−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5822-2-22-22-2-1002i−2i2i−2i00-11-1-1111−3−333−33−33002i−2i2-2i3−i3i3−i3i2i2−i2−i2−2−222−ii−ii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−22i2−i2−iii3−i3-11−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5922-2-22-22-2-1002i−2i2i−2i00-11-1-1111−3−333−33−3300−2i2i-22i3−i3i3−i3−i2−i2i2i222−2−2−ii−iiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−22i2−i2i−i−i3i31-13−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ6022-2-22-22-2-1002i−2i2i−2i00-11-1-1111−3−333−33−3300−2i2i-22i3−i3i3−i3i2i2−i2−i2−2−222−ii−ii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23002−2−i2i2i−i−i3i31-13−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6122-2-22-22-2-100−2i2i−2i2i00-11-1-111133−3−33−33−3002i−2i-22i3−i3i3−i3−i2−i2i2i2−2−222i−ii−iζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002−2i2−i2−ii−i3i31-1−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6222-2-22-22-2-100−2i2i−2i2i00-11-1-111133−3−33−33−3002i−2i-22i3−i3i3−i3i2i2−i2−i222−2−2i−ii−i−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−22−i2i2−ii−i3i31-1−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+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.