Finite Group Databasebeta

← Group #10858916

Character table — Group #10858916

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222222234444666666612121212121212124444446666888888881212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
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
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-11
χ1011111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1
χ1111111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1
χ1211111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-11
χ1311111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-11-1
χ1411111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-11
χ1511111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-11
χ1611111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222222200000000-2-2-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000220000-2-222-2-222000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-10000000011113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1000000001111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ2722222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000222200000000000000002-2000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-2-2-20000000022220000000000000000-220000-2-22222-2-2000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-2222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-22-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-2-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-13333−3−3−3−3−3−3−3−333332-20000-1-11111-1-133−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-1−3−3−3−333333333−3−3−3−32-20000-1-11111-1-1−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222111100000000-1-1-1-13333−3−3−3−3−3−3−3−33333-22000011-1-1-1-111−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−3-22000011-1-1-1-11133−3−3−3−3330000000000000000
χ3722-222-2-2-222-2-2222-2-222-2-2-2-222222-2-2-2-22-2000022-2-20000000022-2-20000000000000000000000000000000000000000002-22-200000000
χ3822-222-2-2-222-2-2222-2-222-2-2-2-222222-2-2-2-22-2000022-2-20000000022-2-2000000000000000000000000000000000000000000-22-2200000000
χ3922-222-2-2-222-2-22-2-22222-2-2-2-22-2-2-2-22222-22000022-2-200000000-2-222000000000000000000000000000000000000002i2i−2i−2i000000002i−2i00
χ4022-222-2-2-222-2-22-2-22222-2-2-2-22-2-2-2-22222-22000022-2-200000000-2-22200000000000000000000000000000000000000−2i−2i2i2i00000000−2i2i00
χ4122-222-2-2-2-2-222222-2-222-2-2-2-222222-2-2-2-2-220000-2-22200000000-2-2220000000000000000000000000000000000000000002-2-2200000000
χ4222-222-2-2-2-2-222222-2-222-2-2-2-222222-2-2-2-2-220000-2-22200000000-2-222000000000000000000000000000000000000000000-222-200000000
χ4322-222-2-2-2-2-2222-2-22222-2-2-2-22-2-2-2-222222-20000-2-2220000000022-2-2000000000000000000000000000000000000002i2i−2i−2i00000000−2i2i00
χ4422-222-2-2-2-2-2222-2-22222-2-2-2-22-2-2-2-222222-20000-2-2220000000022-2-200000000000000000000000000000000000000−2i−2i2i2i000000002i−2i00
χ452-222-2-2-22000022-22-2-2-222-2-2222-2-222-2-200000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002-22-200002i−2i000000
χ462-222-2-2-22000022-22-2-2-222-2-2222-2-222-2-200000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-22-220000−2i2i000000
χ472-222-2-2-22000022-22-2-2-222-2-2222-2-222-2-20000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002-22-20000−2i2i000000
χ482-222-2-2-22000022-22-2-2-222-2-2222-2-222-2-20000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-22-2200002i−2i000000
χ492-22-22-22-22-22-2200002-22-22-2-200000000002i−2i2i−2i2-22-2−i2i2−i2i2−i2−i2i2i20000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2002−22−22i−2i002i−2i002−22−22−22−20000000000000000
χ502-22-22-22-22-22-2200002-22-22-2-200000000002i−2i2i−2i2-22-2i2−i2i2−i2i2i2−i2−i20000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200−22−222i−2i002i−2i00−22−22−22−220000000000000000
χ512-22-22-22-22-22-2200002-22-22-2-20000000000−2i2i−2i2i2-22-2−i2i2−i2i2−i2−i2i2i20000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200−22−22−2i2i00−2i2i00−22−22−22−220000000000000000
χ522-22-22-22-22-22-2200002-22-22-2-20000000000−2i2i−2i2i2-22-2i2−i2i2−i2i2i2−i2−i20000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002−22−2−2i2i00−2i2i002−22−22−22−20000000000000000
χ532-22-22-22-22-22-2-10000-11-11-1113−33−33−33−3002i−2i2i−2i-11-11−i2i2−i2i2−i2−i2i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+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
χ542-22-22-22-22-22-2-10000-11-11-1113−33−33−33−3002i−2i2i−2i-11-11i2−i2i2−i2i2i2−i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−22−22−ii−i3i3−ii−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ552-22-22-22-22-22-2-10000-11-11-1113−33−33−33−300−2i2i−2i2i-11-11−i2i2−i2i2−i2−i2i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−22−22i−ii3−i3i−ii3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ562-22-22-22-22-22-2-10000-11-11-1113−33−33−33−300−2i2i−2i2i-11-11i2−i2i2−i2i2i2−i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−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
χ572-22-22-22-22-22-2-10000-11-11-111−33−33−33−33002i−2i2i−2i-11-11−i2i2−i2i2−i2−i2i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+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
χ582-22-22-22-22-22-2-10000-11-11-111−33−33−33−33002i−2i2i−2i-11-11i2−i2i2−i2i2i2−i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−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
χ592-22-22-22-22-22-2-10000-11-11-111−33−33−33−3300−2i2i−2i2i-11-11−i2i2−i2i2−i2−i2i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+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
χ602-22-22-22-22-22-2-10000-11-11-111−33−33−33−3300−2i2i−2i2i-11-11i2−i2i2−i2i2i2−i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−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
χ612-22-22-22-2-22-22200002-22-22-2-200000000002i−2i−2i2i-22-22−i2i2−i2i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2002−2−222i−2i00−2i2i002−22−2−22−220000000000000000
χ622-22-22-22-2-22-22200002-22-22-2-200000000002i−2i−2i2i-22-22i2−i2i2−i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i200−222−22i−2i00−2i2i00−22−222−22−20000000000000000
χ632-22-22-22-2-22-22200002-22-22-2-20000000000−2i2i2i−2i-22-22−i2i2−i2i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i200−222−2−2i2i002i−2i00−22−222−22−20000000000000000
χ642-22-22-22-2-22-22200002-22-22-2-20000000000−2i2i2i−2i-22-22i2−i2i2−i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2002−2−22−2i2i002i−2i002−22−2−22−220000000000000000
χ652-22-22-22-2-22-22-10000-11-11-1113−33−33−33−3002i−2i−2i2i1-11-1−i2i2−i2i2i2i2−i2−i2−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+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
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.