Finite Group Databasebeta

← Group #10828131

Character table — Group #10828131

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222222222344446666666121212121212121222444466668888888812121212242424242424242424242424242424244466888812121212121224242424242424242222222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-111-11
χ1211111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-11-1
χ1311111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000000000-2-222000022-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2000000000000000022-2-20000-2-22222000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2111111111111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2112222111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-10000000011113333−3−3−3−33333−3−3−3−3-2-2-1-10000-1-1111133−3−333−3−30000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1000000001111−3−3−3−33333−3−3−3−33333-2-2-1-10000-1-11111−3−333−3−3330000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-10000000011113333−3−3−3−33333−3−3−3−32211000011-1-1-1-1−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1000000001111−3−3−3−33333−3−3−3−333332211000011-1-1-1-133−3−333−3−30000000000000000
χ2722222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000222200000000000000002-2220000-2-222-2-2000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022220000000000000000-22-2-2000022-2-222000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-22-1-122-2-21111-1-1-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-22-1-1-2-2221111-1-11111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-211-2-222-1-1-1-1111111-1-1-1-10000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-21122-2-2-1-1-1-111-1-1-1-111110000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-13333−3−3−3−3−3−3−3−333332-2-1-1000011-1-11133−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2111100000000-1-1-1-1−3−3−3−333333333−3−3−3−32-2-1-1000011-1-111−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-13333−3−3−3−3−3−3−3−33333-22110000-1-111-1-1−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-1−3−3−3−333333333−3−3−3−3-22110000-1-111-1-133−3−3−3−3330000000000000000
χ3722-2-222-2-20000222-2-222-2-2-2-222222-2-2-2-2000000000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000022-2-2000000002i−2i00
χ3822-2-222-2-20000222-2-222-2-2-2-222222-2-2-2-2000000000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000-2-22200000000−2i2i00
χ3922-2-222-2-20000222-2-222-2-2-2-222222-2-2-2-200000000000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000022-2-200000000−2i2i00
χ4022-2-222-2-20000222-2-222-2-2-2-222222-2-2-2-200000000000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000-2-222000000002i−2i00
χ412-22-22-22-2000022-22-2-2-222-2-2222-2-222-2-200000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002-22-20000002i−2i0000
χ422-22-22-22-2000022-22-2-2-222-2-2222-2-222-2-200000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-22-22000000−2i2i0000
χ432-22-22-22-2000022-22-2-2-222-2-2222-2-222-2-20000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002-22-2000000−2i2i0000
χ442-22-22-22-2000022-22-2-2-222-2-2222-2-222-2-20000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-22-220000002i−2i0000
χ452-2-222-2-2222-2-222-2-22-2-2-2-222222-2-2-2-222002-20022-2-20000000022-2-2000000000000000000000000000000000000002-2-222-20000000000
χ462-2-222-2-2222-2-222-2-22-2-2-2-222222-2-2-2-222002-20022-2-20000000022-2-200000000000000000000000000000000000000-222-2-220000000000
χ472-2-222-2-2222-2-22-222-2-2-2-2-2222-2-22222-2-200-220022-2-200000000-2-222000000000000000000000000000000000000000000002-22-2000000
χ482-2-222-2-2222-2-22-222-2-2-2-2-2222-2-22222-2-200-220022-2-200000000-2-22200000000000000000000000000000000000000000000-22-22000000
χ492-2-222-2-22-2-22222-2-22-2-2-2-222222-2-2-2-22200-2200-2-22200000000-2-222000000000000000000000000000000000000002-2-22-220000000000
χ502-2-222-2-22-2-22222-2-22-2-2-2-222222-2-2-2-22200-2200-2-22200000000-2-22200000000000000000000000000000000000000-222-22-20000000000
χ512-2-222-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-2002-200-2-2220000000022-2-2000000000000000000000000000000000000000000002-2-22000000
χ522-2-222-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-2002-200-2-2220000000022-2-200000000000000000000000000000000000000000000-222-2000000
χ532-2-2-2-22222-22-2200002-22-22-2-2000000002-2002-22-22-22−22−22−22−200002−22−22−22−22−22−22−22−2002-22−22−22-200002−22−22−22−20000000000000000
χ542-2-2-2-22222-22-2200002-22-22-2-2000000002-2002-22-22-2−22−22−22−220000−22−22−22−22−22−22−22−22002-2−22−222-20000−22−22−22−220000000000000000
χ552-2-2-2-22222-22-2200002-22-22-2-200000000-2200-222-22-22−22−22−22−200002−22−22−22−22−22−22−22−200-22−22−22-220000−22−22−22−220000000000000000
χ562-2-2-2-22222-22-2200002-22-22-2-200000000-2200-222-22-2−22−22−22−220000−22−22−22−22−22−22−22−2200-222−22−2-2200002−22−22−22−20000000000000000
χ572-2-2-2-22222-22-2-10000-11-11-1113−33−33−33−32-2002-2-11-112−22−22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300-112−22−2-113−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ582-2-2-2-22222-22-2-10000-11-11-1113−33−33−33−32-2002-2-11-11−22−22−22−223−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300-11−22−22-113−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ592-2-2-2-22222-22-2-10000-11-11-1113−33−33−33−3-2200-22-11-112−22−22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23001-1−22−221-1−33−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ602-2-2-2-22222-22-2-10000-11-11-1113−33−33−33−3-2200-22-11-11−22−22−22−223−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23001-12−22−21-1−33−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ612-2-2-2-22222-22-2-10000-11-11-111−33−33−33−332-2002-2-11-112−22−22−22−2−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700-112−22−2-11−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ622-2-2-2-22222-22-2-10000-11-11-111−33−33−33−332-2002-2-11-11−22−22−22−22−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700-11−22−22-11−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ632-2-2-2-22222-22-2-10000-11-11-111−33−33−33−33-2200-22-11-112−22−22−22−2−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7001-1−22−221-13−33−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ642-2-2-2-22222-22-2-10000-11-11-111−33−33−33−33-2200-22-11-11−22−22−22−22−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7001-12−22−21-13−33−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ652-2-2-2-2222-22-22200002-22-22-2-2000000002-200-22-22-222−22−2−22−2200002−22−22−22−2−22−22−22−22002-22−2−22-2200002−22−2−22−220000000000000000
χ662-2-2-2-2222-22-22200002-22-22-2-2000000002-200-22-22-22−22−222−22−20000−22−22−22−222−22−22−22−2002-2−222−2-220000−22−222−22−20000000000000000
χ672-2-2-2-2222-22-22200002-22-22-2-200000000-22002-2-22-222−22−2−22−2200002−22−22−22−2−22−22−22−2200-22−222−22-20000−22−222−22−20000000000000000
χ682-2-2-2-2222-22-22200002-22-22-2-200000000-22002-2-22-22−22−222−22−20000−22−22−22−222−22−22−22−200-222−2−222-200002−22−2−22−220000000000000000
χ692-2-2-2-2222-22-22-10000-11-11-1113−33−33−33−32-200-221-11-12−22−2−22−22−33−33ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300-112−2−221-1−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ702-2-2-2-2222-22-22-10000-11-11-1113−33−33−33−32-200-221-11-1−22−222−22−2−33−33−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300-11−222−21-1−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ712-2-2-2-2222-22-22-10000-11-11-1113−33−33−33−3-22002-21-11-12−22−2−22−22−33−33ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23001-1−222−2-113−3−33−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.