Finite Group Databasebeta

← Group #10698210

Character table — Group #10698210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ9222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000
χ10222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000
χ11222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ12222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−3000000000000
χ2022222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−33333000000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−3000000000000
χ23222-22-2-2-2222-20000-22-22-2-22-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−22-20022−2−222-2-2000022−2−222−2−2000000000000
χ24222-22-2-2-2222-20000-22-22-2-22-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−2-2200−2−222-2-2220000−2−222−2−222000000000000
χ25222-22-2-2-2222-20000-22-22-2-22-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−222222-200−2−22222-2-20000−2−222−2−222000000000000
χ26222-22-2-2-2222-20000-22-22-2-22-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−22222-220022−2−2-2-222000022−2−222−2−2000000000000
χ27222-22-2-2-2-122-20000-2-11-111-11333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ232-20022−2−2-1-11133−3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ28222-22-2-2-2-122-20000-2-11-111-11333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23-2200−2−22211-1-1−3−333−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ29222-22-2-2-2-122-20000-2-11-111-11333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ232-200−2−222-1-11133−3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ30222-22-2-2-2-122-20000-2-11-111-11333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23-220022−2−211-1-1−3−333ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ31222-22-2-2-2-122-20000-2-11-111-11−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ72-20022−2−2-1-111−3−333ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ32222-22-2-2-2-122-20000-2-11-111-11−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7-2200−2−22211-1-133−3−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ33222-22-2-2-2-122-20000-2-11-111-11−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ72-200−2−222-1-111−3−333−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ34222-22-2-2-2-122-20000-2-11-111-11−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7-220022−2−211-1-133−3−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ3522-2-2-222-220002-2-22022-22-2-2-22-2-22-2-22200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000002-200−i2−i2i2i20000
χ3622-2-2-222-220002-2-22022-22-2-2-22-2-22-2-22200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000-2200i2i2−i2−i20000
χ3722-2-2-222-220002-2-22022-22-2-2-22-2-22-2-22200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000002-200i2i2−i2−i20000
χ3822-2-2-222-220002-2-22022-22-2-2-22-2-22-2-22200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000-2200−i2−i2i2i20000
χ392-222-2-22-222-2222-2-2-2-2-2222-2-222-222-2-2-22-2000000002-22-222-2-20000000000000000000000000000000000000000000000002-200
χ402-222-2-22-222-2222-2-2-2-2-2222-2-222-222-2-2-22-2000000002-22-222-2-2000000000000000000000000000000000000000000000000-2200
χ412-222-2-22-222-22-2-222-2-2-2222-2-2-2-22-2-2222-22000000002-22-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i0000
χ422-222-2-22-222-22-2-222-2-2-2222-2-2-2-22-2-2222-22000000002-22-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ432-222-2-22-22-22-222-2-22-2-2222-2-222-222-2-2-2-2200000000-22-22-2-222000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ442-222-2-22-22-22-222-2-22-2-2222-2-222-222-2-2-2-2200000000-22-22-2-22200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ452-222-2-22-22-22-2-2-2222-2-2222-2-2-2-22-2-22222-22i−2i2i−2i2i−2i2i−2i-22-2222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ462-222-2-22-22-22-2-2-2222-2-2222-2-2-2-22-2-22222-2−2i2i−2i2i−2i2i−2i2i-22-2222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ472-222-2-22-2-1-22-222-2-2211-1-1-111-1-11-1-1111-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300002i−2i2i−2i3−33−33−33−3−ii−ii−ii−ii000000000000
χ482-222-2-22-2-1-22-222-2-2211-1-1-111-1-11-1-1111-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000−2i2i−2i2i−33−33−33−33i−ii−ii−ii−i000000000000
χ492-222-2-22-2-1-22-222-2-2211-1-1-111-1-11-1-1111-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300002i−2i2i−2i−33−33−33−33−ii−ii−ii−ii000000000000
χ502-222-2-22-2-1-22-222-2-2211-1-1-111-1-11-1-1111-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000−2i2i−2i2i3−33−33−33−3i−ii−ii−ii−i000000000000
χ512-222-2-22-2-1-22-2-2-222211-1-1-11111-111-1-1-12-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i3000000000000
χ522-222-2-22-2-1-22-2-2-222211-1-1-11111-111-1-1-12-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i3000000000000
χ532-222-2-22-2-1-22-2-2-222211-1-1-11111-111-1-1-12-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i3000000000000
χ542-222-2-22-2-1-22-2-2-222211-1-1-11111-111-1-1-12-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i3000000000000
χ552-22-2-22-222-2220000-2-222-2-2-220000000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2002-2−i2i2i2−i20000-222-2−i2i2i2−i2−i2i2i2−i2000000000000
χ562-22-2-22-222-2220000-2-222-2-2-220000000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200-22i2−i2−i2i200002-2-22i2−i2−i2i2i2−i2−i2i2000000000000
χ572-22-2-22-222-2220000-2-222-2-2-220000000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2002-2i2−i2−i2i20000-222-2i2−i2−i2i2i2−i2−i2i2000000000000
χ582-22-2-22-222-2220000-2-222-2-2-220000000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200-22−i2i2i2−i200002-2-22−i2i2i2−i2−i2i2i2−i2000000000000
χ592-22-2-22-22-1-2220000-21-1-1111-133−3−3−33−3300−i2i2−i2i2i2−i2i2−i21-1-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23002-2−i2i2i2−i23−3−331-1-11ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ602-22-2-22-22-1-2220000-21-1-1111-133−3−3−33−3300−i2i2−i2i2i2−i2i2−i21-1-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300-22i2−i2−i2i2−333−3-111-1−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ612-22-2-22-22-1-2220000-21-1-1111-133−3−3−33−3300i2−i2i2−i2−i2i2−i2i21-1-11−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23002-2i2−i2−i2i23−3−331-1-11−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ622-22-2-22-22-1-2220000-21-1-1111-133−3−3−33−3300i2−i2i2−i2−i2i2−i2i21-1-11−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300-22−i2i2i2−i2−333−3-111-1ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ632-22-2-22-22-1-2220000-21-1-1111-1−3−3333−33−300−i2i2−i2i2i2−i2i2−i21-1-113−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7002-2−i2i2i2−i2−333−31-1-11ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.