Finite Group Databasebeta

← Group #10698915

Character table — Group #10698915

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order122222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424444488881212121212121212242424242424242444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-20000000000000000
χ10222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-222220000000000000000
χ112222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i0000
χ122222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i0000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000000000000000000000−2i2i
χ15222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ17222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ18222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ19222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−300000000
χ20222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−3333300000000
χ21222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−3333300000000
χ22222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−300000000
χ232222-2-222-222-2-22-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-2000000000000000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000
χ242222-2-222-222-2-22-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000
χ252222-2-222-2-2-2222-2-2-2-2-2222-2-2-2-22222-222222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ262222-2-222-2-2-2222-2-2-2-2-2222-2-2-2-22222-22-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ272222-2-22-2222-2-2-22-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-222000000000000000000000000000000000000000000002-200
χ282222-2-22-2222-2-2-22-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-22200000000000000000000000000000000000000000000-2200
χ292222-2-22-22-2-222-22-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-200000000000000000000000000000000000000002-2000000
χ302222-2-22-22-2-222-22-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-20000000000000000000000000000000000000000-22000000
χ312222-2-2-12-222-2-22-21111-1-1-1-1-1-1-111112-200000000-1-111-1-1113333−3−3−3−3−3−3−3−3333300002i2i−2i−2i−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00000000
χ322222-2-2-12-222-2-22-21111-1-1-1-1-1-1-111112-200000000-1-111-1-1113333−3−3−3−3−3−3−3−333330000−2i−2i2i2ii3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00000000
χ332222-2-2-12-222-2-22-21111-1-1-1-1-1-1-111112-200000000-1-111-1-111−3−3−3−333333333−3−3−3−300002i2i−2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00000000
χ342222-2-2-12-222-2-22-21111-1-1-1-1-1-1-111112-200000000-1-111-1-111−3−3−3−333333333−3−3−3−30000−2i−2i2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00000000
χ352222-2-2-12-2-2-2222-21111-1-1-11111-1-1-1-1-222222-2-2-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000
χ362222-2-2-12-2-2-2222-21111-1-1-11111-1-1-1-1-222222-2-2-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000
χ372222-2-2-12-2-2-2222-21111-1-1-11111-1-1-1-1-22-2-2-2-22222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000
χ382222-2-2-12-2-2-2222-21111-1-1-11111-1-1-1-1-22-2-2-2-22222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000
χ3922-2-22-22220000-2-222-2-2-22-2000000000022−2−222−2−22-22-2000022−2−222−2−222−2−222−2−22-2002−22−22-22-200002−22−22−22−200000000
χ4022-2-22-22220000-2-222-2-2-22-2000000000022−2−222−2−22-22-2000022−2−222−2−222−2−222−2−2-2200−22−22-22-220000−22−22−22−2200000000
χ4122-2-22-22220000-2-222-2-2-22-20000000000−2−222−2−2222-22-20000−2−222−2−222−2−222−2−2222-200−22−222-22-20000−22−22−22−2200000000
χ4222-2-22-22220000-2-222-2-2-22-20000000000−2−222−2−2222-22-20000−2−222−2−222−2−222−2−222-22002−22−2-22-2200002−22−22−22−200000000
χ4322-2-22-2-1220000-2-2-1-1111-1133−3−33−33−30022−2−222−2−2-11-113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232-2002−22−2-11-113−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ4422-2-22-2-1220000-2-2-1-1111-1133−3−33−33−30022−2−222−2−2-11-113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-2200−22−221-11-1−33−33−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ4522-2-22-2-1220000-2-2-1-1111-1133−3−33−33−300−2−222−2−222-11-113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232-200−22−22-11-113−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ4622-2-22-2-1220000-2-2-1-1111-1133−3−33−33−300−2−222−2−222-11-113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-22002−22−21-11-1−33−33ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ4722-2-22-2-1220000-2-2-1-1111-11−3−333−33−330022−2−222−2−2-11-11−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72-2002−22−2-11-11−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ4822-2-22-2-1220000-2-2-1-1111-11−3−333−33−330022−2−222−2−2-11-11−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-2200−22−221-11-13−33−3−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ4922-2-22-2-1220000-2-2-1-1111-11−3−333−33−3300−2−222−2−222-11-11−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72-200−22−22-11-11−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ5022-2-22-2-1220000-2-2-1-1111-11−3−333−33−3300−2−222−2−222-11-11−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-22002−22−21-11-13−33−3ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ5122-2-2-2222-20000-22-2-222-22-2000000000022−2−2−2−2222-2-22000022−2−2−2−22222−2−2−2−222002i−2i−i2i2i2−i200002i−2i−2i2i−i2i2i2−i2−i2i2i2−i200000000
χ5222-2-2-2222-20000-22-2-222-22-2000000000022−2−2−2−2222-2-22000022−2−2−2−22222−2−2−2−22200−2i2ii2−i2−i2i20000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i200000000
χ5322-2-2-2222-20000-22-2-222-22-20000000000−2−22222−2−22-2-220000−2−22222−2−2−2−22222−2−2002i−2ii2−i2−i2i200002i−2i−2i2ii2−i2−i2i2i2−i2−i2i200000000
χ5422-2-2-2222-20000-22-2-222-22-20000000000−2−22222−2−22-2-220000−2−22222−2−2−2−22222−2−200−2i2i−i2i2i2−i20000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i200000000
χ5522-2-2-22-12-20000-2211-1-11-1133−3−3−33−330022−2−2−2−222-111-13−3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002i−2i−i2i2i2−i2−i3i3i3−i3−iii−iζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ5622-2-2-22-12-20000-2211-1-11-1133−3−3−33−330022−2−2−2−222-111-13−3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−2i2ii2−i2−i2i2i3−i3−i3i3i−i−ii−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ5722-2-2-22-12-20000-2211-1-11-1133−3−3−33−3300−2−22222−2−2-111-13−3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7002i−2ii2−i2−i2i2−i3i3i3−i3−iii−i−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ5822-2-2-22-12-20000-2211-1-11-1133−3−3−33−3300−2−22222−2−2-111-13−3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−2i2i−i2i2i2−i2i3−i3−i3i3i−i−iiζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ5922-2-2-22-12-20000-2211-1-11-11−3−3333−33−30022−2−2−2−222-111-1−333−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23002i−2i−i2i2i2−i2i3−i3−i3i3−iii−iζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ6022-2-2-22-12-20000-2211-1-11-11−3−3333−33−30022−2−2−2−222-111-1−333−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−2i2ii2−i2−i2i2−i3i3i3−i3i−i−ii−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ6122-2-2-22-12-20000-2211-1-11-11−3−3333−33−300−2−22222−2−2-111-1−333−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23002i−2ii2−i2−i2i2i3−i3−i3i3−iii−i−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ6222-2-2-22-12-20000-2211-1-11-11−3−3333−33−300−2−22222−2−2-111-1−333−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−2i2i−i2i2i2−i2−i3i3i3−i3i−i−iiζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ63444444-2-4-44444-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-40000000022222222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-22222222244000000002222-2-2-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-2-4444-4-4-442222-2-2-2-2-2-2-22222-440000000022-2-222-2-2000000000000000000000000000000000000000000000000
χ664444-4-4-2-44-4-444-442222-2-2-22222-2-2-2-24-40000000022-2-2-2-222000000000000000000000000000000000000000000000000
χ6744-4-44-44-4-400004444-4-4-44-4000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ6844-4-44-4-2-4-4000044-2-2222-222323−23−2323−2323−2300000000002-22-2−2323−2323000000000000000000000000000000000000000000000000
χ6944-4-44-4-2-4-4000044-2-2222-22−23−232323−2323−232300000000002-22-223−2323−23000000000000000000000000000000000000000000000000
χ7044-4-4-444-4400004-4-4-444-44-4000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ7144-4-4-44-2-4400004-422-2-22-222323−23−23−2323−232300000000002-2-22−232323−23000000000000000000000000000000000000000000000000
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χ734-44-400400004-40000004-4-4000044-4-400000022−2222−2200000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ744-44-400400004-40000004-4-4000044-4-4000000−2222−2222000000000000−2222−22220000−2222−222200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.