Finite Group Databasebeta

← Group #11781583

Character table — Group #11781583

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222222244444444444444444444444444444666666666666888888888888888881212121212121212121212121212121212122424242424244848487272144
order1222334444666666121212123444446661212121212121212121212121212121212121212888824242424242424241212121212121212121212121212121212888888242424242424242424242424882424242441212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ6111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ7111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11
χ8111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1
χ92222222-2-22222222-2-2-2-2222-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-2-22000000000000-222-2-222-2-22222-2-2-2-2000000000000000000000000000000
χ102222222-2-22222222-2-2-2-22-2-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-22000000000000-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000
χ11222222-222-22222222222200-200222-2-2-2-2-200000000222222-2222222222222-20000-2-2-2-200000000-2-20000-2-2-2-200000000000000000000
χ12222222-222-22222222222200-200222-2-2-2-2-200000000222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-200000000220000222200000000000000000000
χ13222222-2-2-2-2222222-2-2-2-2200200222-2-2-22200000000-2-2-2-2-2-2-200000000000020000-2-22200000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222-2-2-2-2222222-2-2-2-2200200222-2-2-22200000000-2-2-2-2-2-2-200000000000020000-2-2220000000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i000000000000
χ1522222-12222222-1-1-12222-122222-1-1-122-12222222222-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12-1-1000
χ1622222-12222222-1-1-12222-122222-1-1-122-12222222222-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-211000
χ1722222-12222222-1-1-12222-1-2-22-2-2-1-1-122-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1000000000000-11111-1-1-1-11111111100000000000000000022-1-1-1-1-211000
χ1822222-12222222-1-1-12222-1-2-22-2-2-1-1-122-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1000000000000-11111-1-1-1-111111111000000000000000000-2-211112-1-1000
χ1922222-12-2-22222-1-1-1-2-2-2-2-122-2-2-2-1-1-122-1-2-22222-2-2-2-2111111-10000000000001-1-111-1-111-1-1-1-1111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-12-2-22222-1-1-1-2-2-2-2-122-2-2-2-1-1-122-1-2-22222-2-2-2-2111111-10000000000001-1-111-1-111-1-1-1-1111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-12-2-22222-1-1-1-2-2-2-2-1-2-2-222-1-1-122-1-2-2-2-2-2-22222111111-1000000000000111-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-12-2-22222-1-1-1-2-2-2-2-1-2-2-222-1-1-122-1-2-2-2-2-2-22222111111-1000000000000111-1-1-1-1111111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-1-1-1222-1-1-1-1-122222-1-1-1-1-12-1-1-1-1-1-1-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ242222-122222-1-1-1222-1-1-1-1-122222-1-1-1-1-12-1-1-1-1-1-1-1-1-1-122-1-1-1-12-2-2-2-21111111122222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111000000000000
χ252222-122222-1-1-1222-1-1-1-1-1-2-22-2-2-1-1-1-1-12-1-11111111122-1-1-1-122222-1-1-1-1-1-1-1-12-2-2-2-2-1-1-1-11111111122-2-2-2-2-1-1-1-111111111000000000000
χ262222-122222-1-1-1222-1-1-1-1-1-2-22-2-2-1-1-1-1-12-1-11111111122-1-1-1-12-2-2-2-2111111112-2-2-2-2-1-1-1-111111111-2-222221111-1-1-1-1-1-1-1-1000000000000
χ272222-122-2-22-1-1-12221111-122-2-2-2-1-1-1-1-1211-1-1-1-11111-2-21111200003333−3−3−3−3-222-2-2-1-111-1-1-1-1111100000033−3−333−3−333−3−3000000000000
χ282222-122-2-22-1-1-12221111-122-2-2-2-1-1-1-1-1211-1-1-1-11111-2-2111120000−3−3−3−33333-222-2-2-1-111-1-1-1-11111000000−3−333−3−333−3−333000000000000
χ292222-122-2-22-1-1-12221111-1-2-2-222-1-1-1-1-12111111-1-1-1-1-2-21111200003333−3−3−3−3-2-2-222-1-1111111-1-1-1-100000033−3−3−3−333−3−333000000000000
χ302222-122-2-22-1-1-12221111-1-2-2-222-1-1-1-1-12111111-1-1-1-1-2-2111120000−3−3−3−33333-2-2-222-1-1111111-1-1-1-1000000−3−33333−3−333−3−3000000000000
χ312222-12-222-2-1-1-1222-1-1-1-1-100-200-1-1-111-211−i3−i3i3i3−i3−i3i3i322-1-1-1-1-22222-1-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3-2-200001111−i3−i3i3i3i3i3−i3−i3000000000000
χ322222-12-222-2-1-1-1222-1-1-1-1-100-200-1-1-111-211−i3−i3i3i3−i3−i3i3i322-1-1-1-1-2-2-2-2-211111111-200001111−i3−i3i3i3−i3−i3i3i3220000-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ332222-12-222-2-1-1-1222-1-1-1-1-100-200-1-1-111-211i3i3−i3−i3i3i3−i3−i322-1-1-1-1-22222-1-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3-2-200001111i3i3−i3−i3−i3−i3i3i3000000000000
χ342222-12-222-2-1-1-1222-1-1-1-1-100-200-1-1-111-211i3i3−i3−i3i3i3−i3−i322-1-1-1-1-2-2-2-2-211111111-200001111i3i3−i3−i3i3i3−i3−i3220000-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ352222-12-2-2-2-2-1-1-12221111-100200-1-1-111-2-1-1−i3−i3i3i3i3i3−i3−i3-2-21111-200003333−3−3−3−32000011-1-1−i3−i3i3i3i3i3−i3−i3002i2i−2i−2i−3−333−i−i−i−iiiii000000000000
χ362222-12-2-2-2-2-1-1-12221111-100200-1-1-111-2-1-1−i3−i3i3i3i3i3−i3−i3-2-21111-20000−3−3−3−333332000011-1-1−i3−i3i3i3i3i3−i3−i300−2i−2i2i2i33−3−3iiii−i−i−i−i000000000000
χ372222-12-2-2-2-2-1-1-12221111-100200-1-1-111-2-1-1i3i3−i3−i3−i3−i3i3i3-2-21111-200003333−3−3−3−32000011-1-1i3i3−i3−i3−i3−i3i3i300−2i−2i2i2i−3−333iiii−i−i−i−i000000000000
χ382222-12-2-2-2-2-1-1-12221111-100200-1-1-111-2-1-1i3i3−i3−i3−i3−i3i3i3-2-21111-20000−3−3−3−333332000011-1-1i3i3−i3−i3−i3−i3i3i3002i2i−2i−2i33−3−3−i−i−i−iiiii000000000000
χ3922-2-222200-2-22-22-2-2000022-2000-22-22-22002-22-20000000000-222−2−222−2−222−2−202-2002-2002-22-200002−22−22−22−22−22−22−22−22−2000000000000
χ4022-2-222200-2-22-22-2-2000022-2000-22-22-22002-22-20000000000-2−2−222−2−222−2−22202-2002-2002-22-20000−22−22−22−22−22−22−22−22−22000000000000
χ4122-2-222200-2-22-22-2-200002-22000-22-22-2200-22-220000000000-222−2−222−2−222−2−20-22002-200-22-2200002−2−22−222−22−2−22−22−22−22000000000000
χ4222-2-222200-2-22-22-2-200002-22000-22-22-2200-22-220000000000-2−2−222−2−222−2−2220-22002-200-22-220000−222−22−2−22−222−22−22−22−2000000000000
χ4322-2-222-2002-22-22-2-2000020002i−2i-22-2-22-20000002i−2i2i−2i000000222−2−222−2−222−2−20002i−2i-220000002i−2i2i−2i−22−i2i2i2−i2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-2-222-2002-22-22-2-2000020002i−2i-22-2-22-20000002i−2i2i−2i0000002−2−222−2−222−2−2220002i−2i-220000002i−2i2i−2i2−2i2−i2−i2i22−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-222-2002-22-22-2-200002000−2i2i-22-2-22-2000000−2i2i−2i2i000000222−2−222−2−222−2−2000−2i2i-22000000−2i2i−2i2i−22i2−i2−i2i2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ4622-2-222-2002-22-22-2-200002000−2i2i-22-2-22-2000000−2i2i−2i2i0000002−2−222−2−222−2−222000−2i2i-22000000−2i2i−2i2i2−2−i2i2i2−i22−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-2-2-12200-21-112-2-23−33−3-12-20001-11-1123−3-11-113−3−330033−3−3-222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ702-200-113−3-11-113−3−332−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4822-2-2-12200-21-112-2-23−33−3-12-20001-11-1123−3-11-113−3−330033−3−3-2−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ702-200-113−3-11-113−3−33−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ4922-2-2-12200-21-112-2-23−33−3-1-220001-11-1123−31-11-1−333−30033−3−3-222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70-2200-113−31-11-1−333−32−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5022-2-2-12200-21-112-2-23−33−3-1-220001-11-1123−31-11-1−333−30033−3−3-2−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70-2200-113−31-11-1−333−3−222−22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5122-2-2-12200-21-112-2-2−33−33-12-20001-11-112−33-11-11−333−300−3−333-222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2302-200-11−33-11-11−333−32−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5222-2-2-12200-21-112-2-2−33−33-12-20001-11-112−33-11-11−333−300−3−333-2−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2302-200-11−33-11-11−333−3−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5322-2-2-12200-21-112-2-2−33−33-1-220001-11-112−331-11-13−3−3300−3−333-222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230-2200-11−331-11-13−3−332−2−22−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5422-2-2-12200-21-112-2-2−33−33-1-220001-11-112−331-11-13−3−3300−3−333-2−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230-2200-11−331-11-13−3−33−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5522-2-2-12-20021-112-2-23−33−3-10002i−2i1-111-1-2−33−i3i3i3−i3−ii−ii0033−3−3222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70002i−2i1-1−33−i3i3i3−i3−ii−ii−22−i2i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5622-2-2-12-20021-112-2-23−33−3-10002i−2i1-111-1-2−33−i3i3i3−i3−ii−ii0033−3−32−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70002i−2i1-1−33−i3i3i3−i3−ii−ii2−2i2−i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5722-2-2-12-20021-112-2-23−33−3-1000−2i2i1-111-1-2−33i3−i3−i3i3i−ii−i0033−3−3222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000−2i2i1-1−33i3−i3−i3i3i−ii−i−22i2−i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5822-2-2-12-20021-112-2-23−33−3-1000−2i2i1-111-1-2−33i3−i3−i3i3i−ii−i0033−3−32−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000−2i2i1-1−33i3−i3−i3i3i−ii−i2−2−i2i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5922-2-2-12-20021-112-2-2−33−33-10002i−2i1-111-1-23−3i3−i3−i3i3−ii−ii00−3−333222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230002i−2i1-13−3i3−i3−i3i3−ii−ii−22−i2i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ6022-2-2-12-20021-112-2-2−33−33-10002i−2i1-111-1-23−3i3−i3−i3i3−ii−ii00−3−3332−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230002i−2i1-13−3i3−i3−i3i3−ii−ii2−2i2−i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ6122-2-2-12-20021-112-2-2−33−33-1000−2i2i1-111-1-23−3−i3i3i3−i3i−ii−i00−3−333222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000−2i2i1-13−3−i3i3i3−i3i−ii−i−22i2−i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ6222-2-2-12-20021-112-2-2−33−33-1000−2i2i1-111-1-23−3−i3i3i3−i3i−ii−i00−3−3332−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000−2i2i1-13−3−i3i3i3−i3i−ii−i2−2−i2i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.