Finite Group Databasebeta

← Group #11781398

Character table — Group #11781398

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
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11
χ81111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1
χ92222222-22-222222222222-20000222-2-2-2-2-200000000222222-2222222222222-20000-2-2-2-200000000-2-20000-2-2-2-200000000000000000000
χ102222222-22-222222222222-20000222-2-2-2-2-200000000222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-200000000220000222200000000000000000000
χ11222222-22-22222222-2-2-2-22-222-2-2222222-2-22222-2-2-2-2-2-2-2-2-2-22000000000000-222-2-222-2-22222-2-2-2-2000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-22000000000000-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-2220000222-2-2-22200000000-2-2-2-2-2-2-200000000000020000-2-22200000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222-2-2-2-2222222-2-2-2-2220000222-2-2-22200000000-2-2-2-2-2-2-200000000000020000-2-2220000000000−2i−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
χ1722222-12222222-1-1-12222-12-2-2-2-2-1-1-122-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1000000000000-11111-1-1-1-11111111100000000000000000022-1-1-1-1-211000
χ1822222-12222222-1-1-12222-12-2-2-2-2-1-1-122-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1000000000000-11111-1-1-1-111111111000000000000000000-2-211112-1-1000
χ1922222-1-22-22222-1-1-1-2-2-2-2-1-222-2-2-1-1-122-1-2-22222-2-2-2-2111111-10000000000001-1-111-1-111-1-1-1-1111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-1-22-22222-1-1-1-2-2-2-2-1-222-2-2-1-1-122-1-2-22222-2-2-2-2111111-10000000000001-1-111-1-111-1-1-1-1111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-1-22-22222-1-1-1-2-2-2-2-1-2-2-222-1-1-122-1-2-2-2-2-2-22222111111-1000000000000111-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-1-22-22222-1-1-1-2-2-2-2-1-2-2-222-1-1-122-1-2-2-2-2-2-22222111111-1000000000000111-1-1-1-1111111-1-1-1-100000000000000000000i3i3−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
χ252222-122222-1-1-1222-1-1-1-1-12-2-2-2-2-1-1-1-1-12-1-11111111122-1-1-1-122222-1-1-1-1-1-1-1-12-2-2-2-2-1-1-1-11111111122-2-2-2-2-1-1-1-111111111000000000000
χ262222-122222-1-1-1222-1-1-1-1-12-2-2-2-2-1-1-1-1-12-1-11111111122-1-1-1-12-2-2-2-2111111112-2-2-2-2-1-1-1-111111111-2-222221111-1-1-1-1-1-1-1-1000000000000
χ272222-122-22-2-1-1-1222-1-1-1-1-1-20000-1-1-111-211−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−i3i3i3−i3−i3i3i3000000000000
χ282222-122-22-2-1-1-1222-1-1-1-1-1-20000-1-1-111-211−i3−i3i3i3−i3−i3i3i322-1-1-1-1-2-2-2-2-211111111-200001111−i3−i3i3i3−i3−i3i3i3220000-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ292222-122-22-2-1-1-1222-1-1-1-1-1-20000-1-1-111-211i3i3−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−i3i3i3−i3−i3000000000000
χ302222-122-22-2-1-1-1222-1-1-1-1-1-20000-1-1-111-211i3i3−i3−i3i3i3−i3−i322-1-1-1-1-2-2-2-2-211111111-200001111i3i3−i3−i3i3i3−i3−i3220000-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ312222-12-22-22-1-1-12221111-1-222-2-2-1-1-1-1-1211-1-1-1-11111-2-21111200003333−3−3−3−3-222-2-2-1-111-1-1-1-1111100000033−3−333−3−3−3−333000000000000
χ322222-12-22-22-1-1-12221111-1-222-2-2-1-1-1-1-1211-1-1-1-11111-2-2111120000−3−3−3−33333-222-2-2-1-111-1-1-1-11111000000−3−333−3−33333−3−3000000000000
χ332222-12-22-22-1-1-12221111-1-2-2-222-1-1-1-1-12111111-1-1-1-1-2-21111200003333−3−3−3−3-2-2-222-1-1111111-1-1-1-100000033−3−3−3−33333−3−3000000000000
χ342222-12-22-22-1-1-12221111-1-2-2-222-1-1-1-1-12111111-1-1-1-1-2-2111120000−3−3−3−33333-2-2-222-1-1111111-1-1-1-1000000−3−33333−3−3−3−333000000000000
χ352222-12-2-2-2-2-1-1-12221111-120000-1-1-111-2-1-1−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
χ362222-12-2-2-2-2-1-1-12221111-120000-1-1-111-2-1-1−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
χ372222-12-2-2-2-2-1-1-12221111-120000-1-1-111-2-1-1i3i3−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
χ382222-12-2-2-2-2-1-1-12221111-120000-1-1-111-2-1-1i3i3−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
χ392-22-222-20202-2-2-2-22-2-2222000002-2-200000000000002-222-2-202i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000−i2i2−i2i2−i2i20002−20
χ402-22-222-20202-2-2-2-22-2-2222000002-2-200000000000002-222-2-202i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000i2−i2i2−i2i2−i2000−220
χ412-22-222-20202-2-2-2-22-2-2222000002-2-200000000000002-222-2-20−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000−i2i2−i2i2−i2i2000−220
χ422-22-222-20202-2-2-2-22-2-2222000002-2-200000000000002-222-2-20−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000i2−i2i2−i2i2−i20002−20
χ432-2-2222020-2-22-22-2-20000202i−2i00-22-22-2-2002i−2i2i−2i00000000002−i2i2−i2i2−i2i2−i2i2−i2i2−i2i202i−2i002-2002i−2i2i−2i0000−i2i22−22−2−i2i2−i2i22−22−22−22−2000000000000
χ442-2-2222020-2-22-22-2-20000202i−2i00-22-22-2-2002i−2i2i−2i00000000002i2−i2i2−i2i2−i2i2−i2i2−i2i2−i202i−2i002-2002i−2i2i−2i0000i2−i2−22−22i2−i2i2−i2−22−22−22−22000000000000
χ452-2-2222020-2-22-22-2-2000020−2i2i00-22-22-2-200−2i2i−2i2i00000000002−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20−2i2i002-200−2i2i−2i2i0000−i2i2−22−22−i2i2−i2i2−22−22−22−22000000000000
χ462-2-2222020-2-22-22-2-2000020−2i2i00-22-22-2-200−2i2i−2i2i00000000002i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20−2i2i002-200−2i2i−2i2i0000i2−i22−22−2i2−i2i2−i22−22−22−22−2000000000000
χ472-2-22220-202-22-22-2-2000020002-2-22-2-2220000002-22-2000000-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20002-2-220000002-22-2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ482-2-22220-202-22-22-2-2000020002-2-22-2-2220000002-22-2000000-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20002-2-220000002-22-2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ492-2-22220-202-22-22-2-200002000-22-22-2-222000000-22-22000000-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000-22-22000000-22-22i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ502-2-22220-202-22-22-2-200002000-22-22-2-222000000-22-22000000-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000-22-22000000-22-22−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ512-2-22-12020-21-112-2-23−33−3-102i−2i001-11-11-23−3−ii−ii−i3i3i3−i3003−33−32−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2302i−2i00-113−3−ii−ii−i3i3i3−i3−i2i22−22−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ522-2-22-12020-21-112-2-23−33−3-102i−2i001-11-11-23−3−ii−ii−i3i3i3−i3003−33−32i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2302i−2i00-113−3−ii−ii−i3i3i3−i3i2−i2−22−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ532-2-22-12020-21-112-2-23−33−3-10−2i2i001-11-11-23−3i−ii−ii3−i3−i3i3003−33−32−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230−2i2i00-113−3i−ii−ii3−i3−i3i3−i2i2−22−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ542-2-22-12020-21-112-2-23−33−3-10−2i2i001-11-11-23−3i−ii−ii3−i3−i3i3003−33−32i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230−2i2i00-113−3i−ii−ii3−i3−i3i3i2−i22−22−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ552-2-22-12020-21-112-2-2−33−33-102i−2i001-11-11-2−33−ii−iii3−i3−i3i300−33−332−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ702i−2i00-11−33−ii−iii3−i3−i3i3−i2i22−22−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ562-2-22-12020-21-112-2-2−33−33-102i−2i001-11-11-2−33−ii−iii3−i3−i3i300−33−332i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ702i−2i00-11−33−ii−iii3−i3−i3i3i2−i2−22−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ572-2-22-12020-21-112-2-2−33−33-10−2i2i001-11-11-2−33i−ii−i−i3i3i3−i300−33−332−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70−2i2i00-11−33i−ii−i−i3i3i3−i3−i2i2−22−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ582-2-22-12020-21-112-2-2−33−33-10−2i2i001-11-11-2−33i−ii−i−i3i3i3−i300−33−332i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70−2i2i00-11−33i−ii−i−i3i3i3−i3i2−i22−22−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ592-2-22-120-2021-112-2-23−33−3-10002-21-111-12−333−3−33-11-11003−33−3-2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230002-21-1−333−3−33-11-11i2−i2−i2i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ602-2-22-120-2021-112-2-23−33−3-10002-21-111-12−333−3−33-11-11003−33−3-2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230002-21-1−333−3−33-11-11−i2i2i2−i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ612-2-22-120-2021-112-2-23−33−3-1000-221-111-12−33−333−31-11-1003−33−3-2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000-221-1−33−333−31-11-1i2−i2i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ622-2-22-120-2021-112-2-23−33−3-1000-221-111-12−33−333−31-11-1003−33−3-2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000-221-1−33−333−31-11-1−i2i2−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−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.