Finite Group Databasebeta

← Group #4523

Character table — Group #4523

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11111111222222222222222222222222222222222222222222221212121212121212
order122244442234444444444666666612121212121212121212121212121212121212121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1-1-1-1-1111iiii−i−i−i−i11-1-11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i
χ61111-1-1-1-1-1-1111iiii−i−i−i−i11-1-11-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii
χ71111-1-1-1-1-1-1111−i−i−i−iiiii11-1-11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii
χ81111-1-1-1-1-1-1111−i−i−i−iiiii11-1-11-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i
χ911-1-111-1-1-1111-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ1011-1-111-1-1-1111-111-1-111-1-1-1-1-1-111111-1-111-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ1111-1-111-1-1-1111-1-1-111-1-111-1-1-1-111111-1-111-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii
χ1211-1-111-1-1-1111-1-1-111-1-111-1-1-1-111111-1-111-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i
χ1311-1-1-1-1111-111-1ii−i−i−i−iii-1-1111-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1
χ1411-1-1-1-1111-111-1ii−i−i−i−iii-1-1111-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11
χ1511-1-1-1-1111-111-1−i−iiiii−i−i-1-1111-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11
χ1611-1-1-1-1111-111-1−i−iiiii−i−i-1-1111-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1
χ172222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000
χ1922222222-2-22-2-20000000022-2-22-2-2-2-2-2-22222000000000000000000000000
χ2022222222-2-2-1-2-200000000-1-111-1111111-1-1-1-133−3−333−3−333−3−333−3−300000000
χ2122222222-2-2-1-2-200000000-1-111-1111111-1-1-1-1−3−333−3−333−3−333−3−33300000000
χ222222-2-2-2-2222-2-2000000002222222-2-2-2-2-2-2-2-2000000000000000000000000
χ232222-2-2-2-222-1-2-200000000-1-1-1-1-1-1-111111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000
χ242222-2-2-2-222-1-2-200000000-1-1-1-1-1-1-111111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000
χ252222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i-1-111-111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000
χ262222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i-1-111-111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000
χ2722-2-222-2-22-22-2200000000-2-2222-2-2-2-22222-2-2000000000000000000000000
χ2822-2-222-2-22-2-1-220000000011-1-1-11111-1-1-1-11133−3−3−3−33333−3−3−3−33300000000
χ2922-2-222-2-22-2-1-220000000011-1-1-11111-1-1-1-111−3−33333−3−3−3−33333−3−300000000
χ3022-2-222-2-2-22-12-222-2-222-2-21111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111100000000
χ3122-2-222-2-2-22-12-2-2-222-2-2221111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-100000000
χ3222-2-2-2-2222-2-12-22i2i−2i−2i−2i−2i2i2i11-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000
χ3322-2-2-2-2222-2-12-2−2i−2i2i2i2i2i−2i−2i11-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000
χ3422-2-2-2-222-222-2200000000-2-2-2-2222-2-222-2-222000000000000000000000000
χ3522-2-2-2-222-22-1-22000000001111-1-1-111-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000
χ3622-2-2-2-222-22-1-22000000001111-1-1-111-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000
χ372-22-22i−2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200-20000002i−2i2i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000
χ382-22-22i−2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200-20000002i−2i2i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000
χ392-22-22i−2i2i−2i00-1001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11−i3i31−i3i33−33−3−ii−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ402-22-22i−2i2i−2i00-1001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11i3−i31i3−i3−33−33−ii−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ412-22-22i−2i2i−2i00-100−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11−i3i31−i3i33−33−3−ii−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ422-22-22i−2i2i−2i00-100−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11i3−i31i3−i3−33−33−ii−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ432-22-2−2i2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-200-2000000−2i2i−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000
χ442-22-2−2i2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200-2000000−2i2i−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000
χ452-22-2−2i2i−2i2i00-1001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11−i3i31−i3i3−33−33i−ii−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ462-22-2−2i2i−2i2i00-1001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11i3−i31i3−i33−33−3i−ii−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ472-22-2−2i2i−2i2i00-100−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11−i3i31−i3i3−33−33i−ii−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ482-22-2−2i2i−2i2i00-100−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11i3−i31i3−i33−33−3i−ii−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ492-2-222i−2i−2i2i002001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200-20000002i−2i−2i2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ502-2-222i−2i−2i2i00200−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200-20000002i−2i−2i2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ512-2-222i−2i−2i2i00-1001+i−1−i−1−i1+i1−i−1+i−1+i1−i1-1−i3i31i3−i3−333−3−iii−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ522-2-222i−2i−2i2i00-1001+i−1−i−1−i1+i1−i−1+i−1+i1−i1-1i3−i31−i3i33−3−33−iii−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ532-2-222i−2i−2i2i00-100−1−i1+i1+i−1−i−1+i1−i1−i−1+i1-1−i3i31i3−i3−333−3−iii−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ542-2-222i−2i−2i2i00-100−1−i1+i1+i−1−i−1+i1−i1−i−1+i1-1i3−i31−i3i33−3−33−iii−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ552-2-22−2i2i2i−2i002001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200-2000000−2i2i2i−2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000
χ562-2-22−2i2i2i−2i00200−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200-2000000−2i2i2i−2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00000000
χ572-2-22−2i2i2i−2i00-1001−i−1+i−1+i1−i1+i−1−i−1−i1+i1-1−i3i31i3−i33−3−33i−i−ii−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ582-2-22−2i2i2i−2i00-1001−i−1+i−1+i1−i1+i−1−i−1−i1+i1-1i3−i31−i3i3−333−3i−i−ii−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ592-2-22−2i2i2i−2i00-100−1+i1−i1−i−1+i−1−i1+i1+i−1−i1-1−i3i31i3−i33−3−33i−i−iiζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ602-2-22−2i2i2i−2i00-100−1+i1−i1−i−1+i−1−i1+i1+i−1−i1-1i3−i31−i3i3−333−3i−i−iiζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.