Finite Group Databasebeta

← Group #13167446

Character table — Group #13167446

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order122234466612121212336666663366666612121212121212121212121244448888888812121212121212122424242424242424242424242424242444441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ9222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-20000000000000000000000000000
χ112222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ132222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000111111113333−3−3−3−33333−3−3−3−3000000000000
χ142222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000000011111111−3−3−3−33333−3−3−3−33333000000000000
χ152222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-200000000-1-1-1-111113333−3−3−3−3−3−3−3−33333000000000000
χ162222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−3000000000000
χ172222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ182222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-222-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ1922-2-2200-22-200002222-2-2-2-22222-2-2-2-2000000000000002-2000022-2-2000022-2-20000000022-2-222-2-2000000000000
χ2022-2-2200-22-200002222-2-2-2-22222-2-2-2-2000000000000002-20000-2-222000022-2-200000000-2-222-2-222000000000000
χ2122-2-2200-22-200002222-2-2-2-22222-2-2-2-200000000000000-2222-2-200000000-2-22222-2-222-2-200000000000000000000
χ2222-2-2200-22-200002222-2-2-2-22222-2-2-2-200000000000000-22-2-22200000000-2-222-2-222-2-22200000000000000000000
χ2322-2-2-1001-1133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−3002-2000022-2-233−3−3-1-11133−3−3−3−333-1-111-1-111000000000000
χ2422-2-2-1001-1133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−3002-20000-2-22233−3−3-1-111−3−33333−3−311-1-111-1-1000000000000
χ2522-2-2-1001-1133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−300-2222-2-20000−3−33311-1-1-1-111-1-111−3−33333−3−3000000000000
χ2622-2-2-1001-1133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−300-22-2-2220000−3−33311-1-111-1-111-1-133−3−3−3−333000000000000
χ2722-2-2-1001-11−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−33333002-2000022-2-2−3−333-1-111−3−33333−3−3-1-111-1-111000000000000
χ2822-2-2-1001-11−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−33333002-20000-2-222−3−333-1-11133−3−3−3−33311-1-111-1-1000000000000
χ2922-2-2-1001-11−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−3333300-2222-2-2000033−3−311-1-1-1-111-1-11133−3−3−3−333000000000000
χ3022-2-2-1001-11−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−3333300-22-2-222000033−3−311-1-111-1-111-1-1−3−33333−3−3000000000000
χ312-22-22002-2-2000022-2-2-2-22222-2-2-2-2220000000000002i−2i002−22−2−i2i2−i2i22i−2i2i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ322-22-22002-2-2000022-2-2-2-22222-2-2-2-2220000000000002i−2i00−22−22i2−i2i2−i22i−2i2i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ332-22-22002-2-2000022-2-2-2-22222-2-2-2-222000000000000−2i2i002−22−2i2−i2i2−i2−2i2i−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-22002-2-2000022-2-2-2-22222-2-2-2-222000000000000−2i2i00−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-2-100-111−i3i3−i3i322-2-2-2-222-1-11111-1-10000−i3−i3i3i3−i3−i3i3i32i−2i002−22−2−i2i2−i2i2−ii−ii3−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ362-22-2-100-111−i3i3−i3i322-2-2-2-222-1-11111-1-10000−i3−i3i3i3−i3−i3i3i32i−2i00−22−22i2−i2i2−i2−ii−ii3−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ372-22-2-100-111−i3i3−i3i322-2-2-2-222-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3−2i2i002−22−2i2−i2i2−i2i−ii−i−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ382-22-2-100-111−i3i3−i3i322-2-2-2-222-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3−2i2i00−22−22−i2i2−i2i2i−ii−i−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ392-22-2-100-111i3−i3i3−i322-2-2-2-222-1-11111-1-10000i3i3−i3−i3i3i3−i3−i32i−2i002−22−2−i2i2−i2i2−ii−ii−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ402-22-2-100-111i3−i3i3−i322-2-2-2-222-1-11111-1-10000i3i3−i3−i3i3i3−i3−i32i−2i00−22−22i2−i2i2−i2−ii−ii−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ412-22-2-100-111i3−i3i3−i322-2-2-2-222-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3−2i2i002−22−2i2−i2i2−i2i−ii−i3−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ422-22-2-100-111i3−i3i3−i322-2-2-2-222-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3−2i2i00−22−22−i2i2−i2i2i−ii−i3−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ432-2-2222i−2i-2-222i−2i−2i2i22-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00002−2−22i2−i2−i2i2000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ442-2-2222i−2i-2-222i−2i−2i2i22-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000−222−2−i2i2i2−i200000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ452-2-222−2i2i-2-22−2i2i2i−2i22-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00002−2−22−i2i2i2−i2000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ462-2-222−2i2i-2-22−2i2i2i−2i22-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000−222−2i2−i2−i2i200000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ472-2-22-12i−2i11-1−iii−i22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iiiii−i−i00002−2−22i2−i2−i2i2−i3i3i3−i3−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ482-2-22-12i−2i11-1−iii−i22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iiiii−i−i00002−2−22i2−i2−i2i2i3−i3−i3i33−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ492-2-22-12i−2i11-1−iii−i22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iiiii−i−i0000−222−2−i2i2i2−i2−i3i3i3−i3−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ502-2-22-12i−2i11-1−iii−i22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iiiii−i−i0000−222−2−i2i2i2−i2i3−i3−i3i33−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ512-2-22-1−2i2i11-1i−i−ii22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−i−i−iii00002−2−22−i2i2i2−i2−i3i3i3−i33−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ522-2-22-1−2i2i11-1i−i−ii22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−i−i−iii00002−2−22−i2i2i2−i2i3−i3−i3i3−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ532-2-22-1−2i2i11-1i−i−ii22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−i−i−iii0000−222−2i2−i2−i2i2−i3i3i3−i33−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ542-2-22-1−2i2i11-1i−i−ii22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−i−i−iii0000−222−2i2−i2−i2i2i3−i3−i3i3−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ55444444444444441-21-21-21-21-21-21-21-21-21-21-21-21-21-2000000000000000000000000000000000000020200-1-100-1-1
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χ858-88-8-400-4444i3−4i34i3−4i32-4-24-242-4-121-21-2-120000i3−2i3−i32i3i3−2i3−i32i3000000000000000000000000000000000000000000000000
χ868-88-8-400-4444i3−4i34i3−4i3-424-24-2-422-1-21-212-10000−2i3i32i3−i3−2i3i32i3−i3000000000000000000000000000000000000000000000000
χ878-8-88-48i−8i44-4−4i4i4i−4i2-4-242-4-24-121-2-121-22i−4i−2i4i−i2ii−2ii−2i−i2i000000000000000000000000000000000000000000000000
χ888-8-88-48i−8i44-4−4i4i4i−4i-424-2-424-22-1-212-1-21−4i2i4i−2i2i−i−2ii−2ii2i−i000000000000000000000000000000000000000000000000
χ898-8-88-4−8i8i44-44i−4i−4i4i2-4-242-4-24-121-2-121-2−2i4i2i−4ii−2i−i2i−i2ii−2i000000000000000000000000000000000000000000000000
χ908-8-88-4−8i8i44-44i−4i−4i4i-424-2-424-22-1-212-1-214i−2i−4i2i−2ii2i−i2i−i−2ii000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.