Finite Group Databasebeta

← Group #13167594

Character table — Group #13167594

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order1222223666666633666666336666666666666666664444888888881212121212121212242424242424242424242424242424242244666612121212
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
χ51111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ11222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ12222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111111113333−3−3−3−33333−3−3−3−3000000000000
χ13222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000011111111−3−3−3−33333−3−3−3−33333000000000000
χ142222-2-2222-2-2-2-222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-222-200000000-2-22222-2-20000000000000000000000000000
χ152222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-222222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000
χ162222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-22-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000
χ172222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-1113333−3−3−3−3−3−3−3−33333000000000000
χ182222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-222-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−3000000000000
χ1922-2-20022-20000-22222-2-2-2-222000022-2-2-2-20000000002i−2i022−2−2−i2−i2i2i2002i2i−2i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ2022-2-20022-20000-22222-2-2-2-222000022-2-2-2-20000000002i−2i0−2−222i2i2−i2−i2002i2i−2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ2122-2-20022-20000-22222-2-2-2-222000022-2-2-2-2000000000−2i2i022−2−2i2i2−i2−i200−2i−2i2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ2222-2-20022-20000-22222-2-2-2-222000022-2-2-2-2000000000−2i2i0−2−222−i2−i2i2i200−2i−2i2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ2322-2-200-1-11−i3−i3i3i312222-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i302i−2i022−2−2−i2−i2i2i23−3−i−iii3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ2422-2-200-1-11−i3−i3i3i312222-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i302i−2i0−2−222i2i2−i2−i23−3−i−iii3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ2522-2-200-1-11−i3−i3i3i312222-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i30−2i2i022−2−2i2i2−i2−i2−33ii−i−i−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2622-2-200-1-11−i3−i3i3i312222-2-2-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i30−2i2i0−2−222−i2−i2i2i2−33ii−i−i−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2722-2-200-1-11i3i3−i3−i312222-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i302i−2i022−2−2−i2−i2i2i2−33−i−iii−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ2822-2-200-1-11i3i3−i3−i312222-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i302i−2i0−2−222i2i2−i2−i2−33−i−iii−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ2922-2-200-1-11i3i3−i3−i312222-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i30−2i2i022−2−2i2i2−i2−i23−3ii−i−i3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3022-2-200-1-11i3i3−i3−i312222-2-2-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i30−2i2i0−2−222−i2−i2i2i23−3ii−i−i3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ312-22-2002-2-20000222-2-222-2-2220000-2-222-2-200000000200-200002i−2i2i−2i220000-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ322-22-2002-2-20000222-2-222-2-2220000-2-222-2-200000000200-20000−2i2i−2i2i220000-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ332-22-2002-2-20000222-2-222-2-2220000-2-222-2-200000000-20022-22-20000-2-20000222-22-22-22-200000000000000000000
χ342-22-2002-2-20000222-2-222-2-2220000-2-222-2-200000000-2002-22-220000-2-2000022-22-22-22-2200000000000000000000
χ352-22-200-111−i3i3−i3i3-122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3200-200002i−2i2i−2i-1-1−i3i3−i3i3113−33−3−33−33−ii−ii−ii−ii000000000000
χ362-22-200-111−i3i3−i3i3-122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3200-20000−2i2i−2i2i-1-1−i3i3−i3i311−33−333−33−3i−ii−ii−ii−i000000000000
χ372-22-200-111−i3i3−i3i3-122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-20022-22-2000011i3−i3i3−i3-1-1-11-11-11-11−i3i3−i3i3i3−i3i3−i3000000000000
χ382-22-200-111−i3i3−i3i3-122-2-222-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-2002-22-22000011i3−i3i3−i3-1-11-11-11-11-1i3−i3i3−i3−i3i3−i3i3000000000000
χ392-22-200-111i3−i3i3−i3-122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3200-200002i−2i2i−2i-1-1i3−i3i3−i311−33−333−33−3−ii−ii−ii−ii000000000000
χ402-22-200-111i3−i3i3−i3-122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3200-20000−2i2i−2i2i-1-1i3−i3i3−i3113−33−3−33−33i−ii−ii−ii−i000000000000
χ412-22-200-111i3−i3i3−i3-122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-20022-22-2000011−i3i3−i3i3-1-1-11-11-11-11i3−i3i3−i3−i3i3−i3i3000000000000
χ422-22-200-111i3−i3i3−i3-122-2-222-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-2002-22-22000011−i3i3−i3i3-1-11-11-11-11-1−i3i3−i3i3i3−i3i3−i3000000000000
χ432-2-222-22-222-2-22-222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22200002−2−22−222−2000000002−2−222−2−22−222−2−222−2000000000000
χ442-2-222-22-222-2-22-222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2220000−222−22−2−2200000000−222−2−222−22−2−222−2−22000000000000
χ452-2-222-2-11-1-111-1122-2-2-2-222-1-122-2-21111-1-1-1-11111-1-100002−2−22−222−23−33−3−33−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ462-2-222-2-11-1-111-1122-2-2-2-222-1-122-2-21111-1-1-1-11111-1-100002−2−22−222−2−33−333−33−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ472-2-222-2-11-1-111-1122-2-2-2-222-1-122-2-21111-1-1-1-11111-1-10000−222−22−2−223−33−3−33−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ482-2-222-2-11-1-111-1122-2-2-2-222-1-122-2-21111-1-1-1-11111-1-10000−222−22−2−22−33−333−33−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ492-2-22-222-22-222-2-222-2-2-2-22222-2-222-2-2-2-222-2-22222-2-200002−2−222−2−22000000002−2−222−2−222−2−222−2−22000000000000
χ502-2-22-222-22-222-2-222-2-2-2-22222-2-222-2-2-2-222-2-22222-2-20000−222−2−222−200000000−222−2−222−2−222−2−222−2000000000000
χ512-2-22-22-11-11-1-11122-2-2-2-222-1-1-2-2221111-1-111-1-1-1-11100002−2−222−2−223−3−333−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ522-2-22-22-11-11-1-11122-2-2-2-222-1-1-2-2221111-1-111-1-1-1-11100002−2−222−2−22−333−3−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ532-2-22-22-11-11-1-11122-2-2-2-222-1-1-2-2221111-1-111-1-1-1-1110000−222−2−222−23−3−333−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ542-2-22-22-11-11-1-11122-2-2-2-222-1-1-2-2221111-1-111-1-1-1-1110000−222−2−222−2−333−3−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
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χ898-8-88-88-44-44-4-4442-4-24-242-4-12-242-41-21-2-121-2-12-121-2000000000000000000000000000000000000000000000000
χ908-8-88-88-44-44-4-444-424-24-2-422-14-2-42-21-212-1-212-12-1-21000000000000000000000000000000000000000000000000

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