Finite Group Databasebeta

← Group #13167524

Character table — Group #13167524

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444488888888888888888888181818181818181818181818181818181818181818181818181818181818181818181818727272727272727272727272
order12223446661212121233666666336666661212121212121212121212122244666688888888121212122424242424242424242424242424242444441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-20000000000000000000000000000
χ112222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ132222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000000011113333−3−3−3−33333−3−3−3−3000000000000
χ142222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111000000001111−3−3−3−33333−3−3−3−33333000000000000
χ152222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333000000000000
χ162222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3000000000000
χ172222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-22211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ182222-1-2-2-1-1-1111122222222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2221111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ1922-2-22002-2-200002222-2-2-2-22222-2-2-2-20000000000002-20022-2-222−2−222−2−2000022−2−222−2−222−2−222−2−2000000000000
χ2022-2-22002-2-200002222-2-2-2-22222-2-2-2-20000000000002-20022-2-2−2−222−2−2220000−2−222−2−222−2−222−2−222000000000000
χ2122-2-22002-2-200002222-2-2-2-22222-2-2-2-2000000000000-2200-2-22222−2−2−2−222000022−2−222−2−2−2−222−2−222000000000000
χ2222-2-22002-2-200002222-2-2-2-22222-2-2-2-2000000000000-2200-2-222−2−22222−2−20000−2−222−2−22222−2−222−2−2000000000000
χ2322-2-2-100-11133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−32-200-1-11122−2−222−2−23−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ2422-2-2-100-11133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−32-200-1-111−2−222−2−2223−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ2522-2-2-100-11133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−3-220011-1-122−2−2−2−222−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2622-2-2-100-11133−3−32222-2-2-2-2-1-1-1-1111100003333−3−3−3−3-220011-1-1−2−22222−2−2−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ2722-2-2-100-111−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−333332-200-1-11122−2−222−2−2−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ2822-2-2-100-111−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−333332-200-1-111−2−222−2−222−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ2922-2-2-100-111−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−33333-220011-1-122−2−2−2−2223−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3022-2-2-100-111−3−3332222-2-2-2-2-1-1-1-111110000−3−3−3−33333-220011-1-1−2−22222−2−23−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ312-22-222i−2i-22-22i−2i2i−2i22-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000002−22−2−i2i2−i2i200002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
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χ332-22-22−2i2i-22-2−2i2i−2i2i22-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000002−22−2i2−i2i2−i200002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-22−2i2i-22-2−2i2i−2i2i22-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000−22−22−i2i2−i2i20000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
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χ362-22-2-12i−2i1-11−ii−ii22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iii−i−iii0000−i3i3−i3i3−22−22i2−i2i2−i23−3−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ372-22-2-12i−2i1-11−ii−ii22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iii−i−iii0000i3−i3i3−i32−22−2−i2i2−i2i2−333−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ382-22-2-12i−2i1-11−ii−ii22-2-222-2-2-1-111-1-1112i2i−2i−2i−i−iii−i−iii0000i3−i3i3−i3−22−22i2−i2i2−i2−333−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ392-22-2-1−2i2i1-11i−ii−i22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−iii−i−i0000−i3i3−i3i32−22−2i2−i2i2−i2−333−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ402-22-2-1−2i2i1-11i−ii−i22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−iii−i−i0000−i3i3−i3i3−22−22−i2i2−i2i2−333−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ412-22-2-1−2i2i1-11i−ii−i22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−iii−i−i0000i3−i3i3−i32−22−2i2−i2i2−i23−3−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ422-22-2-1−2i2i1-11i−ii−i22-2-222-2-2-1-111-1-111−2i−2i2i2iii−i−iii−i−i0000i3−i3i3−i3−22−22−i2i2−i2i23−3−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ432-2-22200-2-22000022-2-2-2-22222-2-2-2-222000000000000002-2000000002i−2i−2i2i22-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ442-2-22200-2-22000022-2-2-2-22222-2-2-2-222000000000000002-200000000−2i2i2i−2i22-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000
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χ868-8-88800-8-880000-424-24-2-42-424-24-2-42000000000000000000000000000000000000000000000000000000000000
χ878-8-88-40044-4−4i34i34i3−4i32-4-24-242-4-121-21-2-120000−i32i3i3−2i3i3−2i3−i32i3000000000000000000000000000000000000000000000000
χ888-8-88-40044-4−4i34i34i3−4i3-424-24-2-422-1-21-212-100002i3−i3−2i3i3−2i3i32i3−i3000000000000000000000000000000000000000000000000
χ898-8-88-40044-44i3−4i3−4i34i32-4-24-242-4-121-21-2-120000i3−2i3−i32i3−i32i3i3−2i3000000000000000000000000000000000000000000000000
χ908-8-88-40044-44i3−4i3−4i34i3-424-24-2-422-1-21-212-10000−2i3i32i3−i32i3−i3−2i3i3000000000000000000000000000000000000000000000000

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