Finite Group Databasebeta

← Group #13155988

Character table — Group #13155988

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order122233344666666666121212123336666666661212121212121212121212124436661212121212124881212121212121212121212121212121224242424242424242424242424242424266666666448824242424266121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2002222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2200-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-122222-122-1-1222222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-1000000002-1-10000
χ12222222-122222-122-1-1222222-1-122-1-12-1-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-120022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-211111100000000-2110000
χ13222222-122222-122-1-1222222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000222-1-1-1-1-1-100000000-2110000
χ14222222-122222-122-1-1222222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-200-2-211-2-211111111110000000000000000-2-2-2111111000000002-1-10000
χ15222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-1-1-2-211-1-1-1-111110000000000000000000−i3i3−i3−i3i3i3000000000−i3i30000
χ16222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-20022-1-1-2-211-1-1-1-111110000000000000000000i3−i3i3i3−i3−i3000000000i3−i30000
χ17222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i3000000000i3−i30000
χ18222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111200-2-21122-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i3000000000−i3i30000
χ1922222-1222-12-122222-12222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-122000000000-1-100
χ2022222-1222-12-122222-12222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-102200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111-2-20000000001100
χ2122222-1222-12-122222-12222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1-2-20000000001100
χ2222222-1222-12-122222-12222-12-1-1-1-1-1-12-122-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-10-2-20000000000000000-2-2-2-2111111111111-211-2-2111122000000000-1-100
χ232222-122222-122-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ242222-122222-122-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-2-2-1-122-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ252222-122222-122-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-22211-2-211-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ262222-122222-122-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-2-2-211-2-211-2-2111111111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ272222-122-2-22-122-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-1111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ282222-122-2-22-122-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-1-1-1-1-2-21111-200-1-12211-2-2-1-1-1-11111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ292222-122-2-22-122-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ302222-122-2-22-122-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2-1-1-1-1-2-2111120011-2-2-1-1221111-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
χ3122-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-20000000000002-222-2-20000000−i2i22-22-2000022-2-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000−i2i2−i2i2−i2i20000000
χ3222-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-20000000000002-222-2-20000000i2−i22-22-2000022-2-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000i2−i2i2−i2i2−i20000000
χ3322-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-2000000000000-2222-2-20000000−i2i2-22-220000-2-2220000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000i2−i2i2−i2i2−i20000000
χ3422-2-2222002-2-2-22-22-2-200002222-22-2-2-2-22-2000000000000-2222-2-20000000i2−i2-22-220000-2-2220000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000−i2i2−i2i2−i2i20000000
χ3522-2-2-1220021-2-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−32-2-1-1110033−3−30−i2i2-112-23−300-1-11133−3−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
χ3622-2-2-1220021-2-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−32-2-1-1110033−3−30i2−i2-112-23−300-1-11133−3−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ3722-2-2-1220021-2-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−3-22-1-1110033−3−30−i2i21-1-22−330011-1-1−3−333ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ3822-2-2-1220021-2-2-112-2-23−33−3-1-12-112-211-2-110003−333−3−303−3-22-1-1110033−3−30i2−i21-1-22−330011-1-1−3−333−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
χ3922-2-2-1220021-2-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−332-2-1-11100−3−3330−i2i2-112-2−3300-1-111−3−333ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ4022-2-2-1220021-2-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−332-2-1-11100−3−3330i2−i2-112-2−3300-1-111−3−333−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ4122-2-2-1220021-2-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−33-22-1-11100−3−3330−i2i21-1-223−30011-1-133−3−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ4222-2-2-1220021-2-2-112-2-2−33−33-1-12-112-211-2-11000−33−3−3330−33-22-1-11100−3−3330i2−i21-1-223−30011-1-133−3−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ432-2-222222-2-2222-2-2-2-2-222-2-2222-2-2-2-2222-2-222-2222-22-2-2-2-2002-2-222-22-22-2000000000000000000000000000000000000000000002i−2i0000000002i−2i00
χ442-2-222222-2-2222-2-2-2-2-222-2-2222-2-2-2-2222-2-222-2222-22-2-2-2-2002-2-222-22-22-200000000000000000000000000000000000000000000−2i2i000000000−2i2i00
χ452-2-22222-22-2222-2-2-2-2-2-2-222222-2-2-2-2222-2-2-2-22-2-2-22-22222002-2-22-22-22-220000000000000000000000000000000000000000000000000000000002-2
χ462-2-22222-22-2222-2-2-2-2-2-2-222222-2-2-2-2222-2-2-2-22-2-2-22-22222002-2-22-22-22-22000000000000000000000000000000000000000000000000000000000-22
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χ482-2-222-122-212-12-2-2-2-2122-2-2-12-11111-12-1-2-2-12-2-1-12-22-211100-111-1-11-11-11000000000000000000000003−33−33−33−33−33−30i3−i300i3−i3i3−i3−2i2i000000000i−i00
χ492-2-222-122-212-12-2-2-2-2122-2-2-12-11111-12-1-2-2-12-2-1-12-22-211100-111-1-11-11-1100000000000000000000000−33−33−33−33−33−330−i3i300−i3i3−i3i3−2i2i000000000i−i00
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χ5144444-24-4-4-24-244444-2-4-4-4-4-24-2-2-2-2-2-24-2442-4-422-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
χ5244444-2-244-24-2-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ5344444-2-244-24-2-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ5444444-2-2-4-4-24-2-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222001111-1-1-1-1-1-100000000000000000000000000000000000000−2i32i3i3i3−i3−i3000000000000000
χ5544444-2-2-4-4-24-2-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000002i3−2i3−i3−i3i3i3000000000000000
χ564444-24-2444-24-2-2-2-2-24-2-2-2-2-21-2-2-2-2-2-21-2114-2-2-2-211114-2-2441111-2-21111400-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000000000
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χ594444-24-2-4-44-24-2-2-2-2-242222-21-2-2-2-2-2-21-211-42222-1-1-1-1-422-4-4111122-1-1-1-14002222-2-2-2-2-1-1-1-111110000000000000000000000000000000000000000
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χ7044-4-4-24-20042-42-22-22-4−2323−2323-21-2-22-222-121-1000−232333−3−30−23234-411-1-10033−3−3000-22-22−23230011-1-133−3−30000000000000000000000000000000000000000
χ7144-4-4-24-20042-42-22-22-4−2323−2323-21-2-22-222-121-1000−232333−3−30−2323-4411-1-10033−3−30002-22-223−2300-1-111−3−3330000000000000000000000000000000000000000
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χ1178-8-88-4-4-4-884-4-4-44444444-4-4222-2-2-2-2222-2-244-4-2-2-22-22-42200-111-1-221-11-100000000000000000000000000000000000000000000000000000000000

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