Finite Group Databasebeta

← Group #11780013

Character table — Group #11780013

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212122424242424242424242424243636484848727272
order1222334444666666121212123444666121212121212121212121212412121212121212121212121212121212121212121288882424242424242424888824242424242424244441212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ5111111111111111111111-1-11111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11-1-1
χ6111111111111111111111-1-11111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ7111111111111111111111-1-11111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111-1-11111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ92222222-22-2222222-2-2-2-2222-2222-2-2222-2-2-2-2-2-22-2-222-2-2-2-22222-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-22-2222222-2-2-2-22-2-2-2222-2-2222-2-2-2-2-2-222-2-2-22222-2-222-2-2-2-2-2-2222200000000000000000000000000000000
χ11222222-22-222222222222200-222222-2-2-22222-2-2-20-200000000-2-2-2-20000000000000000000000000000000022000-200
χ12222222-22-222222222222200-222222-2-2-22222-2-2-20-200000000-2-2-2-200000000000000000000000000000000-2-2000200
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-20200000000-2-222000000000000000000000000000000000000002-2
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-20200000000-2-22200000000000000000000000000000000000000-22
χ1522222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-12-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-12-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-1-2-2-2-21111-1-1-1-11111111100000000000000220000-1-1-1-100-211000
χ1822222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-1-2-2-2-21111-1-1-1-11111111100000000000000-2-200001111002-1-1000
χ1922222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-2122-2-211-1-1-1-111-1-1-1-1111100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-2122-2-211-1-1-1-111-1-1-1-1111100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-121-2-222-1-111-1-1111111-1-1-1-100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-121-2-222-1-111-1-1111111-1-1-1-100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-221111-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-221111-2-2-2-2-1-1-1-111111111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-122-22-2-12-1-1221111-122-2-1-1-1-2-2-1-121111112-2-2-1-111-2-222-1-111-1-1-1-1111100003333−3−3−3−3000033−3−3000000000000
χ282222-122-22-2-12-1-1221111-122-2-1-1-1-2-2-1-121111112-2-2-1-111-2-222-1-111-1-1-1-111110000−3−3−3−333330000−3−333000000000000
χ292222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-1211111122-211-1-122-2-2-1-1111111-1-1-1-100003333−3−3−3−30000−3−333000000000000
χ302222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-1211111122-211-1-122-2-2-1-1111111-1-1-1-10000−3−3−3−33333000033−3−3000000000000
χ3122-2-222-2020-2-22-2-22000022-20-22-2002-2-20000002002-200002-22-20022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i200−i2i2−i2i2000000000000
χ3222-2-222-2020-2-22-2-22000022-20-22-2002-2-20000002002-200002-22-20022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i200i2−i2i2−i2000000000000
χ3322-2-222-2020-2-22-2-2200002-220-22-2002-2-2000000200-220000-222-200-2-2220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2−i200i2−i2i2−i2000000000000
χ3422-2-222-2020-2-22-2-2200002-220-22-2002-2-2000000200-220000-222-200-2-2220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2i200−i2i2−i2i2000000000000
χ3522-2-2-12-20201-2-11-223−33−3-12-201-1100-11-233−3−33−3200-113−3002-2-113−3-1-11133−3−3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ3622-2-2-12-20201-2-11-223−33−3-12-201-1100-11-233−3−33−3200-113−3002-2-113−3-1-11133−3−3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ3722-2-2-12-20201-2-11-223−33−3-1-2201-1100-11-233−3−33−32001-1−3300-22-113−311-1-1−3−333−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ3822-2-2-12-20201-2-11-223−33−3-1-2201-1100-11-233−3−33−32001-1−3300-22-113−311-1-1−3−333i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ3922-2-2-12-20201-2-11-22−33−33-12-201-1100-11-2−3−333−33200-11−33002-2-11−33-1-111−3−333−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ4022-2-2-12-20201-2-11-22−33−33-12-201-1100-11-2−3−333−33200-11−33002-2-11−33-1-111−3−333i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ4122-2-2-12-20201-2-11-22−33−33-1-2201-1100-11-2−3−333−332001-13−300-22-11−3311-1-133−3−3−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ4222-2-2-12-20201-2-11-22−33−33-1-2201-1100-11-2−3−333−332001-13−300-22-11−3311-1-133−3−3i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ432-22-222020-222-2-2-2-222-2-220002-2-22-20002-22-200000000000000000000000002−22−22−22−22−22−2002−200002−22−22-2000000
χ442-22-222020-222-2-2-2-222-2-220002-2-22-20002-22-200000000000000000000000002−22−22−22−22−22−200−220000−22−22-22000000
χ452-22-222020-222-2-2-2-222-2-220002-2-22-20002-22-20000000000000000000000000−22−22−22−22−22−22002−200002−22−2-22000000
χ462-22-222020-222-2-2-2-222-2-220002-2-22-20002-22-20000000000000000000000000−22−22−22−22−22−2200−220000−22−222-2000000
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χ524444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-21111-2-2-2-4-2222222221111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-22222144-411122-2-2-2-1-1-1-122-2-42-2-22222-2-211-1-11111-1-1-1-100000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-222221-4-4-411122-2-2-2-1-1-1-122-24222-2-2-2-22211-1-1-1-1-1-1111100000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111-2-222211112220200000000-1-1-1-13-33-33-33-300000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111-2-222211112220200000000-1-1-1-1-33-33-33-3300000000000000000000000000000000
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χ584444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222-1-1-1-1-2-220-200000000-1-111-33-333-33-300000000000000000000000000000000
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χ6044-4-44-240-40-424-42-20000-20002-2200-44-2000000200000023−23002-200000023−23−232300000000000000000000000000000000
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χ7244-4-4-2-2-404022-222-2−2323−232314-40-11-100-22233−3−3−2323-200-22−232300-221-13−311-1-133−3−300000000000000000000000000000000
χ7344-4-4-2-2-404022-222-2−2323−23231-440-11-100-22233−3−3−2323-2002-223−23002-21-13−3-1-111−3−33300000000000000000000000000000000
χ744-44-4440-40444-4-4-4-4-4-44440004-4-4-44000-44-44000000000000000000000000000000000000000000000000000000000
χ754-44-44-2040-44-2-4-42244-4-4-2000-222-22000-22-2200000000000000000000000000000000000000022−220000−22−2200000000
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χ774-44-44-20-4044-2-4-422-4-444-2000-2222-20002-22-2000000000000000000000000000000000000000000000i6−i6−i6i600000000
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χ804-44-4-24040-4-2422-4-4-2-222-2000-2224-4000-22-220000000000000000000000000−2222−22222−22−22−22−200000000000000000000
χ814-44-4-240-404-2422-4-422-2-2-2000-222-440002-22-2000000000000000000000000000006−66−6−66−6600000000000000000000
χ824-44-4-240-404-2422-4-422-2-2-2000-222-440002-22-200000000000000000000000000000−66−666−66−600000000000000000000
χ834-4-44440000-4-4-444-400004000-4-4400000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ844-4-44440000-4-4-444-400004000-4-440000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
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χ864-4-44-2400002-42-24-423−23−2323-200022-20000023−23−23230000000000000000000000000−2i2i2i−2iζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ874-4-44-2400002-42-24-4−232323−23-200022-200000−232323−2300000000000000000000000002i−2i−2i2iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ884-4-44-2400002-42-24-4−232323−23-200022-200000−232323−230000000000000000000000000−2i2i2i−2i−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ898-88-8-4-4080-8-4-44444-4-44420002-2-2-440002-22-2000000000000000000000000000000000000000000000000000000000
χ908-88-8-4-40-808-4-4444444-4-420002-2-24-4000-22-22000000000000000000000000000000000000000000000000000000000
χ918-8-888-40000-84-88-440000-400044-4000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-40000444-4-4443−43−43432000-2-2200000−232323−23000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-40000444-4-44−434343−432000-2-220000023−23−2323000000000000000000000000000000000000000000000000000000000

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