Finite Group Databasebeta

← Group #11779469

Character table — Group #11779469

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
χ5111111111111111111111-1-11111111111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11-1-1
χ6111111111111111111111-1-11111111111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ7111111111111111111111-1-11111111111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111-1-11111111111111111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ92222222-22-2222222-2-2-2-2222-2222-2-2222-2-2-2-2-2-22-22222-2-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-22-2222222-2-2-2-22-2-2-2222-2-2222-2-2-2-2-2-222-2-2-2-222-22222-2-2-2-2-2-2222200000000000000000000000000000000
χ11222222-22-222222222222200-222222-2-2-22222-2-2-20000000-200-2-2-2-20000000000000000000000000000000022000-200
χ12222222-22-222222222222200-222222-2-2-22222-2-2-20000000-200-2-2-2-200000000000000000000000000000000-2-2000200
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-20000000200-2-222000000000000000000000000000000000000002-2
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-20000000200-2-22200000000000000000000000000000000000000-22
χ1522222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-2-211-2-2-111-1-1-1-11111111100000000000000220000-1-1-1-100-211000
χ1822222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-2-211-2-2-111-1-1-1-11111111100000000000000-2-200001111002-1-1000
χ1922222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-222-1-1-2-2111-1-111-1-1-1-1111100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-222-1-1-2-2111-1-111-1-1-1-1111100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-12-2-211221-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-12-2-211221-1-1-1-1111111-1-1-1-100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-122-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-122-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-211-2-2112-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-211-2-2112-2-2-1-1-1-111111111-2-2-2-2111111112200-1-1-1-1000000000000
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χ282222-122-22-2-12-1-1221111-122-2-1-1-1-2-2-1-121111112-2-1-12211-2-2-2-1-111-1-1-1-111110000−3−3−3−333330000−3−333000000000000
χ292222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-121111112211-2-2-1-1-222-1-1111111-1-1-1-100003333−3−3−3−30000−3−333000000000000
χ302222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-121111112211-2-2-1-1-222-1-1111111-1-1-1-10000−3−3−3−33333000033−3−3000000000000
χ3122-2-22220-20-2-22-22-2000022-20-22-2002-22000000-202-22-2000002-20022-2-2000022−2−222−2−222−2−22−2002−22−2000000000000
χ3222-2-22220-20-2-22-22-2000022-20-22-2002-22000000-202-22-2000002-20022-2-20000−2−222−2−222−2−222−2200−22−22000000000000
χ3322-2-22220-20-2-22-22-200002-220-22-2002-22000000-20-22-22000002-200-2-222000022−2−222−2−222−2−2−2200−22−22000000000000
χ3422-2-22220-20-2-22-22-200002-220-22-2002-22000000-20-22-22000002-200-2-2220000−2−222−2−222−2−2222−2002−22−2000000000000
χ3522-2-2-1220-201-2-112-23−33−3-12-201-1100-11233−3−33−3-20-112-23−3000-113−3-1-11133−3−322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ3622-2-2-1220-201-2-112-23−33−3-12-201-1100-11233−3−33−3-20-112-23−3000-113−3-1-11133−3−3−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ3722-2-2-1220-201-2-112-23−33−3-1-2201-1100-11233−3−33−3-201-1-22−33000-113−311-1-1−3−33322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ3822-2-2-1220-201-2-112-23−33−3-1-2201-1100-11233−3−33−3-201-1-22−33000-113−311-1-1−3−333−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ3922-2-2-1220-201-2-112-2−33−33-12-201-1100-112−3−333−33-20-112-2−33000-11−33-1-111−3−33322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4022-2-2-1220-201-2-112-2−33−33-12-201-1100-112−3−333−33-20-112-2−33000-11−33-1-111−3−333−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ4122-2-2-1220-201-2-112-2−33−33-1-2201-1100-112−3−333−33-201-1-223−3000-11−3311-1-133−3−322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ4222-2-2-1220-201-2-112-2−33−33-1-2201-1100-112−3−333−33-201-1-223−3000-11−3311-1-133−3−3−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72−200ζ13−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
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χ4744444-2-44-444-244-2-24444-200-4-2-2-2-2-2-4-42-2-2-2-2-4-42000000020022220000000000000000000000000000000000000000
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χ524444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-21111-2-2-2-4222222-2221111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-22222144-411122-2-2-2-1-1-1-122-2-4-2-2-2-22222211-1-11111-1-1-1-100000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-222221-4-4-411122-2-2-2-1-1-1-122-242222-2-22-2-211-1-1-1-1-1-1111100000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111-2-222211112220000000200-1-1-1-13-33-33-33-300000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111-2-222211112220000000200-1-1-1-1-33-33-33-3300000000000000000000000000000000
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χ774-44-44-20-4044-2-4-422-4-444-2000-2222-20002-22-2000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ784-44-44-20-4044-2-4-422-4-444-2000-2222-20002-22-2000000000000000000000000000000000000000000000−i6i6i6−i600000000
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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
χ834-4-44440000-4-4-44-4400004000-4-4400000000000000000000000000000000002-2-222-2-222-2-2200000000000000000000
χ844-4-44440000-4-4-44-4400004000-4-440000000000000000000000000000000000-222-2-222-2-222-200000000000000000000
χ854-4-44-2400002-42-2-4423−23−2323-200022-20000023−23−232300000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000
χ864-4-44-2400002-42-2-4423−23−2323-200022-20000023−23−23230000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000
χ874-4-44-2400002-42-2-44−232323−23-200022-200000−232323−2300000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000
χ884-4-44-2400002-42-2-44−232323−23-200022-200000−232323−230000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000
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
χ918-8-888-40000-84-884-40000-400044-4000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-40000444-44-443−43−43432000-2-2200000−232323−23000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-40000444-44-4−434343−432000-2-220000023−23−2323000000000000000000000000000000000000000000000000000000000

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