Finite Group Databasebeta

← Group #11780449

Character table — Group #11780449

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212122424242424242424242424243636484848727272
order12223344446666661212121222346661212121212121212121212124666666661212121212121212121212121288882424242424242424888824242424242424244441212244
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
χ511111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11-1-1
χ611111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ711111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ92222222-22-22222222222002-2222-2-2-2222222-2-2-2000000000-20000-2-2-2-2000000000000000000000000000022000-200
χ102222222-22-22222222222002-2222-2-2-2222222-2-2-2000000000-20000-2-2-2-20000000000000000000000000000-2-2000200
χ11222222-22-22222222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22-222222222-2-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ12222222-22-22222222-2-2-2-2-2-22-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2222222-2-2222200000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-20022222-2-2-2-2-2-2-2-2-222-200000000020000-2-22200000000000000000000000000000000002-2
χ14222222-2-2-2-2222222-2-2-2-20022222-2-2-2-2-2-2-2-2-222-200000000020000-2-2220000000000000000000000000000000000-22
χ1522222-1222222-1-12-1222222-12-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-1222222-1-12-1222222-12-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-1222222-1-12-12222-2-2-12-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000220000-1-1-1-100-211000
χ1822222-1222222-1-12-12222-2-2-12-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000-2-200001111002-1-1000
χ1922222-1-22-2222-1-12-1-2-2-2-222-1-2-1-1-122-1111111-2-2-1-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-1-22-2222-1-12-1-2-2-2-222-1-2-1-1-122-1111111-2-2-1-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-1-22-2222-1-12-1-2-2-2-2-2-2-1-2-1-1-122-1111111-2-2-12-2-2111111122-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-1-22-2222-1-12-1-2-2-2-2-2-2-1-2-1-1-122-1111111-2-2-12-2-2111111122-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-1-122-12-1-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-1-122-12-1-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-1-122-12-1-1-1-1-2-2-12-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-1-122-12-1-1-1-1-2-2-12-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-11111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-12-22-22-1-122-12111122-1-2-1-1-1-1-12-2-21111112-2-1-122-1-1-1-1-211-2-2-1-111111100003333−3−3−3−3000033−3−3000000000000
χ282222-12-22-22-1-122-12111122-1-2-1-1-1-1-12-2-21111112-2-1-122-1-1-1-1-211-2-2-1-11111110000−3−3−3−333330000−3−333000000000000
χ292222-12-22-22-1-122-121111-2-2-1-2-1-1-1-1-12-2-21111112211-2-21111-2-1-122-1-111-1-1-1-100003333−3−3−3−30000−3−333000000000000
χ302222-12-22-22-1-122-121111-2-2-1-2-1-1-1-1-12-2-21111112211-2-21111-2-1-122-1-111-1-1-1-10000−3−3−3−33333000033−3−3000000000000
χ312-22-22220-20-2-2-2-22222-2-20020-2-220002-222-2-20000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002−200002−22−22i−2i000000
χ322-22-22220-20-2-2-2-22222-2-20020-2-220002-222-2-20000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−220000−22−22−2i2i000000
χ332-22-22220-20-2-2-2-22222-2-20020-2-220002-222-2-20000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002−200002−22−2−2i2i000000
χ342-22-22220-20-2-2-2-22222-2-20020-2-220002-222-2-20000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−220000−22−222i−2i000000
χ352-2-2222020-22-22-2-2-200002-2202-2-22-2200000000-202-22-222-2-2000002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−i2i2−i2i2000000000000
χ362-2-2222020-22-22-2-2-200002-2202-2-22-2200000000-202-22-222-2-2000002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200i2−i2i2−i2000000000000
χ372-2-2222020-22-22-2-2-20000-22202-2-22-2200000000-20-22-22-2-222000002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i200i2−i2i2−i2000000000000
χ382-2-2222020-22-22-2-2-20000-22202-2-22-2200000000-20-22-22-2-222000002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i200−i2i2−i2i2000000000000
χ392-2-22-12020-2-112-21-23−33−32-2-10-111-112003−33−33−3-20-112-2-1-11103−300-113−333−3−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ402-2-22-12020-2-112-21-23−33−32-2-10-111-112003−33−33−3-20-112-2-1-11103−300-113−333−3−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ412-2-22-12020-2-112-21-23−33−3-22-10-111-112003−33−33−3-201-1-2211-1-10−3300-113−3−3−333−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ422-2-22-12020-2-112-21-23−33−3-22-10-111-112003−33−33−3-201-1-2211-1-10−3300-113−3−3−333i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ432-2-22-12020-2-112-21-2−33−332-2-10-111-11200−33−33−33-20-112-2-1-1110−3300-11−33−3−333−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ442-2-22-12020-2-112-21-2−33−332-2-10-111-11200−33−33−33-20-112-2-1-1110−3300-11−33−3−333i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ452-2-22-12020-2-112-21-2−33−33-22-10-111-11200−33−33−33-201-1-2211-1-103−300-11−3333−3−3−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ462-2-22-12020-2-112-21-2−33−33-22-10-111-11200−33−33−33-201-1-2211-1-103−300-11−3333−3−3i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ4744444-24-44-444-2-24-2444400-2-4-2-2-2-4-42-2-2-2-2-2-2-4-42000000000200002222000000000000000000000000000000000000
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χ514444-2-24444-2-2-2-2-2-2-2-2-2-24414111-2-2-2-2-21111-2-2-24-2-2-2-21111-2-2-2-2-21111111100000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-2-4-414111-2-2-2-2-21111-2-2-2-42222-1-1-1-1-222221111-1-1-1-100000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-2-2-2-2-2001-4111222-2-21111222000003-33-320000-1-1-1-13-33-300000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-2-2-2-2-2001-4111222-2-2111122200000-33-3320000-1-1-1-1-33-3300000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-22222441-4111-2-2-222-1-1-1-122-2-4-2-2-2-211112222211-1-1-1-1-1-100000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-22222-4-41-4111-2-2-222-1-1-1-122-242222-1-1-1-12-2-2-2-211-1-1111100000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-22222001411122222-1-1-1-1-2-22000003-33-3-20000-1-111-33-3300000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-22222001411122222-1-1-1-1-2-2200000-33-33-20000-1-1113-33-300000000000000000000000000000000
χ5944-4-4440000-44-44-4-400000040-44-400000000000000000000000000000000002-2-222-2-222-2-2200000000000000000000
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χ6144-4-4-2400002-2-442-423−23−232300-202-220000023−23−232300000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000
χ6244-4-4-2400002-2-442-423−23−232300-202-220000023−23−23230000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000
χ6344-4-4-2400002-2-442-4−232323−2300-202-2200000−232323−2300000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000
χ6444-4-4-2400002-2-442-4−232323−2300-202-2200000−232323−230000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000
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χ684-44-44-2-4040-4-4224-2-4-44400-2022-20002-222-2-2000000000000000000000000000000000000000000000i6−i6−i6i600000000
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χ714-44-4-2440-4022-4-4-24-2-22200-2022-20004-4-2-22200000000000000000000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ724-44-4-24-404022-4-4-2422-2-200-2022-2000-4422-2-200000000000000000000000000000i6i6−i6−i6−i6−i6i6i600000000000000000000
χ734-44-4-24-404022-4-4-2422-2-200-2022-2000-4422-2-200000000000000000000000000000−i6−i6i6i6i6i6−i6−i600000000000000000000
χ744-4-44440-4044-44-4-4-4000000404-4-4-44-400000000400000000000000-4400000000000000000000000000000000000000
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χ774-4-444-20-4044-4-22-42000000-20-222-44200000000-200000000000023−232-20023−23−232300000000000000000000000000000000
χ784-4-444-20-4044-4-22-42000000-20-222-44200000000-2000000000000−23232-200−232323−2300000000000000000000000000000000
χ794-4-44-240-404-224-42-423−2323−2300-20-2222-2-40023−2323−23−23234000000000000002-2−2323000000000000000000000000000000000000
χ804-4-44-240-404-224-42-4−2323−232300-20-2222-2-400−2323−232323−234000000000000002-223−23000000000000000000000000000000000000
χ814-4-44-2-2040-4-22-222223−2323−234-4101-1-1-22-200−33−3323−2320-22-2211-1-1023−23001-1−33−3−33300000000000000000000000000000000
χ824-4-44-2-2040-4-22-222223−2323−23-44101-1-1-22-200−33−3323−23202-22-2-1-1110−2323001-1−3333−3−300000000000000000000000000000000
χ834-4-44-2-2040-4-22-2222−2323−23234-4101-1-1-22-2003−33−3−232320-22-2211-1-10−2323001-13−333−3−300000000000000000000000000000000
χ844-4-44-2-2040-4-22-2222−2323−2323-44101-1-1-22-2003−33−3−2323202-22-2-1-111023−23001-13−3−3−33300000000000000000000000000000000
χ854-4-44-2-20-404-22-222223−2323−2300101-1-12-2200−33−33−2323-2000003-3-33000−2323-113−33−3−3300000000000000000000000000000000
χ864-4-44-2-20-404-22-222223−2323−2300101-1-12-2200−33−33−2323-200000-333-300023−23-113−3−333−300000000000000000000000000000000
χ874-4-44-2-20-404-22-2222−2323−232300101-1-12-22003−33−323−23-2000003-3-3300023−23-11−33−333−300000000000000000000000000000000
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χ928-88-8-4-480-804444-4-4-4-4440020-2-22000-4422-2-2000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-80804444-4-444-4-40020-2-220004-4-2-222000000000000000000000000000000000000000000000000000000000

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