Finite Group Databasebeta

← Group #11780108

Character table — Group #11780108

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
χ92222222-22-22222222222002-2222-2-222-22222-2-2-2000000000-20000-2-2-2-2000000000000000000000000000022000-200
χ102222222-22-22222222222002-2222-2-222-22222-2-2-2000000000-20000-2-2-2-20000000000000000000000000000-2-2000200
χ11222222-22-22222222-2-2-2-2222-222222-2-22-2-2-2-2-2-22-222222222-2-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ12222222-22-22222222-2-2-2-2-2-22-222222-2-22-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2222222-2-2222200000000000000000000000000000000
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
χ1522222-1222222-12-1-1222222-12-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-1222222-12-1-1222222-12-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-1222222-12-1-12222-2-2-12-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000220000-1-1-1-100-211000
χ1822222-1222222-12-1-12222-2-2-12-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000-2-200001111002-1-1000
χ1922222-1-22-2222-12-1-1-2-2-2-222-1-2-1-1-12211-11111-2-2-1-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-1-22-2222-12-1-1-2-2-2-222-1-2-1-1-12211-11111-2-2-1-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-1-22-2222-12-1-1-2-2-2-2-2-2-1-2-1-1-12211-11111-2-2-12-2-2111111122-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-1-22-2222-12-1-1-2-2-2-2-2-2-1-2-1-1-12211-11111-2-2-12-2-2111111122-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-1-12-122-1-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-1-12-122-1-1-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-1-12-122-1-1-1-1-2-2-12-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-1-12-122-1-1-1-1-2-2-12-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-11111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-12-22-22-1-12-122111122-1-2-1-1-1-1-1-2-221111112-2-1-122-1-1-1-1-211-2-2-1-111111100003333−3−3−3−3000033−3−3000000000000
χ282222-12-22-22-1-12-122111122-1-2-1-1-1-1-1-2-221111112-2-1-122-1-1-1-1-211-2-2-1-11111110000−3−3−3−333330000−3−333000000000000
χ292222-12-22-22-1-12-1221111-2-2-1-2-1-1-1-1-1-2-221111112211-2-21111-2-1-122-1-111-1-1-1-100003333−3−3−3−30000−3−333000000000000
χ302222-12-22-22-1-12-1221111-2-2-1-2-1-1-1-1-1-2-221111112211-2-21111-2-1-122-1-111-1-1-1-10000−3−3−3−33333000033−3−3000000000000
χ312-22-222-2020-2-2-222-2-2-2220020-2-22002-2022-2-2000000000000000000000000022−2−222−2−222−2−200−i2i20000−i2i2−i2i22i−2i000000
χ322-22-222-2020-2-2-222-2-2-2220020-2-22002-2022-2-2000000000000000000000000022−2−222−2−222−2−200i2−i20000i2−i2i2−i2−2i2i000000
χ332-22-222-2020-2-2-222-2-2-2220020-2-22002-2022-2-20000000000000000000000000−2−222−2−222−2−22200−i2i20000−i2i2−i2i2−2i2i000000
χ342-22-222-2020-2-2-222-2-2-2220020-2-22002-2022-2-20000000000000000000000000−2−222−2−222−2−22200i2−i20000i2−i2i2−i22i−2i000000
χ352-2-22220-2022-2-2-2-2200002-2202-2-22-200-2000000202-22-222-2-2000002-20000002−22−22−22−22−22−22−2002−22−2000000000000
χ362-2-22220-2022-2-2-2-2200002-2202-2-22-200-2000000202-22-222-2-2000002-2000000−22−22−22−22−22−22−2200−22−22000000000000
χ372-2-22220-2022-2-2-2-220000-22202-2-22-200-200000020-22-22-2-222000002-20000002−22−22−22−22−22−2−2200−22−22000000000000
χ382-2-22220-2022-2-2-2-220000-22202-2-22-200-200000020-22-22-2-222000002-2000000−22−22−22−22−22−222−2002−22−2000000000000
χ392-2-22-120-202-11-21-223−33−32-2-10-111-1100-23−33−33−320-112-2-1-11103−300-113−333−3−32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ402-2-22-120-202-11-21-223−33−32-2-10-111-1100-23−33−33−320-112-2-1-11103−300-113−333−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ412-2-22-120-202-11-21-223−33−3-22-10-111-1100-23−33−33−3201-1-2211-1-10−3300-113−3−3−3332−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ422-2-22-120-202-11-21-223−33−3-22-10-111-1100-23−33−33−3201-1-2211-1-10−3300-113−3−3−333−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ432-2-22-120-202-11-21-22−33−332-2-10-111-1100-2−33−33−3320-112-2-1-1110−3300-11−33−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ442-2-22-120-202-11-21-22−33−332-2-10-111-1100-2−33−33−3320-112-2-1-1110−3300-11−33−3−333−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ452-2-22-120-202-11-21-22−33−33-22-10-111-1100-2−33−33−33201-1-2211-1-103−300-11−3333−3−32−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ462-2-22-120-202-11-21-22−33−33-22-10-111-1100-2−33−33−33201-1-2211-1-103−300-11−3333−3−3−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4744444-24-44-444-24-2-2444400-2-4-2-2-2-4-4-2-22-2-2-2-2-4-42000000000200002222000000000000000000000000000000000000
χ4844444-2-4-4-4-444-24-2-2-4-4-4-400-24-2-2-2-4-42222222442000000000-2000022-2-2000000000000000000000000000000000000
χ494444-244-44-4-2-24-244-2-2-2-200-2-4-2-2-22244-4-2-2-2-222-4000000000-400002222000000000000000000000000000000000000
χ504444-24-4-4-4-4-2-24-244222200-24-2-2-222-4-4-42222-2-2-40000000004000022-2-2000000000000000000000000000000000000
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
χ534444-2-24-44-4-2-2-2-2-2-2-2-2-2-2001-411122-2-221111222000003-33-320000-1-1-1-13-33-300000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-2-2-2-2-2001-411122-2-22111122200000-33-3320000-1-1-1-1-33-3300000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-22222441-4111-2-222-2-1-1-1-122-2-4-2-2-2-211112222211-1-1-1-1-1-100000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-22222-4-41-4111-2-222-2-1-1-1-122-242222-1-1-1-12-2-2-2-211-1-1111100000000000000000000000000000000
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
χ5944-4-4440000-444-4-4-400000040-44-400000000000000000000000000000000002-2-222-2-222-2-2200000000000000000000
χ6044-4-4440000-444-4-4-400000040-44-40000000000000000000000000000000000-222-2-222-2-222-200000000000000000000
χ6144-4-4-2400002-242-4-423−23−232300-202-2200000−232323−2300000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000
χ6244-4-4-2400002-242-4-423−23−232300-202-2200000−232323−230000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000
χ6344-4-4-2400002-242-4-4−232323−2300-202-220000023−23−232300000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000
χ6444-4-4-2400002-242-4-4−232323−2300-202-220000023−23−23230000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000
χ654-44-44440-40-4-4-444-444-4-40040-4-4400-440-4-444000000000000000000000000000000000000000000000000000000000
χ664-44-44-240-40-4-424-2244-4-400-2022-2002-2022-2-20000000000000000000000000000000000000000000006−6−6600000000
χ674-44-44-240-40-4-424-2244-4-400-2022-2002-2022-2-2000000000000000000000000000000000000000000000−666−600000000
χ684-44-44-2-4040-4-424-22-4-44400-2022-200-220-2-222000000000000000000000000000000000000000−2i22i20000i2−i2i2−i200000000
χ694-44-44-2-4040-4-424-22-4-44400-2022-200-220-2-2220000000000000000000000000000000000000002i2−2i20000−i2i2−i2i200000000
χ704-44-4-2440-4022-4-24-4-2-22200-2022-200-44022-2-20000000000000000000000000000066−6−6−6−66600000000000000000000
χ714-44-4-2440-4022-4-24-4-2-22200-2022-200-44022-2-200000000000000000000000000000−6−66666−6−600000000000000000000
χ724-44-4-24-404022-4-24-422-2-200-2022-2004-40-2-22200000000000000000000000002222−22−22−2−222−2−22200000000000000000000
χ734-44-4-24-404022-4-24-422-2-200-2022-2004-40-2-2220000000000000000000000000−22−22222222−2−222−2−200000000000000000000
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χ764-4-444-2040-44-42-42-2000000-20-222-4400-20000002000000000000−23232-200−232323−2300000000000000000000000000000000
χ774-4-444-20-4044-42-42-200004-4-20-2224-4002000000-204-4-22-2-22200000-2200000000000000000000000000000000000000
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χ814-4-44-2-2040-4-22222-223−2323−2300101-1-12-200-2−33−33−23232000003-3-33000−2323-113−33−3−3300000000000000000000000000000000
χ824-4-44-2-2040-4-22222-223−2323−2300101-1-12-200-2−33−33−2323200000-333-300023−23-113−3−333−300000000000000000000000000000000
χ834-4-44-2-2040-4-22222-2−2323−232300101-1-12-200-23−33−323−232000003-3-3300023−23-11−33−333−300000000000000000000000000000000
χ844-4-44-2-2040-4-22222-2−2323−232300101-1-12-200-23−33−323−23200000-333-3000−2323-11−333−3−3300000000000000000000000000000000
χ854-4-44-2-20-404-22222-223−2323−234-4101-1-1-22002−33−3323−23-20-22-2211-1-1023−23001-1−33−3−33300000000000000000000000000000000
χ864-4-44-2-20-404-22222-223−2323−23-44101-1-1-22002−33−3323−23-202-22-2-1-1110−2323001-1−3333−3−300000000000000000000000000000000
χ874-4-44-2-20-404-22222-2−2323−23234-4101-1-1-220023−33−3−2323-20-22-2211-1-10−2323001-13−333−3−300000000000000000000000000000000
χ884-4-44-2-20-404-22222-2−2323−2323-44101-1-1-220023−33−3−2323-202-22-2-1-111023−23001-13−3−3−33300000000000000000000000000000000
χ8988-8-88-40000-88-4-844000000-404-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-400004-4-444443−43−43430020-22-20000023−23−2323000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-400004-4-4444−434343−430020-22-200000−232323−23000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-480-80444-4-44-4-4440020-2-22004-40-2-222000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-8080444-4-4444-4-40020-2-2200-44022-2-2000000000000000000000000000000000000000000000000000000000

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