Finite Group Databasebeta

← Group #11779500

Character table — Group #11779500

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212122424242424242424242424243636484848727272
order12223344446666661212121234446661212121212121212121212122666666661212121212121212121212121288882424242424242424888824242424242424244441212244
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
χ5111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11-1-1
χ6111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ7111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ92222222-22-22222222222200-2222-2-2-2222222-2-2-20000000000000-2-2-2-2-2000000000000000000000000000022000-200
χ102222222-22-22222222222200-2222-2-2-2222222-2-2-20000000000000-2-2-2-2-20000000000000000000000000000-2-2000200
χ11222222-22-22222222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-22222-222-2-2222200000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-2222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-200000000000002-2-22200000000000000000000000000000000002-2
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-200000000000002-2-2220000000000000000000000000000000000-22
χ1522222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-2-211-1-1-1-1-1111100000000000000220000-1-1-1-100-211000
χ1822222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-2-211-1-1-1-1-1111100000000000000-2-200001111002-1-1000
χ1922222-1-22-2222-12-1-1-2-2-2-2-122-2-1-1-122-1111111-2-2-1-2-2-211111122-1-11-1-111-1-1-1-100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-1-22-2222-12-1-1-2-2-2-2-122-2-1-1-122-1111111-2-2-1-2-2-211111122-1-11-1-111-1-1-1-100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-1-22-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1111111-2-2-1222-1-1-1-1-1-1-2-2111-1-111111100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-1-22-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1111111-2-2-1222-1-1-1-1-1-1-2-2111-1-111111100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-1222-1-1-1-1-1-12-211-2-2111111-2-22-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-1222-1-1-1-1-1-12-211-2-2111111-2-22-1-1-1-11111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-12-22-22-1-12-1221111-122-2-1-1-1-1-12-2-21111112-211-2-21111-1-122-2-1-111-1-1-1-100003333−3−3−3−3000033−3−3000000000000
χ282222-12-22-22-1-12-1221111-122-2-1-1-1-1-12-2-21111112-211-2-21111-1-122-2-1-111-1-1-1-10000−3−3−3−333330000−3−333000000000000
χ292222-12-22-22-1-12-1221111-1-2-2-2-1-1-1-1-12-2-211111122-1-122-1-1-1-111-2-2-2-1-111111100003333−3−3−3−30000−3−333000000000000
χ302222-12-22-22-1-12-1221111-1-2-2-2-1-1-1-1-12-2-211111122-1-122-1-1-1-111-2-2-2-1-11111110000−3−3−3−33333000033−3−3000000000000
χ3122-2-222-2020-2-2-222-2-2-2222000-2-220002-222-2-2000000000000000000000000022−2−222−2−222−2−200−i2i20000−i2i2−i2i22i−2i000000
χ3222-2-222-2020-2-2-222-2-2-2222000-2-220002-222-2-2000000000000000000000000022−2−222−2−222−2−200i2−i20000i2−i2i2−i2−2i2i000000
χ3322-2-222-2020-2-2-222-2-2-2222000-2-220002-222-2-20000000000000000000000000−2−222−2−222−2−22200−i2i20000−i2i2−i2i2−2i2i000000
χ3422-2-222-2020-2-2-222-2-2-2222000-2-220002-222-2-20000000000000000000000000−2−222−2−222−2−22200i2−i20000i2−i2i2−i22i−2i000000
χ352-22-2220-2022-22-2-2-2000022i−2i02-2-22-2-20000000020000000002i−2i2i−2i02-2002i2i−2i−2i2−22−22−22−22−22−2−i2i200−i2i2−i2i2000000000000
χ362-22-2220-2022-22-2-2-2000022i−2i02-2-22-2-20000000020000000002i−2i2i−2i02-2002i2i−2i−2i−22−22−22−22−22−22i2−i200i2−i2i2−i2000000000000
χ372-22-2220-2022-22-2-2-200002−2i2i02-2-22-2-2000000002000000000−2i2i−2i2i02-200−2i−2i2i2i2−22−22−22−22−22−2i2−i200i2−i2i2−i2000000000000
χ382-22-2220-2022-22-2-2-200002−2i2i02-2-22-2-2000000002000000000−2i2i−2i2i02-200−2i−2i2i2i−22−22−22−22−22−22−i2i200−i2i2−i2i2000000000000
χ392-22-2-120-202-1121-2-23−33−3-12i−2i0-111-11-2003−33−33−320−i3i300−i3−i3i3i3−ii2i−2i0-113−3−i−iii2−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ402-22-2-120-202-1121-2-23−33−3-12i−2i0-111-11-2003−33−33−320−i3i300−i3−i3i3i3−ii2i−2i0-113−3−i−iii−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ412-22-2-120-202-1121-2-23−33−3-1−2i2i0-111-11-2003−33−33−320i3−i300i3i3−i3−i3i−i−2i2i0-113−3ii−i−i2−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ422-22-2-120-202-1121-2-23−33−3-1−2i2i0-111-11-2003−33−33−320i3−i300i3i3−i3−i3i−i−2i2i0-113−3ii−i−i−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ432-22-2-120-202-1121-2-2−33−33-12i−2i0-111-11-200−33−33−3320i3−i300i3i3−i3−i3−ii2i−2i0-11−33−i−iii2−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ442-22-2-120-202-1121-2-2−33−33-12i−2i0-111-11-200−33−33−3320i3−i300i3i3−i3−i3−ii2i−2i0-11−33−i−iii−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ452-22-2-120-202-1121-2-2−33−33-1−2i2i0-111-11-200−33−33−3320−i3i300−i3−i3i3i3i−i−2i2i0-11−33ii−i−i2−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ462-22-2-120-202-1121-2-2−33−33-1−2i2i0-111-11-200−33−33−3320−i3i300−i3−i3i3i3i−i−2i2i0-11−33ii−i−i−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4744444-24-44-444-24-2-24444-200-4-2-2-2-4-42-2-2-2-2-2-2-4-42000000000000022222000000000000000000000000000000000000
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χ494444-244-44-4-2-24-244-2-2-2-2-200-4-2-2-222-444-2-2-2-222-40000000000000-42222000000000000000000000000000000000000
χ504444-24-4-4-4-4-2-24-2442222-2004-2-2-222-4-4-42222-2-2-40000000000000422-2-2000000000000000000000000000000000000
χ514444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-21111-2-2-24-2-2-2-21111-2-2-2-2-21111111100000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-21111-2-2-2-42222-1-1-1-12222-21111-1-1-1-100000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-4111222-2-21111222000003-33-300002-1-1-1-13-33-300000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-4111222-2-2111122200000-33-3300002-1-1-1-1-33-3300000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-22222144-4111-2-2-222-1-1-1-122-2-42222-1-1-1-1-2-2-2-2211-1-1111100000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-222221-4-4-4111-2-2-222-1-1-1-122-24-2-2-2-211112222211-1-1-1-1-1-100000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222-1-1-1-1-2-22000003-33-30000-2-1-111-33-3300000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222-1-1-1-1-2-2200000-33-330000-2-1-1113-33-300000000000000000000000000000000
χ5944-4-44440-40-4-4-444-444-4-44000-4-44000-44-4-444000000000000000000000000000000000000000000000000000000000
χ6044-4-44-240-40-4-424-2244-4-4-200022-20002-222-2-20000000000000000000000000000000000000000000006−6−6600000000
χ6144-4-44-240-40-4-424-2244-4-4-200022-20002-222-2-2000000000000000000000000000000000000000000000−666−600000000
χ6244-4-44-2-4040-4-424-22-4-444-200022-2000-22-2-222000000000000000000000000000000000000000−2i22i20000i2−i2i2−i200000000
χ6344-4-44-2-4040-4-424-22-4-444-200022-2000-22-2-2220000000000000000000000000000000000000002i2−2i20000−i2i2−i2i200000000
χ6444-4-4-2440-4022-4-24-4-2-222-200022-2000-4422-2-20000000000000000000000000000066−6−6−6−66600000000000000000000
χ6544-4-4-2440-4022-4-24-4-2-222-200022-2000-4422-2-200000000000000000000000000000−6−66666−6−600000000000000000000
χ6644-4-4-24-404022-4-24-422-2-2-200022-20004-4-2-22200000000000000000000000002222−22−22−2−222−2−22200000000000000000000
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χ684-44-444040-44-44-4-4-4000040004-4-4-44400000000-400000000000000-4400000000000000000000000000000000000000
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χ714-44-44-20-4044-4-2-4220000-24i−4i0-2224-4200000000-20000000004i−4i−2i2i0-2200−2i−2i2i2i00000000000000000000000000000000
χ724-44-44-20-4044-4-2-4220000-2−4i4i0-2224-4200000000-2000000000−4i4i2i−2i0-22002i2i−2i−2i00000000000000000000000000000000
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χ744-44-4-24040-4-2242-4-4−2323−2323-2000-2222-2400−2323−232323−23-4000000000000002-223−23000000000000000000000000000000000000
χ754-44-4-2-2040-4-22-222223−2323−2310001-1-12-2-200−33−33−23232000−2i32i3i3−i3−i3i300000-113−3−3i3i3i−3i00000000000000000000000000000000
χ764-44-4-2-2040-4-22-222223−2323−2310001-1-12-2-200−33−33−232320002i3−2i3−i3i3i3−i300000-113−33i−3i−3i3i00000000000000000000000000000000
χ774-44-4-2-2040-4-22-2222−2323−232310001-1-12-2-2003−33−323−232000−2i32i3i3−i3−i3i300000-11−333i−3i−3i3i00000000000000000000000000000000
χ784-44-4-2-2040-4-22-2222−2323−232310001-1-12-2-2003−33−323−2320002i3−2i3−i3i3i3−i300000-11−33−3i3i3i−3i00000000000000000000000000000000
χ794-44-4-2-20-404-22-222223−2323−2314i−4i01-1-1-22200−33−3323−23-20−2i32i300i3i3−i3−i3−2i2i−2i2i01-1−33ii−i−i00000000000000000000000000000000
χ804-44-4-2-20-404-22-222223−2323−231−4i4i01-1-1-22200−33−3323−23-202i3−2i300−i3−i3i3i32i−2i2i−2i01-1−33−i−iii00000000000000000000000000000000
χ814-44-4-2-20-404-22-2222−2323−232314i−4i01-1-1-222003−33−3−2323-202i3−2i300−i3−i3i3i3−2i2i−2i2i01-13−3ii−i−i00000000000000000000000000000000
χ824-44-4-2-20-404-22-2222−2323−23231−4i4i01-1-1-222003−33−3−2323-20−2i32i300i3i3−i3−i32i−2i2i−2i01-13−3−i−iii00000000000000000000000000000000
χ834-4-44440000-44-4-4-4400004000-44-400000000000000000000000000000000002-2-222-2-222-2-2200000000000000000000
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χ854-4-44-2400002-2-42-4423−23−2323-20002-2200000−232323−2300000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000
χ864-4-44-2400002-2-42-4423−23−2323-20002-2200000−232323−230000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000
χ874-4-44-2400002-2-42-44−232323−23-20002-220000023−23−232300000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000
χ884-4-44-2400002-2-42-44−232323−23-20002-220000023−23−23230000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000
χ8988-8-8-4-480-80444-4-44-4-4442000-2-220004-4-2-222000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4-8080444-4-4444-4-42000-2-22000-4422-2-2000000000000000000000000000000000000000000000000000000000
χ918-8-888-40000-884-84-40000-40004-44000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-400004-4444-443−43−43432000-22-20000023−23−2323000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-400004-4444-4−434343−432000-22-200000−232323−23000000000000000000000000000000000000000000000000000000000

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