Finite Group Databasebeta

← Group #11779280

Character table — Group #11779280

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212122424242424242424242424243636484848727272
order12223344446666661212121234446661212121212121212121212124121212121212121212121212121212121212121212888824242424242424248888242424242424242444266244
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
χ92222222-22-2222222-2-2-2-2222-2222-2-2222-2-2-2-2-2-22-2-22222-2-2-2-222-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-22-2222222-2-2-2-22-2-2-2222-2-2222-2-2-2-2-2-222-2-2-2-2-2222222-2-2-2-2-2-2222200000000000000000000000000000000
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
χ1522222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-122-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-1-2-211-2-211-1-1-1-11111111100000000000000220000-1-1-1-100-211000
χ1822222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-1-1-1-122-1-2-1-2-211-2-211-1-1-1-11111111100000000000000-2-200001111002-1-1000
χ1922222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-12-22-22-122-1-1-2-2-2-2-122-2-1-1-11122-11111-2-2-1-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-121-2-21122-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-12-22-22-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-11111-2-2-121-2-21122-1-1-1-1111111-1-1-1-100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-12-1-1-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-2211-2-211-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-12-1-1-1-1-1-12-2211-2-211-2-2-1-1-1-111111111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-122-22-2-12-1-1221111-122-2-1-1-1-2-2-1-121111112-2-2-1-12211-2-2-1-111-1-1-1-1111100003333−3−3−3−3000033−3−3000000000000
χ282222-122-22-2-12-1-1221111-122-2-1-1-1-2-2-1-121111112-2-2-1-12211-2-2-1-111-1-1-1-111110000−3−3−3−333330000−3−333000000000000
χ292222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-1211111122-211-2-2-1-122-1-1111111-1-1-1-100003333−3−3−3−30000−3−333000000000000
χ302222-122-22-2-12-1-1221111-1-2-2-2-1-1-1-2-2-1-1211111122-211-2-2-1-122-1-1111111-1-1-1-10000−3−3−3−33333000033−3−3000000000000
χ312-22-22220-20-2-22-22-2000022i−2i0-22-2002-22000000-2002i−2i2i−2i00002-2002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22−2002−22−2000000000000
χ322-22-22220-20-2-22-22-2000022i−2i0-22-2002-22000000-2002i−2i2i−2i00002-2002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2200−22−22000000000000
χ332-22-22220-20-2-22-22-200002−2i2i0-22-2002-22000000-200−2i2i−2i2i00002-200−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2200−22−22000000000000
χ342-22-22220-20-2-22-22-200002−2i2i0-22-2002-22000000-200−2i2i−2i2i00002-200−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22−2002−22−2000000000000
χ352-22-2-1220-201-2-112-23−33−3-12i−2i01-1100-11233−3−33−3-200−ii2i−2i−i3i300-113−3−i−iii−i3−i3i3i3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ362-22-2-1220-201-2-112-23−33−3-12i−2i01-1100-11233−3−33−3-200−ii2i−2i−i3i300-113−3−i−iii−i3−i3i3i3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ372-22-2-1220-201-2-112-23−33−3-1−2i2i01-1100-11233−3−33−3-200i−i−2i2ii3−i300-113−3ii−i−ii3i3−i3−i3−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−2200−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ382-22-2-1220-201-2-112-23−33−3-1−2i2i01-1100-11233−3−33−3-200i−i−2i2ii3−i300-113−3ii−i−ii3i3−i3−i3i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232−200ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ392-22-2-1220-201-2-112-2−33−33-12i−2i01-1100-112−3−333−33-200−ii2i−2ii3−i300-11−33−i−iiii3i3−i3−i3−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ402-22-2-1220-201-2-112-2−33−33-12i−2i01-1100-112−3−333−33-200−ii2i−2ii3−i300-11−33−i−iiii3i3−i3−i3i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ412-22-2-1220-201-2-112-2−33−33-1−2i2i01-1100-112−3−333−33-200i−i−2i2i−i3i300-11−33ii−i−i−i3−i3i3i3−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−2200−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ422-22-2-1220-201-2-112-2−33−33-1−2i2i01-1100-112−3−333−33-200i−i−2i2i−i3i300-11−33ii−i−i−i3−i3i3i3i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72−200ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ432-2-2222020-222-2-2-2-222-2-220002-2-22-20002-22-200000000000000000000000002−22−22−22−22−22−200−i2i20000−i2i2−i2i22i−2i000000
χ442-2-2222020-222-2-2-2-222-2-220002-2-22-20002-22-200000000000000000000000002−22−22−22−22−22−200i2−i20000i2−i2i2−i2−2i2i000000
χ452-2-2222020-222-2-2-2-222-2-220002-2-22-20002-22-20000000000000000000000000−22−22−22−22−22−2200−i2i20000−i2i2−i2i2−2i2i000000
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χ514444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-21111-2-2-24-2-2-2-2-2-2-2-2-211111111111100000000000000000000000000000000
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
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χ544444-2-24-44-4-2-2-2-2-2-222221-4-4-411122-2-2-2-1-1-1-122-2422222-2-2-2-211-1-1-1-1-1-1111100000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111-2-222211112220200000000-1-1-1-13-33-33-33-300000000000000000000000000000000
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χ654-44-444-4040-4-44-44-400004000-44-400-44-400000040000000000-44000000000000000000000000000000000000000000
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χ734-44-4-2-240-4022-22-2223−2323−231−4i4i0-11-100-22-2−3−33323−232002i−2i2i−2i2i3−2i3001-1−33−i−iii−i3−i3i3i300000000000000000000000000000000
χ744-44-4-2-240-4022-22-22−2323−232314i−4i0-11-100-22-233−3−3−2323200−2i2i−2i2i2i3−2i3001-13−3ii−i−i−i3−i3i3i300000000000000000000000000000000
χ754-44-4-2-240-4022-22-22−2323−23231−4i4i0-11-100-22-233−3−3−23232002i−2i2i−2i−2i32i3001-13−3−i−iiii3i3−i3−i300000000000000000000000000000000
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χ774-44-4-2-2-404022-22-2223−2323−231000-11-1002-22−3−333−2323-2000000002i3−2i3-113−33i−3i−3i3i−i3i3i3−i300000000000000000000000000000000
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χ844-4-444-20-4044-2-4-422-4-444-2000-2222-20002-22-2000000000000000000000000000000000000000000000−666−600000000
χ854-4-44-24040-4-2422-4-4-2-222-2000-2224-4000-22-22000000000000000000000000022−2222−22−22−22−22−2200000000000000000000
χ864-4-44-24040-4-2422-4-4-2-222-2000-2224-4000-22-220000000000000000000000000−2222−22222−22−22−22−200000000000000000000
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χ8988-8-88-40000-84-884-40000-400044-4000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-40000444-44-443−43−43432000-2-2200000−232323−23000000000000000000000000000000000000000000000000000000000
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χ928-8-88-4-4080-8-4-44444-4-44420002-2-2-440002-22-2000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-40-808-4-4444444-4-420002-2-24-4000-22-22000000000000000000000000000000000000000000000000000000000

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