Finite Group Databasebeta

← Group #11798891

Character table — Group #11798891

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222444444444444444466666688888888888812121212121212121212121212121212121212121216161616161624242424242436363636484848144
order1222334466666688883666121212122424242424242424441212121244121212121212242424244881212161616162424242448484848484848481212121212124412121212161616162662
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1
χ922222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222222200000022-2-2-2-22-2-2220000-2-2-2-20000000000000000000000000000
χ1022222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000022-2-2-2-2-222-2-2000022220000000000000000000000000000
χ11222222-2-222222200002222-2-2-2-200000000222222000000-2-20000-200-2-222−2−200002222−2−2−2−200000000000022−2−20000
χ12222222-2-222222200002222-2-2-2-200000000222222000000-2-20000-200-2-2−2−2220000−2−2−2−22222000000000000−2−2220000
χ13222222-2-222222200002222-2-2-2-200000000-2-2-2-2-2-2000000-2-200002002222−2−200002222−2−2−2−2000000000000−2−2220000
χ14222222-2-222222200002222-2-2-2-200000000-2-2-2-2-2-2000000-2-2000020022−2−2220000−2−2−2−2222200000000000022−2−20000
χ1522222-122-1-12-1222222-1-1-1-1-1-1222222-1-1-1-1000000222222-1-1-1-1-1-10000022220000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-10
χ1622222-122-1-12-1222222-1-1-1-1-1-1222222-1-1-1-1000000222222-1-1-1-1-1-100000-2-2-2-2000011111111-1-1-1-1-1-10000000000-2110
χ1722222-122-1-12-1222222-1-1-1-1-1-1222222-1-1-1-1000000-2-2-2-2-2-2-1-1-1-1-1-10000022220000-1-1-1-1-1-1-1-11111110000000000-2110
χ1822222-122-1-12-1222222-1-1-1-1-1-1222222-1-1-1-1000000-2-2-2-2-2-2-1-1-1-1-1-100000-2-2-2-200001111111111111100000000002-1-10
χ192222-122222-12-1-12222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1222-1-10000-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ202222-122222-12-1-12222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-2-21111-1-1-1-1-1-1222-1-10000-1-1-1-100000000-2-21111-2-2111100000000
χ212222-122222-12-1-12222-1-1-1-122-1-1-1-1-1-12222-2-2111122-1-1-1-1-1-1-1-1-1-1-2-2-211000011110000000022-1-1-1-1-2-2111100000000
χ222222-122222-12-1-12222-1-1-1-122-1-1-1-1-1-12222-2-21111-2-21111-1-1-1-1-1-1-2-2-2110000111100000000-2-2111122-1-1-1-100000000
χ232222-122222-12-1-1-2-2-2-2-1-1-1-122-1-11111-2-2-2-222-1-1-1-100−i3−i3i3i3-1-111112-2-2-1-1000011110000000000−i3−i3i3i300−i3−i3i3i300000000
χ242222-122222-12-1-1-2-2-2-2-1-1-1-122-1-11111-2-2-2-222-1-1-1-100i3i3−i3−i3-1-111112-2-2-1-1000011110000000000i3i3−i3−i300i3i3−i3−i300000000
χ252222-122222-12-1-1-2-2-2-2-1-1-1-122-1-11111-2-2-2-2-2-2111100−i3−i3i3i3-1-11111-222110000-1-1-1-10000000000−i3−i3i3i300i3i3−i3−i300000000
χ262222-122222-12-1-1-2-2-2-2-1-1-1-122-1-11111-2-2-2-2-2-2111100i3i3−i3−i3-1-11111-222110000-1-1-1-10000000000i3i3−i3−i300−i3−i3i3i300000000
χ2722-2-222002-22-2-2-22−22−222-2-2000022−2−22−22−22-222-2-20000000022−2−202−200−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4322−2−2−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43000000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
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χ2922-2-222002-22-2-2-22−22−222-2-2000022−2−22−22−2-22-2-2220000000022−2−20−2200−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−2−222−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43000000000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ3022-2-222002-22-2-2-22−22−222-2-2000022−2−22−22−2-22-2-2220000000022−2−20−2200ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−2−222ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43000000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
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χ3222-2-222002-22-2-2-2−22−2222-2-20000−2−222−22−222-222-2-200000000−2−2220−2200−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−2−222−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47000000000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
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χ3422-2-222002-22-2-2-2−22−2222-2-20000−2−222−22−22-22-2-22200000000−2−22202−200−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4722−2−2−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47000000000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ352-2-22222-2-22-2-2-2222-2-22-22-2-222-22-22-222-2-20000002i−2i2i−2i2i−2i-222-22-20000000000000000000002i−2i2i−2i2i−2i00000000000000
χ362-2-22222-2-22-2-2-2222-2-22-22-2-222-22-22-222-2-2000000−2i2i−2i2i−2i2i-222-22-2000000000000000000000−2i2i−2i2i−2i2i00000000000000
χ372-2-22222-2-22-2-2-22-2-2222-22-2-222-2-22-22-2-222000000000000-22-22-220000000000000000000000000002-22-22-200000000
χ382-2-22222-2-22-2-2-22-2-2222-22-2-222-2-22-22-2-222000000000000-22-22-22000000000000000000000000000-22-22-2200000000
χ392-2-222-12-21-1-21-2222-2-2-11-111-12-22-22-2-1-1110000002i−2i2i−2i2i−2i1-1-11-1100000000000003−33−33−33−3−ii−ii−ii00000000000−i3i30
χ402-2-222-12-21-1-21-2222-2-2-11-111-12-22-22-2-1-1110000002i−2i2i−2i2i−2i1-1-11-110000000000000−33−33−33−33−ii−ii−ii00000000000i3−i30
χ412-2-222-12-21-1-21-2222-2-2-11-111-12-22-22-2-1-111000000−2i2i−2i2i−2i2i1-1-11-1100000000000003−33−33−33−3i−ii−ii−i00000000000i3−i30
χ422-2-222-12-21-1-21-2222-2-2-11-111-12-22-22-2-1-111000000−2i2i−2i2i−2i2i1-1-11-110000000000000−33−33−33−33i−ii−ii−i00000000000−i3i30
χ432-2-22-122-2-221-21-122-2-2-11-11-22-11-11-1122-2-2003−33−32i−2i−ii−ii1-1-11-110003−300003−33−3000000002i−2i−ii−ii00−i3i3i3−i300000000
χ442-2-22-122-2-221-21-122-2-2-11-11-22-11-11-1122-2-2003−33−3−2i2ii−ii−i1-1-11-110003−300003−33−300000000−2i2ii−ii−i00i3−i3−i3i300000000
χ452-2-22-122-2-221-21-122-2-2-11-11-22-11-11-1122-2-200−33−332i−2i−ii−ii1-1-11-11000−330000−33−33000000002i−2i−ii−ii00i3−i3−i3i300000000
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χ472-2-22-122-2-221-21-1-2-222-11-11-22-111-11-1-2-222003−33−3003−3−331-11-11-10003−30000−33−3300000000003−3−332-2-11-1100000000
χ482-2-22-122-2-221-21-1-2-222-11-11-22-111-11-1-2-222003−33−300−333−31-11-11-10003−30000−33−330000000000−333−3-221-11-100000000
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χ804-4-444-2-442-2-42-440000-22-22-22-4400000000000000000000-22000000000000000006−66−6−66−6600000000000000000000
χ814-4-444-2-442-2-42-440000-22-22-22-4400000000000000000000-2200000000000000000−66−666−66−600000000000000000000
χ824-4-44-24-44-442-42-20000-22-224-42-2000000000023−2323−23000000-220000000−2323000000000000000000000000000000000000
χ834-4-44-24-44-442-42-20000-22-224-42-20000000000−2323−2323000000-22000000023−23000000000000000000000000000000000000
χ844-4-44-2-24-42-2222-244-4-41-11-12-2-22-22-22-2-2220000004i−4i−2i2i−2i2i-111-11-1000000000000000000000−2i2ii−ii−i00000000000000
χ854-4-44-2-24-42-2222-244-4-41-11-12-2-22-22-22-2-222000000−4i4i2i−2i2i−2i-111-11-10000000000000000000002i−2i−ii−ii00000000000000
χ864-4-44-2-24-42-2222-2-4-4441-11-12-2-222-22-222-2-20000000023−23−2323-11-11-1100000000000000000000000−333−300000000000000
χ874-4-44-2-24-42-2222-2-4-4441-11-12-2-222-22-222-2-200000000−232323−23-11-11-11000000000000000000000003−3−3300000000000000
χ888888-4-4-8-8-4-4-4-4-4-400002222444400000000000000000000-2-2000000000000000000000000000000000000000000000
χ8988-8-8-4-400-44-444442−4242−4222-2-20000−22−222222−2222−22220000000000000022−2−200000000000000000000000000000000000000000
χ9088-8-8-4-400-44-4444−4242−424222-2-200002222−22−2222−2222−2200000000000000−2−22200000000000000000000000000000000000000000
χ918-88-8-4-400444-4-4442−42−42422-2-220000−222222−22−222222−22000000000000002−2−2200000000000000000000000000000000000000000
χ928-88-8-4-400444-4-44−424242−422-2-22000022−22−222222−22−222200000000000000−222−200000000000000000000000000000000000000000
χ938-8-88-4-4-884-4444-400002-22-2-444-4000000000000000000002-2000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.