Finite Group Databasebeta

← Group #11799644

Character table — Group #11799644

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222444444444444444466666688888888888812121212121212121212121212121212121212121216161616161624242424242436363636484848144
order12223344666666888836661212121224242424242424244412121212441212121212122424242448812121616161624242424484848484848484812121212121222666616161616412124
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
χ1522222-1222-1-12-122222-1-1-1-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1222-1-10000-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ1622222-1222-1-12-122222-1-1-1-122-1-122-1-1-1-12222-1-1-1-1-2-21111-1-1-1-1-1-1222-1-10000-1-1-1-100000000-2-21111-2-2111100000000
χ1722222-1222-1-12-122222-1-1-1-122-1-122-1-1-1-122-2-2111122-1-1-1-1-1-1-1-1-1-1-2-2-211000011110000000022-1-1-1-1-2-2111100000000
χ1822222-1222-1-12-122222-1-1-1-122-1-122-1-1-1-122-2-21111-2-21111-1-1-1-1-1-1-2-2-2110000111100000000-2-2111122-1-1-1-100000000
χ1922222-1222-1-12-12-2-2-2-2-1-1-1-122-1-1-2-21111-2-222-1-1-1-100−i3−i3i3i3-1-111112-2-2-1-1000011110000000000−i3−i3i3i300−i3−i3i3i300000000
χ2022222-1222-1-12-12-2-2-2-2-1-1-1-122-1-1-2-21111-2-222-1-1-1-100i3i3−i3−i3-1-111112-2-2-1-1000011110000000000i3i3−i3−i300i3i3−i3−i300000000
χ2122222-1222-1-12-12-2-2-2-2-1-1-1-122-1-1-2-21111-2-2-2-2111100−i3−i3i3i3-1-11111-222110000-1-1-1-10000000000−i3−i3i3i300i3i3−i3−i300000000
χ2222222-1222-1-12-12-2-2-2-2-1-1-1-122-1-1-2-21111-2-2-2-2111100i3i3−i3−i3-1-11111-222110000-1-1-1-10000000000i3i3−i3−i300−i3−i3i3i300000000
χ232222-1222-122-12-12222-1-1-1-1-1-122-1-12222-1-1000000222222-1-1-1-1-1-10000022220000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000002-1-10
χ242222-1222-122-12-12222-1-1-1-1-1-122-1-12222-1-1000000222222-1-1-1-1-1-100000-2-2-2-2000011111111-1-1-1-1-1-10000000000-2110
χ252222-1222-122-12-12222-1-1-1-1-1-122-1-12222-1-1000000-2-2-2-2-2-2-1-1-1-1-1-10000022220000-1-1-1-1-1-1-1-11111110000000000-2110
χ262222-1222-122-12-12222-1-1-1-1-1-122-1-12222-1-1000000-2-2-2-2-2-2-1-1-1-1-1-100000-2-2-2-200001111111111111100000000002-1-10
χ2722-2-2222-222-2-2-2-222-2-22-22-2-222-22222-2-2-2-2000000000000-2222-2-20000000000000000000000000002-22-22-200000000
χ2822-2-2222-222-2-2-2-222-2-22-22-2-222-22222-2-2-2-2000000000000-2222-2-2000000000000000000000000000-22-22-2200000000
χ2922-2-2222-222-2-2-2-2-2-2222-22-2-222-2-2-2-2-222220000002i−2i2i−2i2i−2i-22-2-2220000000000000000000002i−2i2i−2i2i−2i00000000000000
χ3022-2-2222-222-2-2-2-2-2-2222-22-2-222-2-2-2-2-22222000000−2i2i−2i2i−2i2i-22-2-222000000000000000000000−2i2i−2i2i−2i2i00000000000000
χ3122-2-22-12-22-11-21-222-2-2-11-11-22-1122-1-111-2-20033−3−3003−3−331-1-1-1110003−3000033−3−300000000003−3−332-2-11-1100000000
χ3222-2-22-12-22-11-21-222-2-2-11-11-22-1122-1-111-2-20033−3−300−333−31-1-1-1110003−3000033−3−30000000000−333−3-221-11-100000000
χ3322-2-22-12-22-11-21-222-2-2-11-11-22-1122-1-111-2-200−3−333003−3−331-1-1-111000−330000−3−33300000000003−3−33-221-11-100000000
χ3422-2-22-12-22-11-21-222-2-2-11-11-22-1122-1-111-2-200−3−33300−333−31-1-1-111000−330000−3−3330000000000−333−32-2-11-1100000000
χ3522-2-22-12-22-11-21-2-2-222-11-11-22-11-2-211-1-1220033−3−32i−2i−ii−ii1-111-1-10003−30000−3−333000000002i−2i−ii−ii00−i3i3i3−i300000000
χ3622-2-22-12-22-11-21-2-2-222-11-11-22-11-2-211-1-1220033−3−3−2i2ii−ii−i1-111-1-10003−30000−3−33300000000−2i2ii−ii−i00i3−i3−i3i300000000
χ3722-2-22-12-22-11-21-2-2-222-11-11-22-11-2-211-1-12200−3−3332i−2i−ii−ii1-111-1-1000−33000033−3−3000000002i−2i−ii−ii00i3−i3−i3i300000000
χ3822-2-22-12-22-11-21-2-2-222-11-11-22-11-2-211-1-12200−3−333−2i2ii−ii−i1-111-1-1000−33000033−3−300000000−2i2ii−ii−i00−i3i3i3−i300000000
χ3922-2-2-122-2-12-21-21-2-222-11-111-12-211-2-222-1-10000002i−2i2i−2i2i−2i1-111-1-10000000000000−i3−i3i3i3−i3−i3i3i3−ii−ii−ii000000000003−30
χ4022-2-2-122-2-12-21-21-2-222-11-111-12-211-2-222-1-10000002i−2i2i−2i2i−2i1-111-1-10000000000000i3i3−i3−i3i3i3−i3−i3−ii−ii−ii00000000000−330
χ4122-2-2-122-2-12-21-21-2-222-11-111-12-211-2-222-1-1000000−2i2i−2i2i−2i2i1-111-1-10000000000000−i3−i3i3i3−i3−i3i3i3i−ii−ii−i00000000000−330
χ4222-2-2-122-2-12-21-21-2-222-11-111-12-211-2-222-1-1000000−2i2i−2i2i−2i2i1-111-1-10000000000000i3i3−i3−i3i3i3−i3−i3i−ii−ii−i000000000003−30
χ432-22-22200-2-22-2-222−22−222-2-200002−22−22−22−22i−2i2i−2i2i−2i000000002−22−20−i2i200−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−i2i2−i2i2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000
χ442-22-22200-2-22-2-222−22−222-2-200002−22−22−22−22i−2i2i−2i2i−2i000000002−22−20−i2i200ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−i2i2−i2i2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000
χ452-22-22200-2-22-2-222−22−222-2-200002−22−22−22−2−2i2i−2i2i−2i2i000000002−22−20i2−i200−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43i2−i2i2−i2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000
χ462-22-22200-2-22-2-222−22−222-2-200002−22−22−22−2−2i2i−2i2i−2i2i000000002−22−20i2−i200ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43i2−i2i2−i2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000
χ472-22-22200-2-22-2-22−22−2222-2-20000−22−22−22−222i−2i2i−2i2i−2i00000000−22−220i2−i200ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47i2−i2i2−i2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000
χ482-22-22200-2-22-2-22−22−2222-2-20000−22−22−22−222i−2i2i−2i2i−2i00000000−22−220i2−i200−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47i2−i2i2−i2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000
χ492-22-22200-2-22-2-22−22−2222-2-20000−22−22−22−22−2i2i−2i2i−2i2i00000000−22−220−i2i200ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−i2i2−i2i2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000
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χ5144444-2-4-44-2-24-240000-2-2-2-2-4-4220000000044-2-2-2-2000000220000-40022000000000000000000000000000000000000
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χ554444-24-4-4-244-24-20000-2-2-2-222-4-40000000000000000000022000000000−22−22222200002222−2−2−2−200000000000000000000
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χ574444-2-244-2-2-2-2-2-244441111-2-2-2-2-2-2-2-2-2-2-2-2000000-4-4222211111100000000000000000000022-1-1-1-100000000000000
χ584444-2-244-2-2-2-2-2-2-4-4-4-41111-2-2-2-22222222200000000−2i3−2i32i32i311-1-1-1-100000000000000000000000i3i3−i3−i300000000000000
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χ6044-4-444-4444-4-4-4-400004-44-44-4-44000000000000000000004-4000000000000000000000000000000000000000000000
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χ724-44-44-200-42-2-424−2222−2222-2-2220000−22222−22−2−22224i−4i−2i2i−2i2i000000002−22−202i2−2i2000000−i2i2−i2i20000000000000000000000000000
χ734-44-44-200-42-2-424−2222−2222-2-2220000−22222−22−2−2222−4i4i2i−2i2i−2i000000002−22−20−2i22i2000000i2−i2i2−i20000000000000000000000000000
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χ804-4-444-200-4224-2-422−22−2222-222-2000022−22−222−2−222200−2i32i32i3−2i300000000−222−2000000000i6−i6−i6i60000000000000000000000000000
χ814-4-444-200-4224-2-422−22−2222-222-2000022−22−222−2−2222002i3−2i3−2i32i300000000−222−2000000000−i6i6i6−i60000000000000000000000000000
χ824-4-444-200-4224-2-4−222222−22-222-20000−22222−2−2222−2200−2i32i32i3−2i3000000002−2−22000000000−i6i6i6−i60000000000000000000000000000
χ834-4-444-200-4224-2-4−222222−22-222-20000−22222−2−2222−22002i3−2i3−2i32i3000000002−2−22000000000i6−i6−i6i60000000000000000000000000000
χ844-4-44-24002-4-4-24222−22−2222-222-20000−2222−22−22222−200000000000000−222−20000000000000−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000
χ854-4-44-24002-4-4-24222−22−2222-222-20000−2222−22−22222−200000000000000−222−20000000000000ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000
χ864-4-44-24002-4-4-242−222222−22-222-200002−2−222222−22−22000000000000002−2−220000000000000−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000
χ874-4-44-24002-4-4-242−222222−22-222-200002−2−222222−22−22000000000000002−2−220000000000000ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000
χ888888-4-4-8-8-4-4-4-4-4-400002222444400000000000000000000-2-2000000000000000000000000000000000000000000000
χ8988-8-8-4-4-88-4-4444400002-22-2-444-4000000000000000000002-2000000000000000000000000000000000000000000000
χ908-88-8-4-40044-444-442−4242−4222-2-20000−2222−2222−2222−2222000000000000002−22−200000000000000000000000000000000000000000
χ918-88-8-4-40044-444-4−4242−424222-2-2000022−2222−2222−2222−2200000000000000−22−2200000000000000000000000000000000000000000
χ928-8-88-4-400444-4-4442−42−42422-2-220000−2222−222222−2222−22000000000000002−2−2200000000000000000000000000000000000000000
χ938-8-88-4-400444-4-44−424242−422-2-22000022−2222−22−2222−222200000000000000−222−200000000000000000000000000000000000000000

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