Finite Group Databasebeta

← Group #11798892

Character table — Group #11798892

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222222444444444444444488888888121212121212121212121212121212121212121212121212161616161616161618183636364848484848487272
order12223344666666888836661212121224242424242424244412122424242416161616161616164848484848484848484848484848484812121212121212124448822666644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111
χ51111111111111111111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111
χ81111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ922222222222222-2-2-2-222222222-2-2-2-2-2-2-2-20022-2-2-2-200000000000000000000000000000000222-2-200000000
χ1022222222222222-2-2-2-222222222-2-2-2-2-2-2-2-20022-2-2-2-200000000000000000000000000000000-2-2-22200000000
χ11222222-2-222222200002222-2-2-2-20000000000-2-2000022−2−222−2−22222−2−2−2−22222−2−2−2−20000000022-20000000000
χ12222222-2-222222200002222-2-2-2-20000000000-2-2000022−2−2−2−2222222−2−2−2−2−2−2−2−2222200000000-2-220000000000
χ13222222-2-222222200002222-2-2-2-20000000000-2-20000−2−22222−2−2−2−2−2−222222222−2−2−2−200000000-2-220000000000
χ14222222-2-222222200002222-2-2-2-20000000000-2-20000−2−222−2−222−2−2−2−22222−2−2−2−222220000000022-20000000000
χ1522222-1222-12-12-12222-1-1-1-12-12-122-1-122-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000200-1-100
χ1622222-1222-12-12-12222-1-1-1-12-12-122-1-122-1-122-1-1-1-1-1-10000-2-2-2-2000000001111111122-1-1-1-1-1-1000000-2001100
χ1722222-1222-12-12-12222-1-1-1-12-12-122-1-122-1-1-2-2-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-2-2111111000000-2001100
χ1822222-1222-12-12-12222-1-1-1-12-12-122-1-122-1-1-2-2-1-1-1-1-1-10000-2-2-2-20000000011111111-2-2111111000000200-1-100
χ192222-1222-12-12-122222-1-1-1-1-12-12-1-122-1-12222-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000-1-122-1-1-1-10000020-1-10000
χ202222-1222-12-12-122222-1-1-1-1-12-12-1-122-1-12222-1-1-1-1-1-1-2-2-2-200001111111100000000-1-122-1-1-1-100000-20110000
χ212222-1222-12-12-122222-1-1-1-1-12-12-1-122-1-122-2-2-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000011-2-2111100000-20110000
χ222222-1222-12-12-122222-1-1-1-1-12-12-1-122-1-122-2-2-1-1-1-1-1-1-2-2-2-20000111111110000000011-2-211110000020-1-10000
χ2322-2-2220022-2-2-2-22−22−222-2-200002−22−22−22−2000022−2−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−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−ζ43−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−ζ43000000002-202−200000000
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χ2622-2-2220022-2-2-2-22−22−222-2-200002−22−22−22−2000022−2−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+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+ζ43ζ25+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+ζ43000000002-202−200000000
χ2722-2-2220022-2-2-2-2−22−2222-2-20000−22−22−22−220000−2−222ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47000000002-20−2200000000
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χ332-2-22222-2-2-222-2-2-2-2222-22-2-2-222-2-2-2-2222200-22-22-2200000000000000000000000000000000000000000002-2
χ342-2-22222-2-2-222-2-2-2-2222-22-2-2-222-2-2-2-2222200-22-22-220000000000000000000000000000000000000000000-22
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χ362-2-222-12-2-212-1-2122-2-2-11-11-212-122-1-1-2-2112i−2i1-1-11-110000000000000000−33−33−33−332i−2i−ii−i−iii000000000i3−i300
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χ412-2-22-122-21-2-121-222-2-2-11-111-2-12-1-12211-2-2−2i2i1-1-11-11000000003−33−33−33−300000000i−i−2i2iii−i−i0000000i3−i30000
χ422-2-22-122-21-2-121-222-2-2-11-111-2-12-1-12211-2-2−2i2i1-1-11-1100000000−33−33−33−3300000000i−i−2i2iii−i−i0000000−i3i30000
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χ664-44-44-200-42-424-2−222222−22-222-20000−22222−222−22−2200002−2−220000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43000000000000000000000
χ674-44-4-24002-42-4-2422−22−2222-222-20000−2222−222−2−22220000−222−200000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000000000000000000
χ684-44-4-24002-42-4-2422−22−2222-222-20000−2222−222−2−22220000−222−200000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000000000000000000
χ694-44-4-24002-42-4-24−222222−22-222-200002−2−2222−2222−2200002−2−2200000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000000000000000000
χ704-44-4-24002-42-4-24−222222−22-222-200002−2−2222−2222−2200002−2−2200000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000000000000000000
χ714-4-4444-44-4-444-4-400004-44-444-4-400000000004-40000000000000000000000000000000000000000000000000
χ724-4-444-24-4-424-2-42-4-444-22-22-424-2-4-42244-2-2002-22-22-2000000000000000000000000000000000000000000000
χ734-4-444-2-44-424-2-420000-22-224-2-420000000000-22000000000000000000006−66−6−66−66000000000000000000000
χ744-4-444-2-44-424-2-420000-22-224-2-420000000000-2200000000000000000000−66−666−66−6000000000000000000000
χ754-4-44-244-42-4-242-4-4-444-22-222-4-2422-4-4-2-244002-22-22-2000000000000000000000000000000000000000000000
χ764-4-44-24-442-4-242-40000-22-22-242-40000000000-220000000000006−66−6−66−6600000000000000000000000000000
χ774-4-44-24-442-4-242-40000-22-22-242-40000000000-22000000000000−66−666−66−600000000000000000000000000000
χ784-4-44-2-24-422-2-22244-4-41-11-122-2-2-2-2-2-222224i−4i-111-11-1000000000000000000000000−2i2i−2i2iii−i−i0000000000000
χ794-4-44-2-24-422-2-22244-4-41-11-122-2-2-2-2-2-22222−4i4i-111-11-10000000000000000000000002i−2i2i−2i−i−iii0000000000000
χ804-4-44-2-24-422-2-222-4-4441-11-122-2-22222-2-2-2-200-11-11-1100000000000000000000000000003i−3i−3i3i0000000000000
χ814-4-44-2-24-422-2-222-4-4441-11-122-2-22222-2-2-2-200-11-11-110000000000000000000000000000−3i3i3i−3i0000000000000
χ828888-4-4-8-8-4-4-4-4-4-40000222244440000000000-2-20000000000000000000000000000000000000000000000000
χ8388-8-8-4-400-4-4444442−4242−4222-2-20000−2222−2222−2222−2222000022−2−2000000000000000000000000000000000000000000000
χ8488-8-8-4-400-4-44444−4242−424222-2-2000022−2222−2222−2222−220000−2−222000000000000000000000000000000000000000000000
χ858-88-8-4-4004444-4-442−42−42422-2-220000−2222−222222−2222−2200002−2−22000000000000000000000000000000000000000000000
χ868-88-8-4-4004444-4-4−424242−422-2-22000022−2222−22−2222−22220000−222−2000000000000000000000000000000000000000000000
χ878-8-88-4-4-8844-4-44400002-22-2-4-44400000000002-20000000000000000000000000000000000000000000000000

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