Finite Group Databasebeta

← Group #11798942

Character table — Group #11798942

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222222444444444444444488888812121212121212121212121212121212121212121212121216161616161616161618182424242436363648484848144
order122233446666668888366612121212242424242424242412122424242416161616161616164848484848484848484848484848484841212121212121212444444488121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-111-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-111-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1
χ922222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000000002200002-2-200000
χ1022222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000000-2-20000-22200000
χ11222222-2-222222200002222-2-2-2-200000000-2-2000022−2−222−2−22222−2−2−2−22222−2−2−2−2000000000220000-20000000
χ12222222-2-222222200002222-2-2-2-200000000-2-2000022−2−2−2−2222222−2−2−2−2−2−2−2−22222000000000-2-2000020000000
χ13222222-2-222222200002222-2-2-2-200000000-2-20000−2−22222−2−2−2−2−2−222222222−2−2−2−2000000000-2-2000020000000
χ14222222-2-222222200002222-2-2-2-200000000-2-20000−2−222−2−222−2−2−2−22222−2−2−2−22222000000000220000-20000000
χ1522222-12222-1-1-122222-1-1-1-1-12-1222-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000002-1-122-1-1-1-1002200000-1-1000
χ1622222-12222-1-1-122222-1-1-1-1-12-1222-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000-211-2-2111100-2-20000011000
χ1722222-12222-1-1-122222-1-1-1-1-12-1222-1-122-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000002-1-122-1-1-1-100-2-20000011000
χ1822222-12222-1-1-122222-1-1-1-1-12-1222-1-122-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000-211-2-21111002200000-1-1000
χ192222-1222-1-1222-12222-1-1-1-12-12-1-1-122-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1222-1-1-1-1-1-100002200000-1-10
χ202222-1222-1-1222-12222-1-1-1-12-12-1-1-122-1-122-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-2-2-21111110000-2-200000110
χ212222-1222-1-1222-12222-1-1-1-12-12-1-1-122-1-122-1-1-1-1-1-10000-2-2-2-20000000011111111222-1-1-1-1-1-10000-2-200000110
χ222222-1222-1-1222-12222-1-1-1-12-12-1-1-122-1-122-1-1-1-1-1-10000-2-2-2-20000000011111111-2-2-211111100002200000-1-10
χ2322-2-222002-22-2-2-22−22−222-2-200002−22−22−22−20022−2−2−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−ζ430000000002-2000002−200000
χ2422-2-222002-22-2-2-22−22−222-2-200002−22−22−22−20022−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−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−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+ζ43000000000-2200000−2200000
χ2522-2-222002-22-2-2-22−22−222-2-200002−22−22−22−20022−2−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+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+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−ζ43000000000-2200000−2200000
χ2622-2-222002-22-2-2-22−22−222-2-200002−22−22−22−20022−2−2ζ25−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+ζ430000000002-2000002−200000
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χ3022-2-222002-22-2-2-2−22−2222-2-20000−22−22−22−2200−2−222−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−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−ζ47−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−ζ470000000002-200000−2200000
χ312-2-22222-2-2-2-22-2222-2-22-2-22-2-2222222-2-2-2-2-222-22-2000000000000000000000000000000000002i−2i000002i−2i000
χ322-2-22222-2-2-2-22-2222-2-22-2-22-2-2222222-2-2-2-2-222-22-200000000000000000000000000000000000−2i2i00000−2i2i000
χ332-2-22222-2-2-2-22-22-2-2222-2-22-2-222-2-2-2-22222-22-22-2200000000000000000000000000000000000002-2000002-20
χ342-2-22222-2-2-2-22-22-2-2222-2-22-2-222-2-2-2-22222-22-22-220000000000000000000000000000000000000-2200000-220
χ352-2-222-12-2-2-21-11222-2-2-111-11-2-1222-1-1-2-2111-1-11-11000000003−33−33−33−3000000000−i3i300−i3−i3i3i3002i−2i00000−ii000
χ362-2-222-12-2-2-21-11222-2-2-111-11-2-1222-1-1-2-2111-1-11-11000000003−33−33−33−3000000000i3−i300i3i3−i3−i300−2i2i00000i−i000
χ372-2-222-12-2-2-21-11222-2-2-111-11-2-1222-1-1-2-2111-1-11-1100000000−33−33−33−33000000000−i3i300−i3−i3i3i300−2i2i00000i−i000
χ382-2-222-12-2-2-21-11222-2-2-111-11-2-1222-1-1-2-2111-1-11-1100000000−33−33−33−33000000000i3−i300i3i3−i3−i3002i−2i00000−ii000
χ392-2-22-122-211-22-2-1-2-222-111-1-212-111-2-2-1-1221-11-11-10000000000000000−i3i3−i3i3−i3i3−i3i3000−i3i3−i3i3−i3i300002-200000-110
χ402-2-22-122-211-22-2-1-2-222-111-1-212-111-2-2-1-1221-11-11-10000000000000000−i3i3−i3i3−i3i3−i3i3000i3−i3i3−i3i3−i30000-22000001-10
χ412-2-22-122-211-22-2-1-2-222-111-1-212-111-2-2-1-1221-11-11-10000000000000000i3−i3i3−i3i3−i3i3−i3000−i3i3−i3i3−i3i30000-22000001-10
χ422-2-22-122-211-22-2-1-2-222-111-1-212-111-2-2-1-1221-11-11-10000000000000000i3−i3i3−i3i3−i3i3−i3000i3−i3i3−i3i3−i300002-200000-110
χ4344444-24444-2-2-24-4-4-4-4-2-2-2-2-24-24-4-422-4-422-2-2222200000000000000000000000000000000000000000000000
χ4444444-2-4-444-2-2-240000-2-2-2-22-42-4000000002200002222−22−220000−2−2−2−222220000000000000000000000000000000
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χ654-44-44-200-4422-2-4−222222−22-22-220000−22222−222−22−22002−2−2200000000−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−ζ430000000000000000000000000000000
χ664-44-44-200-4422-2-4−222222−22-22-220000−22222−222−22−22002−2−2200000000ζ25+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+ζ430000000000000000000000000000000
χ674-44-4-24002-2-4-44222−22−2222-22-220000−2222−222−2−222200−222−20000000000000000−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+ζ4700000000000000000000000
χ684-44-4-24002-2-4-44222−22−2222-22-220000−2222−222−2−222200−222−20000000000000000ζ11+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−ζ4700000000000000000000000
χ694-44-4-24002-2-4-442−222222−22-22-2200002−2−2222−2222−22002−2−220000000000000000−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+ζ4300000000000000000000000
χ704-44-4-24002-2-4-442−222222−22-22-2200002−2−2222−2222−22002−2−220000000000000000ζ25−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−ζ4300000000000000000000000
χ714-4-4444-44-4-4-44-4400004-4-4444-4-4000000004-4000000000000000000000000000000000000000000000000000
χ724-4-444-24-4-4-42-224-4-444-222-22-4-24-4-42244-2-22-22-22-200000000000000000000000000000000000000000000000
χ734-4-444-2-44-4-42-2240000-222-2-242-400000000-220000000000006−66−6−66−660000000000000000000000000000000
χ744-4-444-2-44-4-42-2240000-222-2-242-400000000-22000000000000−66−666−66−60000000000000000000000000000000
χ754-4-44-244-422-44-4-244-4-4-222-2-424-2-2-24422-4-42-2-22-2200000000000000000000000000000000000000000000000
χ764-4-44-24-4422-44-4-20000-222-24-2-4200000000-2200000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ774-4-44-24-4422-44-4-20000-222-24-2-4200000000-2200000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ784-4-44-2-24-4222-22-244-4-41-1-1122-2-2-2-2-2-22222-111-11-10000000000000000000000000−2i32i300i3i3−i3−i300000000000000
χ794-4-44-2-24-4222-22-244-4-41-1-1122-2-2-2-2-2-22222-111-11-100000000000000000000000002i3−2i300−i3−i3i3i300000000000000
χ804-4-44-2-24-4222-22-2-4-4441-1-1122-2-22222-2-2-2-2-11-11-11000000000000000000000000000−2i32i3i3−i3i3−i300000000000000
χ814-4-44-2-24-4222-22-2-4-4441-1-1122-2-22222-2-2-2-2-11-11-110000000000000000000000000002i3−2i3−i3i3−i3i300000000000000
χ828888-4-4-8-8-4-4-4-4-4-400002222444400000000-2-2000000000000000000000000000000000000000000000000000
χ8388-8-8-4-400-44-444442−4242−4222-2-20000−2222−2222−2222−22220022−2−200000000000000000000000000000000000000000000000
χ8488-8-8-4-400-44-4444−4242−424222-2-2000022−2222−2222−2222−2200−2−22200000000000000000000000000000000000000000000000
χ858-88-8-4-4004-444-4442−42−42422-22-20000−2222−222222−2222−22002−2−2200000000000000000000000000000000000000000000000
χ868-88-8-4-4004-444-44−424242−422-22-2000022−2222−22−2222−222200−222−200000000000000000000000000000000000000000000000
χ878-8-88-4-4-88444-44-400002-2-22-4-444000000002-2000000000000000000000000000000000000000000000000000

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