Finite Group Databasebeta

← Group #13146447

Character table — Group #13146447

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11222444499999918181818181818181824243636363636363636363636364848485454545454545454108108108108
order123462661244888828812122424242436468812122424242424246612161616161616161616161616
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111iiii−i−i−i−iii−i−i
χ411111111111-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111−i−i−i−iiiii−i−iii
χ5111111111-1-1ii−i−i-1i−i-1-1ii−i−i11-1-1i−i-1-1iii−i−i−i111ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ6111111111-1-1ii−i−i-1i−i-1-1ii−i−i11-1-1i−i-1-1iii−i−i−i111−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ7111111111-1-1−i−iii-1−ii-1-1−i−iii11-1-1−ii-1-1−i−i−iiii111−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ8111111111-1-1−i−iii-1−ii-1-1−i−iii11-1-1−ii-1-1−i−i−iiii111ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ911111-1-1-1111111111111111111-11-1-1-1-11-1-11-1-1-1-1111111111-1-1-1-1
χ1011111-1-1-1111111111111111111-11-1-1-1-11-1-11-1-1-1-11-1-1-1-1-1-1-1-11111
χ1111111-1-1-1111-1-1-1-11-1-111-1-1-1-111-1111-1-1-111-111-1-11iiii−i−i−i−i−i−iii
χ1211111-1-1-1111-1-1-1-11-1-111-1-1-1-111-1111-1-1-111-111-1-11−i−i−i−iiiiiii−i−i
χ1311111-1-1-11-1-1ii−i−i-1i−i-1-1ii−i−i111-1−ii11i−i−i−iii-1-11ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1411111-1-1-11-1-1ii−i−i-1i−i-1-1ii−i−i111-1−ii11i−i−i−iii-1-11−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1511111-1-1-11-1-1−i−iii-1−ii-1-1−i−iii111-1i−i11−iiii−i−i-1-11−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1611111-1-1-11-1-1−i−iii-1−ii-1-1−i−iii111-1i−i11−iiii−i−i-1-11ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ17222-22000-2222222-2-2-2222222220-20000-200-20000-2000000000000
χ18222-22000-222-2-2-2-2-22222-2-2-2-2220-2000020020000-2000000000000
χ19222-22000-2-2-22i2i−2i−2i2−2i2i-2-22i2i−2i−2i22020000−2i002i0000-2000000000000
χ20222-22000-2-2-2−2i−2i2i2i22i−2i-2-2−2i−2i2i2i220200002i00−2i0000-2000000000000
χ212-220-200002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ262-2000000000000000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ470000
χ222-220-200002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ262-2000000000000000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ470000
χ232-220-200002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ262-2000000000000000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ470000
χ242-220-200002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ262-2000000000000000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ470000
χ252-220-20000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ462-2000000000000000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ410000
χ262-220-20000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ462-2000000000000000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ410000
χ272-220-20000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ462-2000000000000000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ410000
χ282-220-20000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ462-2000000000000000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ410000
χ2966-36-36-3-3-3222i2i−2i−2i22i−2i-1-1−i−iii002-12i−2i-1-1−i−i−iiii000000000000000
χ3066-36-36-3-3-322−2i−2i2i2i2−2i2i-1-1ii−i−i002-1−2i2i-1-1iii−i−i−i000000000000000
χ3166-36-36-3-3-3-2-22222-22211-1-1-1-100-212211-1-1-1-1-1-1000000000000000
χ3266-36-36-3-3-3-2-2-2-2-2-2-2-2-211111100-21-2-211111111000000000000000
χ3366-36-3-633-3222i2i−2i−2i22i−2i-1-1−i−iii00-2-1−2i2i11−iiii−i−i000000000000000
χ3466-36-3-633-322−2i−2i2i2i2−2i2i-1-1ii−i−i00-2-12i−2i11i−i−i−iii000000000000000
χ3566-36-3-633-3-2-22222-22211-1-1-1-10021-2-2-1-1-111-111000000000000000
χ3666-36-3-633-3-2-2-2-2-2-2-2-2-2111111002122-1-11-1-11-1-1000000000000000
χ3766-3-6-30−3i33i33222i2i−2i−2i-2−2i2i-1-1−i−iii000100−i3i3i3−3−i3−3000000000000000
χ3866-3-6-30−3i33i3322−2i−2i2i2i-22i−2i-1-1ii−i−i000100−i3i3−i−33i−33000000000000000
χ3966-3-6-30−3i33i33-2-222222-2-211-1-1-1-1000-100i3−i31−i3i31i3−i3000000000000000
χ4066-3-6-30−3i33i33-2-2-2-2-2-2222111111000-100i3−i3-1i3−i3-1−i3i3000000000000000
χ4166-3-6-303i3−3i33222i2i−2i−2i-2−2i2i-1-1−i−iii000100i3−i3i−33−i−33000000000000000
χ4266-3-6-303i3−3i3322−2i−2i2i2i-22i−2i-1-1ii−i−i000100i3−i3−i3−3i3−3000000000000000
χ4366-3-6-303i3−3i33-2-222222-2-211-1-1-1-1000-100−i3i31i3−i31−i3i3000000000000000
χ4466-3-6-303i3−3i33-2-2-2-2-2-2222111111000-100−i3i3-1−i3i3-1i3−i3000000000000000
χ45888888888000000000000000-1-1000000000000-1-1-1000000000000
χ4688888-8-8-88000000000000000-1-100000000000011-1000000000000
χ47888-88000-8000000000000000-1-10000000000003-31000000000000
χ48888-88000-8000000000000000-1-1000000000000-331000000000000
χ4912-12-60600004i−4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ46000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000000000000000000000000
χ5012-12-60600004i−4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ46000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000000000000000000000000
χ5112-12-6060000−4i4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ260002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000000000000000000000000
χ5212-12-6060000−4i4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ260002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000000000000000000000000
χ5316-16160-160000000000000000000-22000000000000000000000000000

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