Finite Group Databasebeta

← Group #11772202

Character table — Group #11772202

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111228888888818181818181818182424242424242424242424243636363636363636363672727272
order124488361212242424242488888816161616484848484848484844161616161616161616161616
χ1111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111-1-11111-1-1-1-1111111-1-1ii−i−iiiii−i−i−i−i-1-11111-1-1-1-1ii−i−i
χ61111-1-11111-1-1-1-1111111-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-11111−i−iii
χ71111-1-11111-1-1-1-1111111-1-1−i−iii−i−i−i−iiiii-1-11111-1-1-1-1−i−iii
χ81111-1-11111-1-1-1-1111111-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-11111ii−i−i
χ911-1-1i−i11-1-1ii−i−i-1111-1-1i−iζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26i−i11-1-1ii−i−iζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1011-1-1i−i11-1-1ii−i−i-1111-1-1i−iζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26i−i-1-111−i−iii−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1111-1-1i−i11-1-1ii−i−i-1111-1-1i−i−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26i−i11-1-1ii−i−i−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1211-1-1i−i11-1-1ii−i−i-1111-1-1i−i−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26i−i-1-111−i−iiiζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1311-1-1−ii11-1-1−i−iii-1111-1-1−ii−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ii11-1-1−i−iii−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ1411-1-1−ii11-1-1−i−iii-1111-1-1−ii−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ii-1-111ii−i−iζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1511-1-1−ii11-1-1−i−iii-1111-1-1−iiζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ii11-1-1−i−iiiζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1611-1-1−ii11-1-1−i−iii-1111-1-1−iiζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ii-1-111ii−i−i−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ172222222222222222-2-2-2-222000000000000-2-2000000000000
χ1822222222222222-2-20000-2-200000000000000−i2i2−i2i2−i2i2−i2i20000
χ1922222222222222-2-20000-2-200000000000000i2−i2i2−i2i2−i2i2−i20000
χ202222-2-22222-2-2-2-222-2-2-2-2-2-200000000000022000000000000
χ212222-2-22222-2-2-2-2-2-200002200000000000000−i2i2−i2i2i2−i2i2−i20000
χ222222-2-22222-2-2-2-2-2-200002200000000000000i2−i2i2−i2−i2i2−i2i20000
χ2322-2-22i−2i22-2-22i2i−2i−2i2-20000−2i2i00000000000000−i2i2i2−i22−2−220000
χ2422-2-22i−2i22-2-22i2i−2i−2i2-20000−2i2i00000000000000i2−i2−i2i2−222−20000
χ2522-2-22i−2i22-2-22i2i−2i−2i-22-2-2222i−2i000000000000−2i2i000000000000
χ2622-2-2−2i2i22-2-2−2i−2i2i2i2-200002i−2i00000000000000−i2i2i2−i2−222−20000
χ2722-2-2−2i2i22-2-2−2i−2i2i2i2-200002i−2i00000000000000i2−i2−i2i22−2−220000
χ2822-2-2−2i2i22-2-2−2i−2i2i2i-22-2-222−2i2i0000000000002i−2i000000000000
χ294-44i−4i004-44i−4i000000−2i22i222−220000000000000000000000000000
χ304-44i−4i004-44i−4i0000002i2−2i2−22220000000000000000000000000000
χ314-4−4i4i004-4−4i4i000000−2i22i2−22220000000000000000000000000000
χ324-4−4i4i004-4−4i4i0000002i2−2i222−220000000000000000000000000000
χ33888888-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ34888888-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ358888-8-8-1-1-1-11111000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ368888-8-8-1-1-1-1111100000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ3788-8-88i−8i-1-111−i−iii000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2600000000000000
χ3888-8-88i−8i-1-111−i−iii00000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2600000000000000
χ3988-8-8−8i8i-1-111ii−i−i00000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4600000000000000
χ4088-8-8−8i8i-1-111ii−i−i000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4600000000000000
χ418-88i−8i00-11−ii3ζ14+3ζ46−3ζ14−3ζ46−3ζ10−3ζ263ζ10+3ζ26000000000000−ζ11+ζ43ζ11−ζ43−ζ31+ζ47ζ31−ζ47ζ13−ζ29−ζ13+ζ29−ζ25+ζ41ζ25−ζ4100000000000000
χ428-88i−8i00-11−ii3ζ14+3ζ46−3ζ14−3ζ46−3ζ10−3ζ263ζ10+3ζ26000000000000ζ11−ζ43−ζ11+ζ43ζ31−ζ47−ζ31+ζ47−ζ13+ζ29ζ13−ζ29ζ25−ζ41−ζ25+ζ4100000000000000
χ438-88i−8i00-11−ii−3ζ14−3ζ463ζ14+3ζ463ζ10+3ζ26−3ζ10−3ζ26000000000000−ζ31+ζ47ζ31−ζ47ζ11−ζ43−ζ11+ζ43−ζ25+ζ41ζ25−ζ41−ζ13+ζ29ζ13−ζ2900000000000000
χ448-88i−8i00-11−ii−3ζ14−3ζ463ζ14+3ζ463ζ10+3ζ26−3ζ10−3ζ26000000000000ζ31−ζ47−ζ31+ζ47−ζ11+ζ43ζ11−ζ43ζ25−ζ41−ζ25+ζ41ζ13−ζ29−ζ13+ζ2900000000000000
χ458-8−8i8i00-11i−i−3ζ10−3ζ263ζ10+3ζ263ζ14+3ζ46−3ζ14−3ζ46000000000000ζ13−ζ29−ζ13+ζ29−ζ25+ζ41ζ25−ζ41−ζ11+ζ43ζ11−ζ43−ζ31+ζ47ζ31−ζ4700000000000000
χ468-8−8i8i00-11i−i−3ζ10−3ζ263ζ10+3ζ263ζ14+3ζ46−3ζ14−3ζ46000000000000−ζ13+ζ29ζ13−ζ29ζ25−ζ41−ζ25+ζ41ζ11−ζ43−ζ11+ζ43ζ31−ζ47−ζ31+ζ4700000000000000
χ478-8−8i8i00-11i−i3ζ10+3ζ26−3ζ10−3ζ26−3ζ14−3ζ463ζ14+3ζ46000000000000−ζ25+ζ41ζ25−ζ41−ζ13+ζ29ζ13−ζ29−ζ31+ζ47ζ31−ζ47ζ11−ζ43−ζ11+ζ4300000000000000
χ488-8−8i8i00-11i−i3ζ10+3ζ26−3ζ10−3ζ26−3ζ14−3ζ463ζ14+3ζ46000000000000ζ25−ζ41−ζ25+ζ41ζ13−ζ29−ζ13+ζ29ζ31−ζ47−ζ31+ζ47−ζ11+ζ43ζ11−ζ4300000000000000

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