Finite Group Databasebeta

← Group #13136665

Character table — Group #13136665

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order124436881212242433661212121224242424248824242424242424688121616161616161616484848484848484848484848484848486122424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-11-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ7111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111
χ8111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ911-1-111i−i-1-1i−i1111-1-1-1-1ii−i−i1-1i−iii−i−ii−i1-11i−i-1ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ261-1i−i
χ1011-1-111i−i-1-1i−i1111-1-1-1-1ii−i−i1-1i−iii−i−ii−i1-11i−i-1−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ261-1i−i
χ1111-1-111i−i-1-1i−i1111-1-1-1-1ii−i−i1-1i−iii−i−ii−i-111−ii-1ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-11−ii
χ1211-1-111i−i-1-1i−i1111-1-1-1-1ii−i−i1-1i−iii−i−ii−i-111−ii-1−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-11−ii
χ1311-1-111−ii-1-1−ii1111-1-1-1-1−i−iii1-1−ii−i−iii−ii1-11−ii-1−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ461-1−ii
χ1411-1-111−ii-1-1−ii1111-1-1-1-1−i−iii1-1−ii−i−iii−ii1-11−ii-1ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ461-1−ii
χ1511-1-111−ii-1-1−ii1111-1-1-1-1−i−iii1-1−ii−i−iii−ii-111i−i-1−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-11i−i
χ1611-1-111−ii-1-1−ii1111-1-1-1-1−i−iii1-1−ii−i−iii−ii-111i−i-1ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-11i−i
χ17222222222222222222222222-2-2-2-2-2-2-2-22200-200-20000000000000000000000000000
χ18222222-2-222-2-222222222-2-2-2-2-2-2222222-2-200-200-20000000000000000000000000000
χ1922-2-2222i−2i-2-22i−2i2222-2-2-2-22i2i−2i−2i-22−2i2i−2i−2i2i2i2i−2i00-20020000000000000000000000000000
χ2022-2-222−2i2i-2-2−2i2i2222-2-2-2-2−2i−2i2i2i-222i−2i2i2i−2i−2i−2i2i00-20020000000000000000000000000000
χ214444444444441-21-211-2-2111100000000-2-200000022220000-1-1-1-1-1-1-1-1000000000000
χ224444444444441-21-211-2-2111100000000-2-2000000-2-2-2-2000011111111000000000000
χ23444444444444-21-21-2-211-2-2-2-20000000011220220000000000000000000000000-1-1-1-1
χ24444444444444-21-21-2-211-2-2-2-20000000011-2-20-2-200000000000000000000000001111
χ25444444-4-444-4-41-21-211-2-2-1-1-1-100000000220000002i2i−2i−2i0000−i−i−i−iiiii000000000000
χ26444444-4-444-4-41-21-211-2-2-1-1-1-10000000022000000−2i−2i2i2i0000iiii−i−i−i−i000000000000
χ27444444-4-444-4-4-21-21-2-211222200000000-1-1220-2-20000000000000000000000000-1-111
χ28444444-4-444-4-4-21-21-2-211222200000000-1-1-2-2022000000000000000000000000011-1-1
χ2944-4-4444i−4i-4-44i−4i1-21-2-1-122ii−i−i00000000−2i2i0000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26000000000000
χ3044-4-4444i−4i-4-44i−4i1-21-2-1-122ii−i−i00000000−2i2i000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26000000000000
χ3144-4-4444i−4i-4-44i−4i-21-2122-1-1−2i−2i2i2i00000000i−i2-202i−2i0000000000000000000000000-11−ii
χ3244-4-4444i−4i-4-44i−4i-21-2122-1-1−2i−2i2i2i00000000i−i-220−2i2i00000000000000000000000001-1i−i
χ3344-4-444−4i4i-4-4−4i4i1-21-2-1-122−i−iii000000002i−2i000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ460000ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46000000000000
χ3444-4-444−4i4i-4-4−4i4i1-21-2-1-122−i−iii000000002i−2i0000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ460000−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46000000000000
χ3544-4-444−4i4i-4-4−4i4i-21-2122-1-12i2i−2i−2i00000000−ii2-20−2i2i0000000000000000000000000-11i−i
χ3644-4-444−4i4i-4-4−4i4i-21-2122-1-12i2i−2i−2i00000000−ii-2202i−2i00000000000000000000000001-1−ii
χ374-44i−4i4-4004i−4i001-2-12i−i2i−2i3ζ14+3ζ46−3ζ14−3ζ46−3ζ10−3ζ263ζ10+3ζ26000000000000000000000000−ζ11+ζ43ζ11−ζ43−ζ31+ζ47ζ31−ζ47ζ13−ζ29−ζ13+ζ29−ζ25+ζ41ζ25−ζ41000000000000
χ384-44i−4i4-4004i−4i001-2-12i−i2i−2i3ζ14+3ζ46−3ζ14−3ζ46−3ζ10−3ζ263ζ10+3ζ26000000000000000000000000ζ11−ζ43−ζ11+ζ43ζ31−ζ47−ζ31+ζ47−ζ13+ζ29ζ13−ζ29ζ25−ζ41−ζ25+ζ41000000000000
χ394-44i−4i4-4004i−4i001-2-12i−i2i−2i−3ζ14−3ζ463ζ14+3ζ463ζ10+3ζ26−3ζ10−3ζ26000000000000000000000000−ζ31+ζ47ζ31−ζ47ζ11−ζ43−ζ11+ζ43−ζ25+ζ41ζ25−ζ41−ζ13+ζ29ζ13−ζ29000000000000
χ404-44i−4i4-4004i−4i001-2-12i−i2i−2i−3ζ14−3ζ463ζ14+3ζ463ζ10+3ζ26−3ζ10−3ζ26000000000000000000000000ζ31−ζ47−ζ31+ζ47−ζ11+ζ43ζ11−ζ43ζ25−ζ41−ζ25+ζ41ζ13−ζ29−ζ13+ζ29000000000000
χ414-44i−4i4-4004i−4i0044-4-44i−4i−4i4i000000000000000000000000000000000000000000000000
χ424-4−4i4i4-400−4i4i001-2-12−ii−2i2i−3ζ10−3ζ263ζ10+3ζ263ζ14+3ζ46−3ζ14−3ζ46000000000000000000000000ζ13−ζ29−ζ13+ζ29−ζ25+ζ41ζ25−ζ41−ζ11+ζ43ζ11−ζ43−ζ31+ζ47ζ31−ζ47000000000000
χ434-4−4i4i4-400−4i4i001-2-12−ii−2i2i−3ζ10−3ζ263ζ10+3ζ263ζ14+3ζ46−3ζ14−3ζ46000000000000000000000000−ζ13+ζ29ζ13−ζ29ζ25−ζ41−ζ25+ζ41ζ11−ζ43−ζ11+ζ43ζ31−ζ47−ζ31+ζ47000000000000
χ444-4−4i4i4-400−4i4i001-2-12−ii−2i2i3ζ10+3ζ26−3ζ10−3ζ26−3ζ14−3ζ463ζ14+3ζ46000000000000000000000000−ζ25+ζ41ζ25−ζ41−ζ13+ζ29ζ13−ζ29−ζ31+ζ47ζ31−ζ47ζ11−ζ43−ζ11+ζ43000000000000
χ454-4−4i4i4-400−4i4i001-2-12−ii−2i2i3ζ10+3ζ26−3ζ10−3ζ26−3ζ14−3ζ463ζ14+3ζ46000000000000000000000000ζ25−ζ41−ζ25+ζ41ζ13−ζ29−ζ13+ζ29ζ31−ζ47−ζ31+ζ47−ζ11+ζ43ζ11−ζ43000000000000
χ464-4−4i4i4-400−4i4i0044-4-4−4i4i4i−4i000000000000000000000000000000000000000000000000
χ476666-3-366-3-3-3-30000000000002222-1-1-1-10000-100-100000000000000003−33−33−33−30000
χ486666-3-366-3-3-3-30000000000002222-1-1-1-10000-100-10000000000000000−33−33−33−330000
χ496666-3-366-3-3-3-3000000000000-2-2-2-21111000010010000222200000000-1-1-1-1-1-1-1-10000
χ506666-3-366-3-3-3-3000000000000-2-2-2-21111000010010000-2-2-2-200000000111111110000
χ516666-3-3-6-6-3-33300000000000022-2-211110000-100-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ526666-3-3-6-6-3-33300000000000022-2-211110000-100-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ536666-3-3-6-6-3-333000000000000-2-222-1-1-1-10000100100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ546666-3-3-6-6-3-333000000000000-2-222-1-1-1-1000010010000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ5566-6-6-3-36i−6i33−3i3i0000000000002-22i−2i−i−iii0000-10010000000000000000ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ460000
χ5666-6-6-3-36i−6i33−3i3i0000000000002-22i−2i−i−iii0000-10010000000000000000−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ460000
χ5766-6-6-3-36i−6i33−3i3i000000000000-22−2i2iii−i−i0000100-100002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ260000
χ5866-6-6-3-36i−6i33−3i3i000000000000-22−2i2iii−i−i0000100-10000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ260000
χ5966-6-6-3-3−6i6i333i−3i0000000000002-2−2i2iii−i−i0000-10010000000000000000−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ260000
χ6066-6-6-3-3−6i6i333i−3i0000000000002-2−2i2iii−i−i0000-10010000000000000000ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ260000
χ6166-6-6-3-3−6i6i333i−3i000000000000-222i−2i−i−iii0000100-10000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ460000
χ6266-6-6-3-3−6i6i333i−3i000000000000-222i−2i−i−iii0000100-100002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ460000
χ638-88i−8i8-8008i−8i00-424-2−4i4i−2i2i000000000000000000000000000000000000000000000000
χ648-8−8i8i8-800−8i8i00-424-24i−4i2i−2i000000000000000000000000000000000000000000000000
χ6512-1212i−12i-6600−6i6i000000000000000000−2ζ14+2ζ462ζ14−2ζ462ζ10−2ζ26−2ζ10+2ζ26000000000000000000000000000000000000
χ6612-1212i−12i-6600−6i6i0000000000000000002ζ14−2ζ46−2ζ14+2ζ46−2ζ10+2ζ262ζ10−2ζ26000000000000000000000000000000000000
χ6712-12−12i12i-66006i−6i0000000000000000002ζ10−2ζ26−2ζ10+2ζ26−2ζ14+2ζ462ζ14−2ζ46000000000000000000000000000000000000
χ6812-12−12i12i-66006i−6i000000000000000000−2ζ10+2ζ262ζ10−2ζ262ζ14−2ζ46−2ζ14+2ζ46000000000000000000000000000000000000

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