Finite Group Databasebeta

← Group #10589144

Character table — Group #10589144

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222244444444444444444444444444441818181818181818242424242424242424242424
order124423346688881212121236666612121212121224242424242424242424242424242424161616161616161688882424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511-1-1-111111-1-111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ611-1-1-111111-1-111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ711-1-1-111111-1-111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii
χ811-1-1-111111-1-111-1-1-1-11-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i
χ92222222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000
χ10222222-122-1222222-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000220000-1-1-1-1
χ11222222-122-1222222-1-1-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000-2-200001111
χ12222222-122-1-2-2-2-222-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000000000000000−i3i3−i3i3
χ13222222-122-1-2-2-2-222-1-1-12-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000000000000000i3−i3i3−i3
χ1422222-122-122222-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000002200-1-1-1-10000
χ1522222-122-122222-1-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000-2-20011110000
χ1622222-122-12-2-2-2-2-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-21111000000000000−i3i3−i3i30000
χ1722222-122-12-2-2-2-2-1-122-1-12-1-1-1-1-1-12-1-111-2-2111111-2-21111000000000000i3−i3i3−i30000
χ182222-222-222000022222-2-2-2-2222-2-2-2-2000000000000000022−2−222−2−2000000000000
χ192222-222-222000022222-2-2-2-2222-2-2-2-20000000000000000−2−222−2−222000000000000
χ2022-2-2222-2220000-2-2-2-2222222-2-2-2-2-2-2000000000000000022−2−2−2−222000000000000
χ2122-2-2222-2220000-2-2-2-2222222-2-2-2-2-2-20000000000000000−2−22222−2−2000000000000
χ2222-2-2-22222222-2-2-2-2-2-22-2-2-2-22-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000
χ2322-2-2-22-122-122-2-2-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-100000000000000003−3−33
χ2422-2-2-22-122-122-2-2-2-211-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-10000000000000000−333−3
χ2522-2-2-22-122-1-2-222-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-211111100000000002i−2i0000−i−iii
χ2622-2-2-22-122-1-2-222-2-211-1-2111-1112-1-1-122-1-1-1-1-1-1-2-21111110000000000−2i2i0000ii−i−i
χ2722-2-2-2-122-1222-2-211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-10000000000003−3−330000
χ2822-2-2-2-122-1222-2-211-2-2-11-211-111-12-1-111-2-21111-1-122-1-1-1-1000000000000−333−30000
χ2922-2-2-2-122-12-2-22211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-21111000000002i−2i00−i−iii0000
χ3022-2-2-2-122-12-2-22211-2-2-11-211-111-12-1-1-1-122-1-1-1-111-2-2111100000000−2i2i00ii−i−i0000
χ312-22i−2i0220-2-2−i2i22−22i−2i2i−2i20000-22i−2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000000
χ322-22i−2i0220-2-2−i2i22−22i−2i2i−2i20000-22i−2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000000
χ332-22i−2i0220-2-2i2−i2−222i−2i2i−2i20000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000000000
χ342-22i−2i0220-2-2i2−i2−222i−2i2i−2i20000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000000000
χ352-2−2i2i0220-2-2−i2i2−22−2i2i−2i2i20000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000000000
χ362-2−2i2i0220-2-2−i2i2−22−2i2i−2i2i20000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000000000
χ372-2−2i2i0220-2-2i2−i22−2−2i2i−2i2i20000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000000
χ382-2−2i2i0220-2-2i2−i22−2−2i2i−2i2i20000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000000
χ3944444-2-24-2-24444-2-2-2-21-2-211111-2-211-2-2-2-21111-2-2-2-2111100000000000000000000
χ4044444-2-24-2-2-4-4-4-4-2-2-2-21-2-211111-2-2112222-1-1-1-12222-1-1-1-100000000000000000000
χ414444-44-2-44-2000044-2-2-2-4222-2-2-2-4222000000000000000000000000000000000000
χ424444-4-24-4-240000-2-244-22-422-2-2-22-422000000000000000000000000000000000000
χ434444-4-2-2-4-2-20000-2-2-2-2122-1-111122-1-100003i−3i3i−3i00003i−3i3i−3i00000000000000000000
χ444444-4-2-2-4-2-20000-2-2-2-2122-1-111122-1-10000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000
χ4544-4-444-2-44-20000-4-422-24-2-2-2-222-4222000000000000000000000000000000000000
χ4644-4-44-24-4-24000022-4-4-2-24-2-2-2222-422000000000000000000000000000000000000
χ4744-4-44-2-2-4-2-2000022221-2-2111-1-122-1-100003i−3i3i−3i0000−3i3i−3i3i00000000000000000000
χ4844-4-44-2-2-4-2-2000022221-2-2111-1-122-1-10000−3i3i−3i3i00003i−3i3i−3i00000000000000000000
χ4944-4-4-4-2-24-2-244-4-42222122-1-11-1-1-2-2112222-1-1-1-1-2-2-2-2111100000000000000000000
χ5044-4-4-4-2-24-2-2-4-4442222122-1-11-1-1-2-211-2-2-2-211112222-1-1-1-100000000000000000000
χ514-44i−4i04-20-42−2i22i222−224i−4i−2i2i-200002−2i2i000022−22−22−2−222−2i22i2i2−i2i2i2−i2−i200000000000000000000
χ524-44i−4i04-20-422i2−2i2−22224i−4i−2i2i-200002−2i2i0000−22222−222−2−22i2−2i2−i2i2−i2−i2i2i200000000000000000000
χ534-44i−4i0-2402-4−2i22i222−22−2i2i4i−4i-200002−2i2i0000−2222−22−2−222i2−i2−2i22i2i2i2−i2−i200000000000000000000
χ544-44i−4i0-2402-42i2−2i2−2222−2i2i4i−4i-200002−2i2i00002−2−222222−2−2−i2i22i2−2i2−i2−i2i2i200000000000000000000
χ554-44i−4i0-2-2022−2i22i222−22−2i2i−2i2i1003-3-1i−i003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46i2−i2i2−i2ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ46−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ4600000000000000000000
χ564-44i−4i0-2-2022−2i22i222−22−2i2i−2i2i100-33-1i−i00−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46i2−i2i2−i2−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ462ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ4600000000000000000000
χ574-44i−4i0-2-20222i2−2i2−2222−2i2i−2i2i1003-3-1i−i003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−i2i2−i2i2−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ46ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ4600000000000000000000
χ584-44i−4i0-2-20222i2−2i2−2222−2i2i−2i2i100-33-1i−i00−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−i2i2−i2i22ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ46−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ4600000000000000000000
χ594-4−4i4i04-20-42−2i22i2−2222−4i4i2i−2i-2000022i−2i0000−22222−222−2−2−2i22i2i2−i2i2i2−i2−i200000000000000000000
χ604-4−4i4i04-20-422i2−2i222−22−4i4i2i−2i-2000022i−2i000022−22−22−2−2222i2−2i2−i2i2−i2−i2i2i200000000000000000000
χ614-4−4i4i0-2402-4−2i22i2−22222i−2i−4i4i-2000022i−2i00002−2−222222−2−2i2−i2−2i22i2i2i2−i2−i200000000000000000000
χ624-4−4i4i0-2402-42i2−2i222−222i−2i−4i4i-2000022i−2i0000−2222−22−2−222−i2i22i2−2i2−i2−i2i2i200000000000000000000
χ634-4−4i4i0-2-2022−2i22i2−22222i−2i2i−2i1003-3-1−ii00−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46i2−i2i2−i2−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ462ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ4600000000000000000000
χ644-4−4i4i0-2-2022−2i22i2−22222i−2i2i−2i100-33-1−ii003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46i2−i2i2−i2ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ46−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ4600000000000000000000
χ654-4−4i4i0-2-20222i2−2i222−222i−2i2i−2i1003-3-1−ii00−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−i2i2−i2i22ζ10−ζ14+2ζ26−ζ46−ζ10+2ζ14−ζ26+2ζ46−2ζ10+ζ14−2ζ26+ζ46ζ10−2ζ14+ζ26−2ζ4600000000000000000000
χ664-4−4i4i0-2-20222i2−2i222−222i−2i2i−2i100-33-1−ii003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−i2i2−i2i2−ζ10+2ζ14−ζ26+2ζ462ζ10−ζ14+2ζ26−ζ46ζ10−2ζ14+ζ26−2ζ46−2ζ10+ζ14−2ζ26+ζ4600000000000000000000

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