Finite Group Databasebeta

← Group #13155250

Character table — Group #13155250

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222222244444444444444444444466666688888888888888121212121212121212121212121212242424242424363636363636484848484848727272727272108108
order123334666883336661212121212242424242424242424242466121236121212122424242424242424666812121224242424242424244412121212161648484848121212121212246612121616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111-11-1-111-1-1-1-1-1-1-11-1-111-11-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11-111-1-1-11-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-11-1-1111-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ9222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2-200000000000000000000000000
χ10222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-22-2-2-22222222200000000000000000000000000
χ1122222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-2000000002220-2-2-2000000000000002−222−2−20000000000002−2
χ1222222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-2000000002220-2-2-200000000000000−22−2−222000000000000−22
χ1322222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-200000000-2-2-20222000000000000002−222−2−2000000000000−22
χ1422222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-200000000-2-2-2022200000000000000−22−2−2220000000000002−2
χ152222-12-122222-1-1-12-12-12-1-122-1-1-1-1-1-1222222-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-120-1-10000000020-1-10020-1-10000
χ162222-12-122222-1-1-12-12-12-1-122-1-1-1-1-1-1222222-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-201100000000-201100-20110000
χ172222-12-122222-1-1-12-12-12-1-122-1-1-1-1-1-122-2-2-2-211-1-12-1-1-122-1-1-1-1-1-1111-2-211-2-211111120-1-10000000020-1-100-20110000
χ182222-12-122222-1-1-12-12-12-1-122-1-1-1-1-1-122-2-2-2-211-1-12-1-1-122-1-1-1-1-1-1111-2-211-2-2111111-201100000000-20110020-1-10000
χ192222-12-122-2-22-1-1-12-12-12-1-1-2-2111111-2-22222-1-1-1-12-1-1-1-2-2111111-1-1-1-22-1-1-2-211111100−i3i30000000000−i3i30000−i3i30000
χ202222-12-122-2-22-1-1-12-12-12-1-1-2-2111111-2-22222-1-1-1-12-1-1-1-2-2111111-1-1-1-22-1-1-2-211111100i3−i30000000000i3−i30000i3−i30000
χ212222-12-122-2-22-1-1-12-12-12-1-1-2-2111111-2-2-2-2-2-211-1-12-1-1-1-2-21111111112-21122-1-1-1-1-1-100−i3i30000000000−i3i30000i3−i30000
χ222222-12-122-2-22-1-1-12-12-12-1-1-2-2111111-2-2-2-2-2-211-1-12-1-1-1-2-21111111112-21122-1-1-1-1-1-100i3−i30000000000i3−i30000−i3i30000
χ23222-12222-122-12-1-1-1222-1-1-1-1-122-1-1-1-12222-1-122-1-1-12-1-1-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-10200-1-10000000200-1-10200-1-100
χ24222-12222-122-12-1-1-1222-1-1-1-1-122-1-1-1-12222-1-122-1-1-12-1-1-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-10-200110000000-200110-2001100
χ25222-12222-122-12-1-1-1222-1-1-1-1-122-1-1-1-122-2-211-2-2-1-1-12-1-1-1-122-1-1-1-1-211-211111-2-211110200-1-10000000200-1-10-2001100
χ26222-12222-122-12-1-1-1222-1-1-1-1-122-1-1-1-122-2-211-2-2-1-1-12-1-1-1-122-1-1-1-1-211-211111-2-211110-200110000000-200110200-1-100
χ27222-12222-1-2-2-12-1-1-1222-1-1-111-2-21111-2-222-1-122-1-1-12-1-111-2-211112-1-1-2-1-1-111-2-211110000−i3i30000000000−i3i30000−i3i300
χ28222-12222-1-2-2-12-1-1-1222-1-1-111-2-21111-2-222-1-122-1-1-12-1-111-2-211112-1-1-2-1-1-111-2-211110000i3−i30000000000i3−i30000i3−i300
χ29222-12222-1-2-2-12-1-1-1222-1-1-111-2-21111-2-2-2-211-2-2-1-1-12-1-111-2-21111-2112111-1-122-1-1-1-10000−i3i30000000000−i3i30000i3−i300
χ30222-12222-1-2-2-12-1-1-1222-1-1-111-2-21111-2-2-2-211-2-2-1-1-12-1-111-2-21111-2112111-1-122-1-1-1-10000i3−i30000000000i3−i30000−i3i300
χ3122-12222-1222-1-122-1-1-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000022222222-1-1-1-1-1-1-1-1-1-100000000
χ3222-12222-1222-1-122-1-1-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000002-222-2-2-2-21111-11-1-11100000000
χ3322-12222-1222-1-122-1-1-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-22-2-222-2-211111-111-1-100000000
χ3422-12222-1222-1-122-1-1-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-2-2-2-2-2-222-1-1-1-111111100000000
χ354444-2-4-244004-2-2-24-2-42-42200000000004-44422-2-2-422200000000-2-2-20-4220000000000000000000000000000000000
χ364444-2-4-244004-2-2-24-2-42-4220000000000-44-4-4-2-2-2-2-42220000000022204-2-20000000000000000000000000000000000
χ37444-24-444-200-24-2-2-24-4-422200000000004-4-2-2-4-4-2-22-422000000004-2-202220000000000000000000000000000000000
χ38444-24-444-200-24-2-2-24-4-42220000000000-442244-2-22-42200000000-4220-2-2-20000000000000000000000000000000000
χ39444-2-24-24-244-2-211-2-24-2-211-2-2-2-211114444-2-2-2-211-2-211-2-2-2-21111-2114-211-2-2-2-2111100000000000000000000000000
χ40444-2-24-24-244-2-211-2-24-2-211-2-2-2-2111144-4-4222211-2-211-2-2-2-211112-1-1-42-1-12222-1-1-1-100000000000000000000000000
χ41444-2-24-24-2-4-4-2-211-2-24-2-2112222-1-1-1-1-4-444-2-2-2-211-2-2112222-1-1-1-1-211-4-2112222-1-1-1-100000000000000000000000000
χ42444-2-24-24-2-4-4-2-211-2-24-2-2112222-1-1-1-1-4-4-4-4222211-2-2112222-1-1-1-12-1-142-1-1-2-2-2-2111100000000000000000000000000
χ43444-2-2-4-24-200-2-211-2-2-422-1-100003i3i−3i−3i004-4-2-2221122-1-100003i3i−3i−3i-21102-1-100003i3i−3i−3i00000000000000000000000000
χ44444-2-2-4-24-200-2-211-2-2-422-1-100003i3i−3i−3i00-4422-2-21122-1-100003i3i−3i−3i2-1-10-2110000−3i−3i3i3i00000000000000000000000000
χ45444-2-2-4-24-200-2-211-2-2-422-1-10000−3i−3i3i3i004-4-2-2221122-1-10000−3i−3i3i3i-21102-1-10000−3i−3i3i3i00000000000000000000000000
χ46444-2-2-4-24-200-2-211-2-2-422-1-10000−3i−3i3i3i00-4422-2-21122-1-10000−3i−3i3i3i2-1-10-21100003i3i−3i−3i00000000000000000000000000
χ4744-24444-24-4-4-2-244-2-2-24444-4-4-4-4-4-4-4-422000000-2-2-2-2-2-22222222200000000000000000000000000000000000000000
χ4844-244-44-2400-2-244-2-22-4-4-4-40000000000000000-2-222220000000000000000000000000000022−22−2−22200000000000000
χ4944-244-44-2400-2-244-2-22-4-4-4-40000000000000000-2-2222200000000000000000000000000000−222222−2−200000000000000
χ5044-24-24-2-2444-21-2-2-21-2-24-2-244-2-2-2-2-2-2-2-200000011-2111-2-211111100000000000000040-2-200000000-20110000000000
χ5144-24-24-2-2444-21-2-2-21-2-24-2-244-2-2-2-2-2-2-2-200000011-2111-2-2111111000000000000000-40220000000020-1-10000000000
χ5244-24-24-2-24-4-4-21-2-2-21-2-24-2-2-4-42222222200000011-211122-1-1-1-1-1-100000000000000000−2i32i30000000000i3−i30000000000
χ5344-24-24-2-24-4-4-21-2-2-21-2-24-2-2-4-42222222200000011-211122-1-1-1-1-1-1000000000000000002i3−2i30000000000−i3i30000000000
χ5444-2-2444-2-2441-2-2-21-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-211110000000000000000400-2-20000000-2001100000000
χ5544-2-2444-2-2441-2-2-21-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-211110000000000000000-400220000000200-1-100000000
χ5644-2-2444-2-2-4-41-2-2-21-2-24-2-2-222-4-4222222000000111-211-1-122-1-1-1-10000000000000000000−2i32i30000000000i3−i300000000
χ5744-2-2444-2-2-4-41-2-2-21-2-24-2-2-222-4-4222222000000111-211-1-122-1-1-1-100000000000000000002i3−2i30000000000−i3i300000000
χ584-44440-4-4-422−22444-4-4-40000022−2222−2222−2222−2222−220000004-4000022−2222−2222−2222−2200000000000000000000000000000000000000000
χ594-44440-4-4-4−2222444-4-4-400000−2222−2222−2222−2222−22220000004-40000−2222−2222−2222−222200000000000000000000000000000000000000000
χ604-444-202-4-422−224-2-22-420000022−22−22−22−2222−22000023−23-22000022−22−22−22−220000023−23006−66−66−600000000000000000000000000
χ614-444-202-4-422−224-2-22-420000022−22−22−22−2222−220000−2323-22000022−22−22−22−2200000−232300−66−66−6600000000000000000000000000
χ624-444-202-4-4−22224-2-22-4200000−22222−22−22−2−2222000023−23-220000−22222−22−22−20000023−2300−66−66−6600000000000000000000000000
χ634-444-202-4-4−22224-2-22-4200000−22222−22−22−2−22220000−2323-220000−22222−22−22−200000−2323006−66−66−600000000000000000000000000
χ644-44-240-4-4222−22-24-222-400000−2222−22−22−2222−2200−2i32i300-220000−2222−22−22−220−2i32i30000i6−i600i6−i6−i6i600000000000000000000000000
χ654-44-240-4-4222−22-24-222-400000−2222−22−22−2222−22002i3−2i300-220000−2222−22−22−2202i3−2i30000−i6i600−i6i6i6−i600000000000000000000000000
χ664-44-240-4-42−2222-24-222-4000002−2−22222−22−2−222200−2i32i300-2200002−2−22222−22−20−2i32i30000−i6i600−i6i6i6−i600000000000000000000000000
χ674-44-240-4-42−2222-24-222-4000002−2−22222−22−2−2222002i3−2i300-2200002−2−22222−22−202i3−2i30000i6−i600i6−i6−i6i600000000000000000000000000
χ684-44-2-202-4222−22-2-21-1220003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4622−2200−2i32i3−23231-1003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ460i3−i3003−3i6−i6−66−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ2600000000000000000000000000
χ694-44-2-202-4222−22-2-21-1220003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4622−22002i3−2i323−231-1003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ460−i3i300−33−i6i66−6ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ2600000000000000000000000000
χ704-44-2-202-4222−22-2-21-122000−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ4622−2200−2i32i323−231-100−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ460i3−i300−33i6−i66−6−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ4600000000000000000000000000
χ714-44-2-202-4222−22-2-21-122000−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ4622−22002i3−2i3−23231-100−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ460−i3i3003−3−i6i6−66ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ4600000000000000000000000000
χ724-44-2-202-42−2222-2-21-1220003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ46−222200−2i32i3−23231-1003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ460i3−i3003−3−i6i66−6ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ2600000000000000000000000000
χ734-44-2-202-42−2222-2-21-1220003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ46−2222002i3−2i323−231-1003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ460−i3i300−33i6−i6−66−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ2600000000000000000000000000
χ744-44-2-202-42−2222-2-21-122000−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−222200−2i32i323−231-100−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ460i3−i300−33−i6i6−66ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ4600000000000000000000000000
χ754-44-2-202-42−2222-2-21-122000−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−2222002i3−2i3−23231-100−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ460−i3i3003−3i6−i66−6−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ4600000000000000000000000000
χ764-4-2440-42-422−22-2-24-4220000022−2222−2222−2222−22−22000000-220000−22−22−22−2200000000000000000000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000
χ774-4-2440-42-422−22-2-24-4220000022−2222−2222−2222−22−22000000-220000−22−22−22−2200000000000000000000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000
χ784-4-2440-42-4−2222-2-24-42200000−2222−2222−2222−22222−2000000-2200002−22−22−22−200000000000000000000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000
χ794-4-2440-42-4−2222-2-24-42200000−2222−2222−2222−22222−2000000-2200002−22−22−22−200000000000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000
χ8088-48-4-8-4-4800-42-4-4-4244-8440000000000000000224-2-2-20000000000000000000000000000000000000000000000000
χ8188-4-48-88-4-4002-4-4-42-44-8444000000000000000022-24-2-20000000000000000000000000000000000000000000000000
χ8288-4-4-48-4-4-488222222-4-4-422-4-4-4-42222-4-4000000-1-122-1-12222-1-1-1-100000000000000000000000000000000000000000
χ8388-4-4-48-4-4-4-8-8222222-4-4-4224444-2-2-2-244000000-1-122-1-1-2-2-2-2111100000000000000000000000000000000000000000
χ8488-4-4-4-8-4-4-400222222444-2-200006i6i−6i−6i00000000-1-1-2-2110000−3i−3i3i3i00000000000000000000000000000000000000000
χ8588-4-4-4-8-4-4-400222222444-2-20000−6i−6i6i6i00000000-1-1-2-21100003i3i−3i−3i00000000000000000000000000000000000000000
χ868-8-48-4044-842−42-42-444-20000042−42−2222−2222−2222−22220000002-20000−22222−22−22−200000000000000000000000000000000000000000
χ878-8-48-4044-8−4242-42-444-200000−424222−2222−2222−2222−220000002-2000022−22−22−22−2200000000000000000000000000000000000000000
χ888-8-4-480-84442−422-4-44-2400000−222242−42−2222−2222−22220000002-200002−2−22222−22−200000000000000000000000000000000000000000
χ898-8-4-480-844−42422-4-44-240000022−22−424222−2222−2222−220000002-20000−2222−22−22−2200000000000000000000000000000000000000000
χ908-8-4-4-4044442−42222-2-2-20006i−6i−2222−2222−4ζ10−2ζ14−4ζ26−2ζ464ζ10+2ζ14+4ζ26+2ζ462ζ10+4ζ14+2ζ26+4ζ46−2ζ10−4ζ14−2ζ26−4ζ46−2222000000-1100−3i3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ4600000000000000000000000000000000000000000
χ918-8-4-4-4044442−42222-2-2-2000−6i6i−2222−22222ζ10+4ζ14+2ζ26+4ζ46−2ζ10−4ζ14−2ζ26−4ζ46−4ζ10−2ζ14−4ζ26−2ζ464ζ10+2ζ14+4ζ26+2ζ46−2222000000-11003i−3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ4600000000000000000000000000000000000000000
χ928-8-4-4-40444−4242222-2-2-20006i−6i22−2222−224ζ10+2ζ14+4ζ26+2ζ46−4ζ10−2ζ14−4ζ26−2ζ46−2ζ10−4ζ14−2ζ26−4ζ462ζ10+4ζ14+2ζ26+4ζ4622−22000000-1100−3i3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4600000000000000000000000000000000000000000
χ938-8-4-4-40444−4242222-2-2-2000−6i6i22−2222−22−2ζ10−4ζ14−2ζ26−4ζ462ζ10+4ζ14+2ζ26+4ζ464ζ10+2ζ14+4ζ26+2ζ46−4ζ10−2ζ14−4ζ26−2ζ4622−22000000-11003i−3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ4600000000000000000000000000000000000000000

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