Finite Group Databasebeta

← Group #13155233

Character table — Group #13155233

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222222244444444444444444444466666688888888888888121212121212121212121212121212242424242424363636363636484848484848727272727272108108
order12333466688333666121212121224242424242424242424246612123612121212242424242424242466681212122424242424242424226666161648484848666666246612121616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-11-111-1-1-11-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111-11-1-111-1-1-1-1-1-1-11-1-1111-111-1-1-1-1
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
χ611111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11-111-1-11-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-11-1-111-11-1-11111
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
χ152222-122-1222-12-12-1-12-12-1-122-1-1-1-1-1-12222-1-122-1-12-1-1-122-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-10200-1-10000000200-1-120-1-10000
χ162222-122-1222-12-12-1-12-12-1-122-1-1-1-1-1-12222-1-122-1-12-1-1-122-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-10-200110000000-20011-20110000
χ172222-122-1222-12-12-1-12-12-1-122-1-1-1-1-1-122-2-211-2-2-1-12-1-1-122-1-1-1-1-1-1-211-2111-2-21111110200-1-10000000200-1-1-20110000
χ182222-122-1222-12-12-1-12-12-1-122-1-1-1-1-1-122-2-211-2-2-1-12-1-1-122-1-1-1-1-1-1-211-2111-2-21111110-200110000000-2001120-1-10000
χ192222-122-12-2-2-12-12-1-12-12-1-1-2-2111111-2-222-1-122-1-12-1-1-1-2-21111112-1-1-2-1-1-1-2-21111110000−i3i30000000000−i3i300−i3i30000
χ202222-122-12-2-2-12-12-1-12-12-1-1-2-2111111-2-222-1-122-1-12-1-1-1-2-21111112-1-1-2-1-1-1-2-21111110000i3−i30000000000i3−i300i3−i30000
χ212222-122-12-2-2-12-12-1-12-12-1-1-2-2111111-2-2-2-211-2-2-1-12-1-1-1-2-2111111-211211122-1-1-1-1-1-10000−i3i30000000000−i3i300i3−i30000
χ222222-122-12-2-2-12-12-1-12-12-1-1-2-2111111-2-2-2-211-2-2-1-12-1-1-1-2-2111111-211211122-1-1-1-1-1-10000i3−i30000000000i3−i300−i3i30000
χ23222-122-122222-1-1-1-12-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000022222222-1-1-1-1-1-1-1-1-1-100000000
χ24222-122-122222-1-1-1-12-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000002-222-2-2-2-21111-11-1-11100000000
χ25222-122-122222-1-1-1-12-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-22-2-222-2-211111-111-1-100000000
χ26222-122-122222-1-1-1-12-1222222222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000-2-2-2-2-2-222-1-1-1-111111100000000
χ2722-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-1222222-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-120-1-10000000020-1-1000200-1-100
χ2822-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-1222222-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-201100000000-2011000-2001100
χ2922-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-2-2-2-211-1-1-12-1-1-1-122-1-1-1-1111-2-21111-2-2111120-1-10000000020-1-1000-2001100
χ3022-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-2-2-2-211-1-1-12-1-1-1-122-1-1-1-1111-2-21111-2-21111-201100000000-2011000200-1-100
χ3122-122222-1-2-2-1-12-12-122-1-1-111-2-21111-2-22222-1-1-1-1-12-1-111-2-21111-1-1-1-22-1-111-2-2111100−i3i30000000000−i3i3000000−i3i300
χ3222-122222-1-2-2-1-12-12-122-1-1-111-2-21111-2-22222-1-1-1-1-12-1-111-2-21111-1-1-1-22-1-111-2-2111100i3−i30000000000i3−i3000000i3−i300
χ3322-122222-1-2-2-1-12-12-122-1-1-111-2-21111-2-2-2-2-2-211-1-1-12-1-111-2-211111112-211-1-122-1-1-1-100−i3i30000000000−i3i3000000i3−i300
χ3422-122222-1-2-2-1-12-12-122-1-1-111-2-21111-2-2-2-2-2-211-1-1-12-1-111-2-211111112-211-1-122-1-1-1-100i3−i30000000000i3−i3000000−i3i300
χ354444-2-44-2400-24-24-2-2-42-42200000000004-4-2-2-4-4-2-2-4222000000004-2-202220000000000000000000000000000000000
χ364444-2-44-2400-24-24-2-2-42-4220000000000-442244-2-2-422200000000-4220-2-2-20000000000000000000000000000000000
χ37444-244-244-4-44-2-2-2-24-24444-4-4-4-4-4-4-4-422000000-2-2-2-2-2-22222222200000000000000000000000000000000000000000
χ38444-24-4-244004-2-2-2-242-4-4-4-40000000000000000-2-222220000000000000000000000000000022−22−2−22200000000000000
χ39444-24-4-244004-2-2-2-242-4-4-4-40000000000000000-2-2222200000000000000000000000000000−222222−2−200000000000000
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χ41444-2-24-2-2444-2-21-21-2-2-24-2-244-2-2-2-2-2-2-2-200000011-2111-2-21111110000000000000000-400220000000200-1-100000000
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χ43444-2-24-2-24-4-4-2-21-21-2-2-24-2-2-4-42222222200000011-211122-1-1-1-1-1-100000000000000000002i3−2i30000000000−i3i300000000
χ4444-244-444-200-2-24-24-2-4-422200000000004-44422-2-22-42200000000-2-2-20-4220000000000000000000000000000000000
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χ4644-24-244-2-2441-2-2-2-214-2-211-2-2-2-211114444-2-2-2-211-2-211-2-2-2-21111-2114-211-2-2-2-2111100000000000000000000000000
χ4744-24-244-2-2441-2-2-2-214-2-211-2-2-2-2111144-4-4222211-2-211-2-2-2-211112-1-1-42-1-12222-1-1-1-100000000000000000000000000
χ4844-24-244-2-2-4-41-2-2-2-214-2-2112222-1-1-1-1-4-444-2-2-2-211-2-2112222-1-1-1-1-211-4-2112222-1-1-1-100000000000000000000000000
χ4944-24-244-2-2-4-41-2-2-2-214-2-2112222-1-1-1-1-4-4-4-4222211-2-2112222-1-1-1-12-1-142-1-1-2-2-2-2111100000000000000000000000000
χ5044-24-2-44-2-2001-2-2-2-21-422-1-100003i3i−3i−3i004-4-2-2221122-1-100003i3i−3i−3i-21102-1-100003i3i−3i−3i00000000000000000000000000
χ5144-24-2-44-2-2001-2-2-2-21-422-1-100003i3i−3i−3i00-4422-2-21122-1-100003i3i−3i−3i2-1-10-2110000−3i−3i3i3i00000000000000000000000000
χ5244-24-2-44-2-2001-2-2-2-21-422-1-10000−3i−3i3i3i004-4-2-2221122-1-10000−3i−3i3i3i-21102-1-10000−3i−3i3i3i00000000000000000000000000
χ5344-24-2-44-2-2001-2-2-2-21-422-1-10000−3i−3i3i3i00-4422-2-21122-1-10000−3i−3i3i3i2-1-10-21100003i3i−3i−3i00000000000000000000000000
χ5444-2-244-24-244-21-21-2-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-2111100000000000000040-2-200000000-20110000000000
χ5544-2-244-24-244-21-21-2-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-21111000000000000000-40220000000020-1-10000000000
χ5644-2-244-24-2-4-4-21-21-2-2-24-2-2-222-4-4222222000000111-211-1-122-1-1-1-100000000000000000−2i32i30000000000i3−i30000000000
χ5744-2-244-24-2-4-4-21-21-2-2-24-2-2-222-4-4222222000000111-211-1-122-1-1-1-1000000000000000002i3−2i30000000000−i3i30000000000
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
χ604-444-20-42-422−22-24-2-4220000022−22−22−22−2222−2200−2i32i300-22000022−22−22−22−220−2i32i3000000i6−i6i6−i6i6−i600000000000000000000000000
χ614-444-20-42-422−22-24-2-4220000022−22−22−22−2222−22002i3−2i300-22000022−22−22−22−2202i3−2i3000000−i6i6−i6i6−i6i600000000000000000000000000
χ624-444-20-42-4−2222-24-2-42200000−22222−22−22−2−222200−2i32i300-220000−22222−22−22−20−2i32i3000000−i6i6−i6i6−i6i600000000000000000000000000
χ634-444-20-42-4−2222-24-2-42200000−22222−22−22−2−2222002i3−2i300-220000−22222−22−22−202i3−2i3000000i6−i6i6−i6i6−i600000000000000000000000000
χ644-44-2402-4-422−224-2-222-40000022−2222−2222−2222−22−22000000-220000−22−22−22−2200000000000000000000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000
χ654-44-2402-4-422−224-2-222-40000022−2222−2222−2222−22−22000000-220000−22−22−22−2200000000000000000000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000
χ664-44-2402-4-4−22224-2-222-400000−2222−2222−2222−22222−2000000-2200002−22−22−22−200000000000000000000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000
χ674-44-2402-4-4−22224-2-222-400000−2222−2222−2222−22222−2000000-2200002−22−22−22−200000000000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000
χ684-4-2440-4-4222−22-2-242-4200000−2222−22−22−2222−22000023−23-220000−2222−22−22−220000023−236−6006−6−6600000000000000000000000000
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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.