Finite Group Databasebeta

← Group #13155259

Character table — Group #13155259

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222224444444444444444444448888888888888812121212121212121212121212121212121218181818242424242424363636364848484848487272108108144144
order1233346668833366612121212122424242424242424242436121212122424242424242424161648484848484848484848484848484848246644121212128122424121212121212241616612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-1-1-1-1-11-111-1-11-1-1-11-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-1-1-1-11-1-111-11-1-1-11
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-11-111-1-1-1111-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-11-1-1111-1111-1
χ9222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000002222000000-22-2-2000000000000
χ10222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000-2-2-2-20000002-222000000000000
χ1122222-222200222222-2-2-2-2-2000000000022-2-2-2-2000000002−222222222−2−2−2−2−2−2−2−22-2220000000-200000000002−200
χ1222222-222200222222-2-2-2-2-2000000000022-2-2-2-2000000002−222222222−2−2−2−2−2−2−2−2-22-2-2000000020000000000−2200
χ1322222-222200222222-2-2-2-2-2000000000022-2-2-2-200000000−22−2−2−2−2−2−2−2−2222222222-2220000000-20000000000−2200
χ1422222-222200222222-2-2-2-2-2000000000022-2-2-2-200000000−22−2−2−2−2−2−2−2−222222222-22-2-20000000200000000002−200
χ152222-12-122222-1-1-12-1-12-1-122222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-100002022000000-10-1-1002000-10
χ162222-12-122222-1-1-12-1-12-1-122222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-10000-20-2-2000000101100-200010
χ172222-12-122222-1-1-12-1-12-1-122222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-211111100002022000000-10-1-100-200010
χ182222-12-122222-1-1-12-1-12-1-122222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-21111110000-20-2-20000001011002000-10
χ19222-1222-1222-12-12-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-122-1-1-1-12-1-1-122-1-1-1-1000000
χ20222-1222-1222-12-12-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-2-211112-1-1-1-2-21111000000
χ21222-1222-1222-12-12-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2112-2-1-111-21112-2-1-111000000
χ22222-1222-1222-12-12-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-211-2211-1-1-2111-2211-1-1000000
χ23222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111100000000000000000022-1-100−i3i3−i3i3-2-11100−i3i3−i3i3000000
χ24222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111100000000000000000022-1-100i3−i3i3−i3-2-11100i3−i3i3−i3000000
χ25222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111000000000000000000-2-21100−i3i3i3−i321-1-100−i3i3i3−i3000000
χ26222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111000000000000000000-2-21100i3−i3−i3i321-1-100i3−i3−i3i3000000
χ2722-122222-122-1-12-1-122-1-1-1222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1000002002200000-100-1-102000-1
χ2822-122222-122-1-12-1-122-1-1-1222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-100000-200-2-200000100110-20001
χ2922-122222-122-1-12-1-122-1-1-1222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-2-211-2-2111111-2-21111000002002200000-100-1-10-20001
χ3022-122222-122-1-12-1-122-1-1-1222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-2-211-2-2111111-2-2111100000-200-2-2000001001102000-1
χ314444-24-244-4-44-2-2-24-2-24-2-24-4-4-4-4222222-2-24-2-2-2-4-422222200000000000000000000000000000000000000000000
χ324444-2-4-244004-2-2-24-22-422-40000000000-2-2-42220000000022−222222−2−2−2−2−2−2−22−2222222200000000000000000000000000
χ334444-2-4-244004-2-2-24-22-422-40000000000-2-2-422200000000−2222−22−222222222222−2−2−2−2−2−200000000000000000000000000
χ34444-24-44-2400-24-24-2-2-4-4-4-420000000000-2-22222000000000000000000000000004-4-2-20000000200000000000000
χ35444-24-44-2400-24-24-2-2-4-4-4-420000000000-2-2222200000000000000000000000000-44220000000-200000000000000
χ36444-2-24-2-2444-2-21-2-21-24-2-2-2-2-244-2-2-2-2-2-211-2111-2-2111111000000000000000000000040-2-2000000-201100000000
χ37444-2-24-2-2444-2-21-2-21-24-2-2-2-2-244-2-2-2-2-2-211-2111-2-21111110000000000000000000000-402200000020-1-100000000
χ38444-2-24-2-24-4-4-2-21-2-21-24-2-2-222-4-422222211-211122-1-1-1-1-1-1000000000000000000000000−2i32i300000000i3−i300000000
χ39444-2-24-2-24-4-4-2-21-2-21-24-2-2-222-4-422222211-211122-1-1-1-1-1-10000000000000000000000002i3−2i300000000−i3i300000000
χ4044-244444-2-4-4-2-24-2-244-2-2-24-4-422-4-42222-2-2-24-2-222-4-4222200000000000000000000000000000000000000000000
χ4144-244-444-200-2-24-2-24-4222-40000000000-2-22-4220000000022−22−2−22222−2−2−2−222−22−22222200000000000000000000000000
χ4244-244-444-200-2-24-2-24-4222-40000000000-2-22-42200000000−222222−22−222222−2−22222−2−2−2−200000000000000000000000000
χ4344-24-24-24-244-21-21-2-2-2-211444-2-2-2-2111111-2-211-2-2-2-2111144-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ4444-24-24-24-244-21-21-2-2-2-211444-2-2-2-2111111-2-211-2-2-2-21111-4-42222-1-1-1-12222-1-1-1-100000000000000000000000000
χ4544-24-24-24-2-4-4-21-21-2-2-2-2114-4-42222-1-1-1-111-2-2112222-1-1-1-10000003i3i−3i−3i00003i3i−3i−3i00000000000000000000000000
χ4644-24-24-24-2-4-4-21-21-2-2-2-2114-4-42222-1-1-1-111-2-2112222-1-1-1-1000000−3i−3i3i3i0000−3i−3i3i3i00000000000000000000000000
χ4744-24-2-4-24-200-21-21-2-222-1-1-40000003i3i−3i−3i1122-1-100003i3i−3i−3i22−22−2−2−2−2−2ζ10−ζ14−2ζ26−ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46ζ10+2ζ14+ζ26+2ζ4622222ζ10+ζ14+2ζ26+ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−ζ10−2ζ14−ζ26−2ζ4600000000000000000000000000
χ4844-24-2-4-24-200-21-21-2-222-1-1-40000003i3i−3i−3i1122-1-100003i3i−3i−3i−222222222ζ10+ζ14+2ζ26+ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−ζ10−2ζ14−ζ26−2ζ46−2−2−2−2−2ζ10−ζ14−2ζ26−ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46ζ10+2ζ14+ζ26+2ζ4600000000000000000000000000
χ4944-24-2-4-24-200-21-21-2-222-1-1-4000000−3i−3i3i3i1122-1-10000−3i−3i3i3i22−22−2−2−2−2ζ10+2ζ14+ζ26+2ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−2ζ10−ζ14−2ζ26−ζ462222−ζ10−2ζ14−ζ26−2ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ462ζ10+ζ14+2ζ26+ζ4600000000000000000000000000
χ5044-24-2-4-24-200-21-21-2-222-1-1-4000000−3i−3i3i3i1122-1-10000−3i−3i3i3i−22222222−ζ10−2ζ14−ζ26−2ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ462ζ10+ζ14+2ζ26+ζ46−2−2−2−2ζ10+2ζ14+ζ26+2ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−2ζ10−ζ14−2ζ26−ζ4600000000000000000000000000
χ5144-2-2444-2-2441-2-2-21-24-2-2-2-2-2-2-2-244-2-2-2-2111-21111-2-2111100000000000000000000000400-2-200000-20011000000
χ5244-2-2444-2-2441-2-2-21-24-2-2-2-2-2-2-2-244-2-2-2-2111-21111-2-2111100000000000000000000000-4002200000200-1-1000000
χ5344-2-2444-2-2-4-41-2-2-21-24-2-2-2-22222-4-42222111-211-1-122-1-1-1-100000000000000000000000000−2i32i300000000i3−i3000000
χ5444-2-2444-2-2-4-41-2-2-21-24-2-2-2-22222-4-42222111-211-1-122-1-1-1-1000000000000000000000000002i3−2i300000000−i3i3000000
χ554-44440-4-4-422−22444-4-4-40000022−2222−2222−2222−2222−224-4000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ564-44440-4-4-4−2222444-4-4-400000−2222−2222−2222−2222−22224-40000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ574-444-202-4-422−224-2-22-420000022−2222−22−22−22−22-22000022−22−22−22−220000−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000000000000000000
χ584-444-202-4-422−224-2-22-420000022−2222−22−22−22−22-22000022−22−22−22−220000ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000000000000000000
χ594-444-202-4-4−22224-2-22-4200000−2222−22222−22−22−2-220000−22222−22−22−20000−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000000000000000000
χ604-444-202-4-4−22224-2-22-4200000−2222−22222−22−22−2-220000−22222−22−22−20000ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000000000000000000
χ614-44-240-42-422−22-24-2-42200000−2222−2222−2222−2222−22-220000−22−22−22−2200000000000000000000−2i32i300000000i6−i6000000000000
χ624-44-240-42-422−22-24-2-42200000−2222−2222−2222−2222−22-220000−22−22−22−22000000000000000000002i3−2i300000000−i6i6000000000000
χ634-44-240-42-4−2222-24-2-422000002−2−2222−2222−2222−2222-2200002−22−22−22−200000000000000000000−2i32i300000000−i6i6000000000000
χ644-44-240-42-4−2222-24-2-422000002−2−2222−2222−2222−2222-2200002−22−22−22−2000000000000000000002i3−2i300000000i6−i6000000000000
χ654-4-2440-4-4222−22-2-2422-40000022−22−2222−22−22−22-220000−2222−22−22−2200−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000000000000000000000000
χ664-4-2440-4-4222−22-2-2422-40000022−22−2222−22−22−22-220000−2222−22−22−2200ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000000000000000000000000
χ674-4-2440-4-42−2222-2-2422-400000−22222−2−22222−22−2-2200002−2−22222−22−200−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000000000000000000000000
χ684-4-2440-4-42−2222-2-2422-400000−22222−2−22222−22−2-2200002−2−22222−22−200ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000000000000000000000000
χ694-4-24-202-4222−22-21-2-122003i−3i022−22−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ461-1003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4600−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ13−ζ29−ζ13+ζ29−ζ11+ζ43ζ11−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ25+ζ41ζ25−ζ41−ζ31+ζ47ζ31−ζ4700000000000000000000000000
χ704-4-24-202-4222−22-21-2-122003i−3i022−22−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ461-1003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4600ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ13+ζ29ζ13−ζ29ζ11−ζ43−ζ11+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ25−ζ41−ζ25+ζ41ζ31−ζ47−ζ31+ζ4700000000000000000000000000
χ714-4-24-202-4222−22-21-2-12200−3i3i022−22−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ461-100−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ4600−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ11−ζ43−ζ11+ζ43−ζ13+ζ29ζ13−ζ29−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ31−ζ47−ζ31+ζ47ζ25−ζ41−ζ25+ζ4100000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.