Finite Group Databasebeta

← Group #13155240

Character table — Group #13155240

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222224444444444444448888888888888888818181818242424242424243636363636363636363636363636363648484848484848484848216
order1233346668833366612121224242424242436121212121224242424242424242424246622466668121616161624244848484848484848666666121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111111-1-1-1-11-1111-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-11111-1
χ61111111111111111111111111111111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-1-1-11
χ71111111111111111111111111111111111111111111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-11-1-1111111-1
χ81111111111111111111111111111111111111111111-1-1-1-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-11
χ9222222222-2-2222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222220000000-220000-2-20000000000000000000
χ10222222222-2-2222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000002-20000220000000000000000000
χ1122222-222200222222-2-2-200000022-2-2-2-2-200000000002-22200000000-22−22−20022−2−222−2−200000000000
χ1222222-222200222222-2-2-200000022-2-2-2-2-200000000002-22200000000-2−22−2200−2−222−2−22200000000000
χ1322222-222200222222-2-2-200000022-2-2-2-2-20000000000-22-2-20000000022−2−220022−2−2−2−22200000000000
χ1422222-222200222222-2-2-200000022-2-2-2-2-20000000000-22-2-2000000002−222−200−2−22222−2−200000000000
χ152222-12-122222-1-1-1-1222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1220-1-1-1-12-10000-1-10000000022-1-1-1-100000
χ162222-12-122222-1-1-1-1222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-2-2011112-10000-1-100000000-2-2111100000
χ172222-12-122222-1-1-1-1222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2112-20-1-111-21000011000000002-2-1-11100000
χ182222-12-122222-1-1-1-1222-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-211-22011-1-1-2100001100000000-2211-1-100000
χ192222-12-122-2-22-1-1-1-1222-111-2-2-2-2-1-1-1-12-1-1-2-21111111122-1-1000−i3i3−i3i3-2-10000110000000000−i3i3−i3i300000
χ202222-12-122-2-22-1-1-1-1222-111-2-2-2-2-1-1-1-12-1-1-2-21111111122-1-1000i3−i3i3−i3-2-10000110000000000i3−i3i3−i300000
χ212222-12-122-2-22-1-1-1-1222-111-2-2-2-2-1-1-1-12-1-1-2-211111111-2-211000−i3i3i3−i3210000-1-10000000000−i3i3i3−i300000
χ222222-12-122-2-22-1-1-1-1222-111-2-2-2-2-1-1-1-12-1-1-2-211111111-2-211000i3−i3−i3i3210000-1-10000000000i3−i3−i3i300000
χ23222-12222-122-12-12-1-12-122222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100000220022000022000000-1-1-1-10-100-1-12-1-1-10
χ24222-12222-122-12-12-1-12-122222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1000002-200220000-2-200000011110-100-1-1-21110
χ25222-12222-122-12-12-1-12-122222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100000-2200-2-20000-2-200000011110100112-1-1-10
χ26222-12222-122-12-12-1-12-122222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100000-2-200-2-2000022000000-1-1-1-1010011-21110
χ2722-12222-1222-1-12-12-1-12222-1-122-1-1-12-1-1-1-1-1-1-122-1-1-1-10000202220000220000-1-1-1-10000-10-1-100-12-1-10
χ2822-12222-1222-1-12-12-1-12222-1-122-1-1-12-1-1-1-1-1-1-122-1-1-1-1000020-2220000-2-2000011110000-10-1-1001-2110
χ2922-12222-1222-1-12-12-1-12222-1-122-1-1-12-1-1-1-1-1-1-122-1-1-1-10000-202-2-20000-2-2000011110000101100-12-1-10
χ3022-12222-1222-1-12-12-1-12222-1-122-1-1-12-1-1-1-1-1-1-122-1-1-1-10000-20-2-2-20000220000-1-1-1-100001011001-2110
χ314444-2-4-244004-2-2-2-24-4-42000000-2-222-42200000000004-4-2-20000000020000000000000000000000000
χ324444-2-4-244004-2-2-2-24-4-42000000-2-222-4220000000000-442200000000-20000000000000000000000000
χ33444-24444-2-4-4-24-24-2-24-24-4-4-4-422-2-24-2-2-2-222-4-422222200000000000000000000000000000000000000
χ34444-24-444-200-24-24-2-2-42-4000000-2-2-42222000000000000000000000000022−22000000−2−22200000000000
χ35444-24-444-200-24-24-2-2-42-4000000-2-2-422220000000000000000000000000−222200000022−2−200000000000
χ36444-2-24-24-244-2-21-21-24-2-2-2-244-2-211-21-211-2-2-2-2111111000004000-2-200000000000000000-2001100000
χ37444-2-24-24-244-2-21-21-24-2-2-2-244-2-211-21-211-2-2-2-211111100000-40002200000000000000000200-1-100000
χ38444-2-24-24-2-4-4-2-21-21-24-2-222-4-42211-21-2112222-1-1-1-1-1-1000000000−2i32i300000000000000000000i3−i300000
χ39444-2-24-24-2-4-4-2-21-21-24-2-222-4-42211-21-2112222-1-1-1-1-1-10000000002i3−2i300000000000000000000−i3i300000
χ4044-24444-24-4-4-2-24-24-2-244-4-422-4-4-2-2-24-2-2-22222-4-4222200000000000000000000000000000000000000
χ4144-244-44-2400-2-24-24-22-4-4000000-2-22-42220000000000000000000000022−220000−2−222000000000000000
χ4244-244-44-2400-2-24-24-22-4-4000000-2-22-422200000000000000000000000−2222000022−2−2000000000000000
χ4344-24-24-2-2444-21-21-2-2-24-2-2-2-2-244111-2-211-2-211-2-211110000400-2-2000000000000000000-20110000000
χ4444-24-24-2-2444-21-21-2-2-24-2-2-2-2-244111-2-211-2-211-2-211110000-4002200000000000000000020-1-10000000
χ4544-24-24-2-24-4-4-21-21-2-2-24-22222-4-4111-2-21122-1-122-1-1-1-10000000−2i32i300000000000000000000i3−i30000000
χ4644-24-24-2-24-4-4-21-21-2-2-24-22222-4-4111-2-21122-1-122-1-1-1-100000002i3−2i300000000000000000000−i3i30000000
χ4744-2-2444-2-2441-2-2-2-21-2-2444-2-2-2-211-2-211111-2-2-2-21111000000400000000000000000000000000-2-2110
χ4844-2-2444-2-2441-2-2-2-21-2-2444-2-2-2-211-2-211111-2-2-2-21111000000-40000000000000000000000000022-1-10
χ4944-2-2444-2-2-4-41-2-2-2-21-2-24-4-4222211-2-2111-1-12222-1-1-1-1000000000000000000000000000000000003-30
χ5044-2-2444-2-2-4-41-2-2-2-21-2-24-4-4222211-2-2111-1-12222-1-1-1-100000000000000000000000000000000000-330
χ514-44440-4-4-422−22444-4-4-400022−2222−2222−224-40000022−2222−2222−222222−22−2200000000000000000000000000000000000000
χ524-44440-4-4-4−2222444-4-4-4000−2222−2222−22224-400000−2222−2222−2222−22−22222200000000000000000000000000000000000000
χ534-444-202-4-422−224-2-222-4000−2222−2222−22-220000022−22−22−22−2−22200−2i32i30000000000000i6−i60000000000000000000
χ544-444-202-4-422−224-2-222-4000−2222−2222−22-220000022−22−22−22−2−222002i3−2i30000000000000−i6i60000000000000000000
χ554-444-202-4-4−22224-2-222-40002−2−2222−2222-2200000−22222−22−222−2−200−2i32i30000000000000−i6i60000000000000000000
χ564-444-202-4-4−22224-2-222-40002−2−2222−2222-2200000−22222−22−222−2−2002i3−2i30000000000000i6−i60000000000000000000
χ574-44-240-4-4222−22-24-2-42200022−2222−22−22-2200000−2222−22−22−2−22200000000000000000000000−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ4300000000000
χ584-44-240-4-4222−22-24-2-42200022−2222−22−22-2200000−2222−22−22−2−22200000000000000000000000ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ4300000000000
χ594-44-240-4-42−2222-24-2-422000−2222−22222−2-22000002−2−22222−222−2−200000000000000000000000−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ4700000000000
χ604-44-240-4-42−2222-24-2-422000−2222−22222−2-22000002−2−22222−222−2−200000000000000000000000ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ4700000000000
χ614-4-2440-42-422−22-2-242-4200022−22−2222−22-2200000−22−2222−22−2−2220000000000000000000−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47000000000000000
χ624-4-2440-42-422−22-2-242-4200022−22−2222−22-2200000−22−2222−22−2−2220000000000000000000ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47000000000000000
χ634-4-2440-42-4−2222-2-242-42000−22222−2−2222-22000002−22−2−222222−2−20000000000000000000−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43000000000000000
χ644-4-2440-42-4−2222-2-242-42000−22222−2−2222-22000002−22−2−222222−2−20000000000000000000ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43000000000000000
χ65888-4-4-8-48-400-4-42-42-4-844000000224-24-2-2000000000000000000000000000000000000000000000000
χ6688-48-4-8-4-4800-42-42-4-44-8400000022-244-2-2000000000000000000000000000000000000000000000000
χ6788-4-48-88-4-4002-4-4-4-4244-80000002244-2-2-2000000000000000000000000000000000000000000000000
χ6888-4-4-48-4-4-488222222-4-4-4-4-4-4-4-4-4-1-1222-1-1222222-1-1-1-100000000000000000000000000000000000000
χ6988-4-4-48-4-4-4-8-8222222-4-4-4444444-1-1222-1-1-2-2-2-2-2-2111100000000000000000000000000000000000000
χ7088-4-4-4-8-4-4-400222222444000000-1-1-2-2-21100000033−3333−3300000000000000000000000000000000000000
χ7188-4-4-4-8-4-4-400222222444000000-1-1-2-2-211000000−3333−333300000000000000000000000000000000000000
χ728-88-4-404-8442−42-4-424-24000−222242−42−22222-200000−2222−22222−222−2−200000000000000000000000000000000000000
χ738-88-4-404-84−4242-4-424-2400022−22−424222−222-20000022−2222−22−22−2−22200000000000000000000000000000000000000
χ748-8-48-4044-842−42-42-4-244000−2222−222242−422-200000−22222−2−222222−2−200000000000000000000000000000000000000
χ758-8-48-4044-8−4242-42-4-24400022−2222−22−42422-20000022−22−2222−22−2−22200000000000000000000000000000000000000
χ768-8-4-480-84442−422-4-444-200042−42−2222−22222-2000002−2−2222−222222−2−200000000000000000000000000000000000000
χ778-8-4-480-844−42422-4-444-2000−424222−2222−222-200000−2222−2222−22−2−22200000000000000000000000000000000000000
χ788-8-4-4-4044442−42222-2-2-2000−2222−2222−2222-1100033−332−22−22−22ζ10−2ζ14−ζ26+ζ46−ζ10+ζ14+2ζ26−2ζ46−2ζ10+2ζ14+ζ26−ζ46ζ10−ζ14−2ζ26+2ζ4600000000000000000000000000000000000000
χ798-8-4-4-4044442−42222-2-2-2000−2222−2222−2222-11000−33332−22−22−2−ζ10+ζ14+2ζ26−2ζ462ζ10−2ζ14−ζ26+ζ46ζ10−ζ14−2ζ26+2ζ46−2ζ10+2ζ14+ζ26−ζ4600000000000000000000000000000000000000
χ808-8-4-4-40444−4242222-2-2-200022−2222−2222−22-1100033−33−22−22−22−2ζ10+2ζ14+ζ26−ζ46ζ10−ζ14−2ζ26+2ζ462ζ10−2ζ14−ζ26+ζ46−ζ10+ζ14+2ζ26−2ζ4600000000000000000000000000000000000000
χ818-8-4-4-40444−4242222-2-2-200022−2222−2222−22-11000−3333−22−22−22ζ10−ζ14−2ζ26+2ζ46−2ζ10+2ζ14+ζ26−ζ46−ζ10+ζ14+2ζ26−2ζ462ζ10−2ζ14−ζ26+ζ4600000000000000000000000000000000000000

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