Finite Group Databasebeta

← Group #13155227

Character table — Group #13155227

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1122222222244444444444444444444466668888888888888899121212121212121212121212121212121818181818242424242424363636484848484848545454547272144144
order1233346668833366612121212122424242424242424242416161616361212121224242424242424244448484848484848484848484848484848288121224661212624246661212121616161624612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-11-111-1-1-1-1-1111-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1111-1-1-1-1-11-11
χ511111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1111-1-1-11111-11-11
χ811111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111111111-11-1
χ9222222222-2-222222222222-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-22200000000000000002-2-2220000002-2-200000000000000
χ10222222222-2-222222222222-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-2-2-20000000000000000-222-2-2000000-22200000000000000
χ1122222-222200222222-2-2-2-2-2000000000022−2−222-2-2-2-2000000002222222222−2−2−2−2−2−2−2−2-20022000000-20000000022−2−20000
χ1222222-222200222222-2-2-2-2-2000000000022−2−222-2-2-2-200000000-2-222222222−2−2−2−2−2−2−2−2200-2-2000000200000000−2−2220000
χ1322222-222200222222-2-2-2-2-20000000000−2−22222-2-2-2-20000000022−2−2−2−2−2−2−2−222222222-20022000000-200000000−2−2220000
χ1422222-222200222222-2-2-2-2-20000000000−2−22222-2-2-2-200000000-2-2−2−2−2−2−2−2−2−222222222200-2-200000020000000022−2−20000
χ152222-12-122222-1-1-1-12-12-1-122222-1-1-1-1-1-12222-1-1-12-1-122-1-1-1-1-1-10022-1-1-1-1-1-122-1-1-1-1-1-100000202200000-1-1-1000000020-10
χ162222-12-122222-1-1-1-12-12-1-122222-1-1-1-1-1-12222-1-1-12-1-122-1-1-1-1-1-10022-1-1-1-1-1-122-1-1-1-1-1-100000-20-2-2000001110000000-2010
χ172222-12-122222-1-1-1-12-12-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-12-1-122-1-1-1-1-1-100-2-2111111-2-211111100000202200000-1-1-10000000-2010
χ182222-12-122222-1-1-1-12-12-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-12-1-122-1-1-1-1-1-100-2-2111111-2-211111100000-20-2-200000111000000020-10
χ19222-1222-1222-12-12-1-12222-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000000000000222-1-122-1-1-1-1-1-1-12-1-12-1-100000000
χ20222-1222-1222-12-12-1-12222-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000000000000222-1-1-2-21111-1-1-1-211-21100000000
χ21222-1222-1222-12-12-1-12222-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000000000-2-2-2112-2-1-1111112-1-1-21100000000
χ22222-1222-1222-12-12-1-12222-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000000000-2-2-211-2211-1-1111-2112-1-100000000
χ23222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-20000-1-1-1-1-1-1111111112200000000000000002-2-2-1-100−i3i3−i3i3-1110−i3i30−i3i300000000
χ24222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-20000-1-1-1-1-1-1111111112200000000000000002-2-2-1-100i3−i3i3−i3-1110i3−i30i3−i300000000
χ25222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-20000-1-1-1-1-1-111111111-2-20000000000000000-2221100−i3i3i3−i31-1-10−i3i30i3−i300000000
χ26222-1222-12-2-2-12-12-1-12222-111-2-2-2-2-2-2-2-20000-1-1-1-1-1-111111111-2-20000000000000000-2221100i3−i3−i3i31-1-10i3−i30−i3i300000000
χ2722-122222-122-1-12-12-12-1-1-1222-1-122-1-1-1-12222-1-12-1-1-1-1-122-1-1-1-100-1-122-1-1-1-1-1-122-1-1-1-100000020022000000-1-1-10000020-1
χ2822-122222-122-1-12-12-12-1-1-1222-1-122-1-1-1-12222-1-12-1-1-1-1-122-1-1-1-100-1-122-1-1-1-1-1-122-1-1-1-1000000-200-2-200000011100000-201
χ2922-122222-122-1-12-12-12-1-1-1222-1-122-1-1-1-1-2-2-2-2-1-12-1-1-1-1-122-1-1-1-10011-2-2111111-2-2111100000020022000000-1-1-100000-201
χ3022-122222-122-1-12-12-12-1-1-1222-1-122-1-1-1-1-2-2-2-2-1-12-1-1-1-1-122-1-1-1-10011-2-2111111-2-21111000000-200-2-20000001110000020-1
χ312-22220-2-2-22−2222-2-2-2000002−22−22−222−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ432-200002−22−222−2−22i−2i−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ430−i2i22i−2i0000000−i2i2000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ322-22220-2-2-22−2222-2-2-2000002−22−22−222−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ432-200002−22−222−2−2−2i2i−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ430i2−i2−2i2i0000000i2−i2000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ332-22220-2-2-22−2222-2-2-2000002−22−22−222−2−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ432-200002−22−222−2−22i−2iζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ430−i2i22i−2i0000000−i2i2000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ342-22220-2-2-22−2222-2-2-2000002−22−22−222−2−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ432-200002−22−222−2−2−2i2iζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ430i2−i2−2i2i0000000i2−i2000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ352-22220-2-2-2−22222-2-2-200000−22−22−22−2−222ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ472-20000−22−22−2−2222i−2iζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ470i2−i22i−2i0000000i2−i2000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ362-22220-2-2-2−22222-2-2-200000−22−22−22−2−222ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ472-20000−22−22−2−222−2i2iζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ470−i2i2−2i2i0000000−i2i2000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ372-22220-2-2-2−22222-2-2-200000−22−22−22−2−222−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ472-20000−22−22−2−2222i−2i−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ470i2−i22i−2i0000000i2−i2000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ382-22220-2-2-2−22222-2-2-200000−22−22−22−2−222−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ472-20000−22−22−2−222−2i2i−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ470−i2i2−2i2i0000000−i2i2000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ394444-24-244-4-44-2-2-2-24-24-2-24-4-4-4-42222220000-2-2-24-2-2-4-42222220000000000000000000000000000000000000000000000
χ404444-2-4-244004-2-2-2-242-422-400000000002222−22−22-2-22-42200000000002222−2−2−2−2−2−2−22−222222220000000000000000000000000000
χ414444-2-4-244004-2-2-2-242-422-40000000000−22−222222-2-22-4220000000000−22−222222222222−2−2−2−2−2−20000000000000000000000000000
χ42444-24-44-2400-24-24-2-2-4-4-4-4200000000000000-2-2222200000000440000000000000000-400-2-200000020000000000000000
χ43444-24-44-2400-24-24-2-2-4-4-4-4200000000000000-2-2222200000000-4-4000000000000000040022000000-20000000000000000
χ44444-2-24-2-2444-2-21-21-2-24-2-2-2-2-244-2-2-2-2-2-20000111-211-2-21111110000000000000000000000040-2-200000-21100000000000
χ45444-2-24-2-2444-2-21-21-2-24-2-2-2-2-244-2-2-2-2-2-20000111-211-2-211111100000000000000000000000-4022000002-1-100000000000
χ46444-2-24-2-24-4-4-2-21-21-2-24-2-2-222-4-42222220000111-21122-1-1-1-1-1-10000000000000000000000000−2i32i3000000i3−i300000000000
χ47444-2-24-2-24-4-4-2-21-21-2-24-2-2-222-4-42222220000111-21122-1-1-1-1-1-100000000000000000000000002i3−2i3000000−i3i300000000000
χ4844-244444-2-4-4-2-24-24-24-2-2-24-4-422-4-422220000-2-24-2-2-222-4-422220000000000000000000000000000000000000000000000
χ4944-244-444-200-2-24-24-2-4222-400000000002222−22−22-2-2-42220000000000−2−22222−2−2−2−222−22−2222220000000000000000000000000000
χ5044-244-444-200-2-24-24-2-4222-40000000000−22−222222-2-2-4222000000000022−22−222222−2−22222−2−2−2−20000000000000000000000000000
χ5144-24-24-24-244-21-21-2-2-2-211444-2-2-2-21111444411-2-211-2-2-2-2111100-2-2-2-21111-2-2-2-211110000000000000000000000000000
χ5244-24-24-24-244-21-21-2-2-2-211444-2-2-2-21111-4-4-4-411-2-211-2-2-2-21111002222-1-1-1-12222-1-1-1-10000000000000000000000000000
χ5344-24-24-24-2-4-4-21-21-2-2-2-2114-4-42222-1-1-1-1000011-2-2112222-1-1-1-10000003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000
χ5444-24-24-24-2-4-4-21-21-2-2-2-2114-4-42222-1-1-1-1000011-2-2112222-1-1-1-1000000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000
χ5544-24-2-4-24-200-21-21-2-222-1-1-40000003i−3i3i−3i2222−22−221122-1-100003i−3i3i−3i00−2−2−2−2−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ4622222ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ460000000000000000000000000000
χ5644-24-2-4-24-200-21-21-2-222-1-1-40000003i−3i3i−3i−22−2222221122-1-100003i−3i3i−3i0022222ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2−2−2−2−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ460000000000000000000000000000
χ5744-24-2-4-24-200-21-21-2-222-1-1-4000000−3i3i−3i3i2222−22−221122-1-10000−3i3i−3i3i00−2−2−2−2ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ462222−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ460000000000000000000000000000
χ5844-24-2-4-24-200-21-21-2-222-1-1-4000000−3i3i−3i3i−22−2222221122-1-10000−3i3i−3i3i002222−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46−2−2−2−2ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ460000000000000000000000000000
χ5944-2-2444-2-2441-2-2-2-214-2-2-2-2-2-2-2-244-2-2-2-2000011-211111-2-21111000000000000000000000000400-2-2000000-21100000000
χ6044-2-2444-2-2441-2-2-2-214-2-2-2-2-2-2-2-244-2-2-2-2000011-211111-2-21111000000000000000000000000-400220000002-1-100000000
χ6144-2-2444-2-2-4-41-2-2-2-214-2-2-2-22222-4-42222000011-2111-1-122-1-1-1-1000000000000000000000000000−2i32i30000000i3−i300000000
χ6244-2-2444-2-2-4-41-2-2-2-214-2-2-2-22222-4-42222000011-2111-1-122-1-1-1-10000000000000000000000000002i3−2i30000000−i3i300000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.