Finite Group Databasebeta

← Group #13155260

Character table — Group #13155260

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222444444444444444444444888888888888881212121212121212121212121212121212122424363636363636484848484848484854547272108144144
order123334666883336661212121212242424242424242424243612121212242424242424242416164848484848484848484848484848484824161648484848666612121212244481212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1
χ31111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-11
χ41111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-11-1-1
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-111-111-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111-111-1
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-111
χ9222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000002200-200
χ10222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-200200
χ1122222-222200222222-2-2-2-2-2000000000022-2-2-2-2000000002−222222222−2−2−2−2−2−2−2−2002−222−2−2000000002-200000
χ1222222-222200222222-2-2-2-2-2000000000022-2-2-2-2000000002−222222222−2−2−2−2−2−2−2−200−22−2−22200000000-2200000
χ1322222-222200222222-2-2-2-2-2000000000022-2-2-2-200000000−22−2−2−2−2−2−2−2−222222222002−222−2−200000000-2200000
χ1422222-222200222222-2-2-2-2-2000000000022-2-2-2-200000000−22−2−2−2−2−2−2−2−22222222200−22−2−222000000002-200000
χ152222-122-12222-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-12-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1200000002-1-1-1000000200-10
χ162222-122-12222-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-12-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-20000000-2111000000-20010
χ172222-122-12222-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-2-2-2-2111111-2-2111111200000002-1-1-1000000-20010
χ182222-122-12222-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-2-2-2-2111111-2-2111111-20000000-2111000000200-10
χ19222-122-12222-12-12-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-12-1-1-12-1-10000000
χ20222-122-12222-12-12-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-2-2-21111-12-1-11-2110000000
χ21222-122-12222-12-12-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-22-2-211111-211-12-1-10000000
χ22222-122-12222-12-12-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-222-1-1-1-11-2111-2110000000
χ2322-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-10200000000002-1-1-1000200-1
χ2422-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-10-20000000000-2111000-2001
χ2522-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-2-211-2-2111111-2-211110200000000002-1-1-1000-2001
χ2622-122222-122-1-12-12-122-1-1-1-1-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-2-211-2-2111111-2-211110-20000000000-2111000200-1
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χ30444-244-244-4-4-24-24-2-2-24444-4-4-4-4-4-4-4-422-2-2-2-2-2-22222222200000000000000000000000000000000000000000
χ31444-24-4-24400-24-24-2-22-4-4-4-40000000000-2-22222000000000000000000000000000022−22−2−222000000000000000
χ32444-24-4-24400-24-24-2-22-4-4-4-40000000000-2-222220000000000000000000000000000−222222−2−2000000000000000
χ33444-2-24-2-2444-2-21-21-2-2-24-2-244-2-2-2-2-2-2-2-2111-211-2-211111100000000000000000040000000-2-21100000000000
χ34444-2-24-2-2444-2-21-21-2-2-24-2-244-2-2-2-2-2-2-2-2111-211-2-2111111000000000000000000-4000000022-1-100000000000
χ35444-2-24-2-24-4-4-2-21-21-2-2-24-2-2-4-422222222111-21122-1-1-1-1-1-100000000000000000000000000003-300000000000
χ36444-2-24-2-24-4-4-2-21-21-2-2-24-2-2-4-422222222111-21122-1-1-1-1-1-10000000000000000000000000000-3300000000000
χ3744-244444-2-4-4-2-24-24-244-2-2-222-4-42222-4-4-2-24-2-2-222-4-4222200000000000000000000000000000000000000000
χ3844-244-444-200-2-24-24-2-4-42220000000000-2-2-42220000000022−22−2−22222−2−2−2−222−22−22222200000000000000000000000
χ3944-244-444-200-2-24-24-2-4-42220000000000-2-2-422200000000−222222−22−222222−2−22222−2−2−2−200000000000000000000000
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χ4144-24-244-2-244-21-21-2-24-2-211-2-2-2-211114411-2-211-2-2-2-21111-4-42222-1-1-1-12222-1-1-1-100000000000000000000000
χ4244-24-244-2-2-4-4-21-21-2-24-2-2112222-1-1-1-1-4-411-2-2112222-1-1-1-10000003i3i−3i−3i00003i3i−3i−3i00000000000000000000000
χ4344-24-244-2-2-4-4-21-21-2-24-2-2112222-1-1-1-1-4-411-2-2112222-1-1-1-1000000−3i−3i3i3i0000−3i−3i3i3i00000000000000000000000
χ4444-24-2-44-2-200-21-21-2-2-422-1-100003i3i−3i−3i001122-1-100003i3i−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−ζ26−2ζ4600000000000000000000000
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χ4644-24-2-44-2-200-21-21-2-2-422-1-10000−3i−3i3i3i001122-1-10000−3i−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+ζ4600000000000000000000000
χ4744-24-2-44-2-200-21-21-2-2-422-1-10000−3i−3i3i3i001122-1-10000−3i−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−ζ4600000000000000000000000
χ4844-2-244-24-2441-2-2-2-21-24-2-2-2-2-244-2-2-2-2-2-211-211111-2-21111000000000000000000040000000000-2-2110000000
χ4944-2-244-24-2441-2-2-2-21-24-2-2-2-2-244-2-2-2-2-2-211-211111-2-211110000000000000000000-4000000000022-1-10000000
χ5044-2-244-24-2-4-41-2-2-2-21-24-2-2-222-4-422222211-2111-1-122-1-1-1-1000000000000000000000000000000003-30000000
χ5144-2-244-24-2-4-41-2-2-2-21-24-2-2-222-4-422222211-2111-1-122-1-1-1-100000000000000000000000000000000-330000000
χ524-44440-4-4-422−22444-4-4-40000022−2222−2222−2222−2222−224-4000022−2222−2222−2222−2200000000000000000000000000000000000000000
χ534-44440-4-4-4−2222444-4-4-400000−2222−2222−2222−2222−22224-40000−2222−2222−2222−222200000000000000000000000000000000000000000
χ544-444-20-42-422−224-2-222-40000022−22−22−22−2222−22-22000022−22−22−22−220000−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−ζ4700000000000000000000000
χ554-444-20-42-422−224-2-222-40000022−22−22−22−2222−22-22000022−22−22−22−220000ζ11−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+ζ4700000000000000000000000
χ564-444-20-42-4−22224-2-222-400000−22222−22−22−2−2222-220000−22222−22−22−20000−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+ζ4300000000000000000000000
χ574-444-20-42-4−22224-2-222-400000−22222−22−22−2−2222-220000−22222−22−22−20000ζ25+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−ζ4300000000000000000000000
χ584-44-2402-4-422−22-24-2-4220000022−2222−2222−2222−22−22-220000−22−22−22−220000000000000000000000−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43000000000000000
χ594-44-2402-4-422−22-24-2-4220000022−2222−2222−2222−22−22-220000−22−22−22−220000000000000000000000ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43000000000000000
χ604-44-2402-4-4−2222-24-2-42200000−2222−2222−2222−22222−2-2200002−22−22−22−20000000000000000000000−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47000000000000000
χ614-44-2402-4-4−2222-24-2-42200000−2222−2222−2222−22222−2-2200002−22−22−22−20000000000000000000000ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47000000000000000
χ624-4-2440-4-4222−22-2-242-4200000−2222−22−22−2222−22-220000−2222−22−22−2200−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+ζ4700000000000000000000000
χ634-4-2440-4-4222−22-2-242-4200000−2222−22−22−2222−22-220000−2222−22−22−2200ζ11+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−ζ4700000000000000000000000
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χ714-4-24-20-422−2222-21-2-1220003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ46−22221-1003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ4600ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ25+ζ41ζ25−ζ41−ζ31+ζ47ζ31−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ13+ζ29ζ13−ζ29ζ11−ζ43−ζ11+ζ4300000000000000000000000
χ724-4-24-20-422−2222-21-2-122000−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−22221-100−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ4600−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−ζ31+ζ47ζ31−ζ47−ζ25+ζ41ζ25−ζ41ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ11−ζ43−ζ11+ζ43−ζ13+ζ29ζ13−ζ2900000000000000000000000
χ734-4-24-20-422−2222-21-2-122000−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−22221-100−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ4600ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ31−ζ47−ζ31+ζ47ζ25−ζ41−ζ25+ζ41−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−ζ11+ζ43ζ11−ζ43ζ13−ζ29−ζ13+ζ2900000000000000000000000
χ74888-4-4-8-4-4800-4-42-42-444-844000000000022-24-2-20000000000000000000000000000000000000000000000000
χ7588-4-48-8-48-4002-4-4-4-424-84440000000000224-2-2-20000000000000000000000000000000000000000000000000
χ7688-4-4-48-4-4-488222222-4-4-422-4-4-4-42222-4-4-1-122-1-12222-1-1-1-100000000000000000000000000000000000000000
χ7788-4-4-48-4-4-4-8-8222222-4-4-4224444-2-2-2-244-1-122-1-1-2-2-2-2111100000000000000000000000000000000000000000
χ7888-4-4-4-8-4-4-400222222444-2-200006i6i−6i−6i00-1-1-2-2110000−3i−3i3i3i00000000000000000000000000000000000000000
χ7988-4-4-4-8-4-4-400222222444-2-20000−6i−6i6i6i00-1-1-2-21100003i3i−3i−3i00000000000000000000000000000000000000000
χ808-88-4-4044-842−42-4-424-240000042−42−2222−2222−2222−22222-20000−22222−22−22−200000000000000000000000000000000000000000
χ818-88-4-4044-8−4242-4-424-2400000−424222−2222−2222−2222−222-2000022−22−22−22−2200000000000000000000000000000000000000000
χ828-8-4-4804-8442−422-4-444-200000−222242−42−2222−2222−22222-200002−2−22222−22−200000000000000000000000000000000000000000
χ838-8-4-4804-84−42422-4-444-20000022−22−424222−2222−2222−222-20000−2222−22−22−2200000000000000000000000000000000000000000
χ848-8-4-4-4044442−42222-2-2-20006i−6i−2222−2222−4ζ10−2ζ14−4ζ26−2ζ464ζ10+2ζ14+4ζ26+2ζ462ζ10+4ζ14+2ζ26+4ζ46−2ζ10−4ζ14−2ζ26−4ζ46−2222-1100−3i3i2−22−22ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ4600000000000000000000000000000000000000000
χ858-8-4-4-4044442−42222-2-2-2000−6i6i−2222−22222ζ10+4ζ14+2ζ26+4ζ46−2ζ10−4ζ14−2ζ26−4ζ46−4ζ10−2ζ14−4ζ26−2ζ464ζ10+2ζ14+4ζ26+2ζ46−2222-11003i−3i2−22−2−ζ10−2ζ14−ζ26−2ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−2ζ10−ζ14−2ζ26−ζ4600000000000000000000000000000000000000000
χ868-8-4-4-40444−4242222-2-2-20006i−6i22−2222−224ζ10+2ζ14+4ζ26+2ζ46−4ζ10−2ζ14−4ζ26−2ζ46−2ζ10−4ζ14−2ζ26−4ζ462ζ10+4ζ14+2ζ26+4ζ4622−22-1100−3i3i−22−22−2ζ10−ζ14−2ζ26−ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−ζ10−2ζ14−ζ26−2ζ4600000000000000000000000000000000000000000
χ878-8-4-4-40444−4242222-2-2-2000−6i6i22−2222−22−2ζ10−4ζ14−2ζ26−4ζ462ζ10+4ζ14+2ζ26+4ζ464ζ10+2ζ14+4ζ26+2ζ46−4ζ10−2ζ14−4ζ26−2ζ4622−22-11003i−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.