Finite Group Databasebeta

← Group #10709268

Character table — Group #10709268

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888121212121212121216161616161616161624242424484896
order122234444666888844488121212121212121224242424224666688121212242424242424161616161616161644412121212121216161616884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111-1-11111-1-1-1-111111111-11111-1-1-1-1111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1
χ611111111111111111-1-11111-1-1-1-111111111-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11
χ711111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111-111-1-11111-1-1-1-1-1-11
χ811111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1
χ9222222222222-2-2-2-2222-2-222222222-2-2-2-20020000-2-2222-2-2-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-22-2-2-2-222-2-2-2-222-2-2-2-200-2000022-2-22-2-22222000000000000000000000000
χ11222222-2-222220000-22200222222-2-2000000-2000000-2-2-20000002222−2−2−2−200000000022−2−2000
χ12222222-2-222220000-22200222222-2-2000000-2000000-2-2-2000000−2−2−2−22222000000000−2−222000
χ13222222-2-222220000-2-2-20022-2-2-2-2-2-2000000200000022-20000002222−2−2−2−2000000000−2−222000
χ14222222-2-222220000-2-2-20022-2-2-2-2-2-2000000200000022-2000000−2−2−2−2222200000000022−2−2000
χ1522222-222-22222222-200-2-2-2-2000022222222022220000-2-2-2000000000000-200-2-200000000000
χ1622222-222-22222222-200-2-2-2-20000222222-2-20-2-2-2-20000-2-2-20000000000002002200000000000
χ1722222-222-2222-2-2-2-2-20022-2-2000022-2-2-2-200000000000-22200000000000002-20022-2-20000000
χ1822222-222-2222-2-2-2-2-20022-2-2000022-2-2-2-200000000000-2220000000000000-2200-2-2220000000
χ192222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-100000000222-1-1-1-1-1-10000000
χ202222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22111122-1-1-1-1-1-1-1-1-100000000-2-2-21111110000000
χ212222-12222-1-1-122222-2-222-1-11111-1-1-1-1-1-122-2-1-1-1-1-2-211-1-1-11111000000002-2-2-1-111110000000
χ222222-12222-1-1-122222-2-222-1-11111-1-1-1-1-1-1-2-2-21111-2-211-1-1-1111100000000-22211-1-1-1-10000000
χ232222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-11111002−i3−i3i3i3-2-2-1-1-111111100000000000−i3i3−i3i3−i3i30000000
χ242222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-11111002i3i3−i3−i3-2-2-1-1-111111100000000000i3−i3i3−i3i3−i30000000
χ252222-12222-1-1-1-2-2-2-22-2-2-2-2-1-11111-1-1111100-2−i3−i3i3i32211-111-1-1-1-100000000000−i3i3i3−i3i3−i30000000
χ262222-12222-1-1-1-2-2-2-22-2-2-2-2-1-11111-1-1111100-2i3i3−i3−i32211-111-1-1-1-100000000000i3−i3−i3i3−i3i30000000
χ272222-1-222-2-1-1-12222-200-2-211−i3−i3i3i3-1-1-1-1-1-1220-1-1-1-100−i3i3111−i3−i3i3i300000000-20011−i3i3i3−i30000000
χ282222-1-222-2-1-1-12222-200-2-211−i3−i3i3i3-1-1-1-1-1-1-2-20111100−i3i3111−i3−i3i3i300000000200-1-1i3−i3−i3i30000000
χ292222-1-222-2-1-1-12222-200-2-211i3i3−i3−i3-1-1-1-1-1-1220-1-1-1-100i3−i3111i3i3−i3−i300000000-20011i3−i3−i3i30000000
χ302222-1-222-2-1-1-12222-200-2-211i3i3−i3−i3-1-1-1-1-1-1-2-20111100i3−i3111i3i3−i3−i300000000200-1-1−i3i3i3−i30000000
χ312222-1-222-2-1-1-1-2-2-2-2-2002211−i3−i3i3i3-1-11111000−i3−i3i3i300−i3i31-1-1i3i3−i3−i30000000002-2i3−i3-1-1110000000
χ322222-1-222-2-1-1-1-2-2-2-2-2002211−i3−i3i3i3-1-11111000i3i3−i3−i300−i3i31-1-1i3i3−i3−i3000000000-22−i3i311-1-10000000
χ332222-1-222-2-1-1-1-2-2-2-2-2002211i3i3−i3−i3-1-11111000−i3−i3i3i300i3−i31-1-1−i3−i3i3i3000000000-22i3−i311-1-10000000
χ342222-1-222-2-1-1-1-2-2-2-2-2002211i3i3−i3−i3-1-11111000i3i3−i3−i300i3−i31-1-1−i3−i3i3i30000000002-2−i3i3-1-1110000000
χ3522-2-2202-202-2-222-2-2000000000002-222-2-22-202-22-20000000000022−2−222−2−200000000000002−20
χ3622-2-2202-202-2-222-2-2000000000002-222-2-22-202-22-200000000000−2−222−2−2220000000000000−220
χ3722-2-2202-202-2-222-2-2000000000002-222-2-2-220-22-220000000000022−2−222−2−20000000000000−220
χ3822-2-2202-202-2-222-2-2000000000002-222-2-2-220-22-2200000000000−2−222−2−22200000000000002−20
χ392-22-22-2002-22-22−22−202i−2i2−22-22i−2i2i−2i002−22−20000000−i2i20002−2−i2i2−i2i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000
χ402-22-22-2002-22-22−22−202i−2i2−22-22i−2i2i−2i002−22−20000000−i2i20002−2−i2i2−i2i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000
χ412-22-22-2002-22-22−22−20−2i2i2−22-2−2i2i−2i2i002−22−20000000i2−i20002−2i2−i2i2−i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000
χ422-22-22-2002-22-22−22−20−2i2i2−22-2−2i2i−2i2i002−22−20000000i2−i20002−2i2−i2i2−i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000
χ432-22-22-2002-22-2−22−2202i−2i−222-22i−2i2i−2i00−22−220000000i2−i2000−22i2−i2i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000
χ442-22-22-2002-22-2−22−2202i−2i−222-22i−2i2i−2i00−22−220000000i2−i2000−22i2−i2i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000
χ452-22-22-2002-22-2−22−220−2i2i−222-2−2i2i−2i2i00−22−220000000−i2i2000−22−i2i2−i2i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000
χ462-22-22-2002-22-2−22−220−2i2i−222-2−2i2i−2i2i00−22−220000000−i2i2000−22−i2i2−i2i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000
χ4744444-4-4-4-4444000040000-4-40000-4-40000000000000004000000000000000000000000000000
χ484444-24-4-44-2-2-20000-44400-2-2-2-2-2-222000000-4000000222000000000000000000000000000000
χ494444-24-4-44-2-2-20000-4-4-400-2-22222220000004000000-2-22000000000000000000000000000000
χ504444-2-4-4-4-4-2-2-200004000022−2i3−2i32i32i32200000000000002i3−2i3-2000000000000000000000000000000
χ514444-2-4-4-4-4-2-2-2000040000222i32i3−2i3−2i3220000000000000−2i32i3-2000000000000000000000000000000
χ5244-4-4404-404-4-4-4-444000000000004-4-4-444000000000000000000000000000000000000000000
χ5344-4-440-4404-4-4000000000000000-44000000000000000000000022-2-2-2-2220000000000000000
χ5444-4-440-4404-4-4000000000000000-440000000000000000000000-2-22222-2-20000000000000000
χ5544-4-4-204-40-22244-4-400000000000-22-2-2224-40-22-2200000000000000000000000000000000000
χ5644-4-4-204-40-22244-4-400000000000-22-2-222-4402-22-200000000000000000000000000000000000
χ5744-4-4-204-40-222-4-44400000000000-2222-2-2000−2i32i32i3−2i300000000000000000000000000000000000
χ5844-4-4-204-40-222-4-44400000000000-2222-2-20002i3−2i3−2i32i300000000000000000000000000000000000
χ594-44-44400-4-44-422−2222−22000−2222-4400000022−2222−22000000000000−22220000000000000000000000000000
χ604-44-44400-4-44-4−2222−222200022−22-44000000−2222−222200000000000022−220000000000000000000000000000
χ614-44-4-2400-42-2222−2222−22000−22222-223−23−232300−22−220000000000002−2−666−6000000000000000000000000
χ624-44-4-2400-42-2222−2222−22000−22222-2−232323−2300−22−220000000000002−26−6−66000000000000000000000000
χ634-44-4-2400-42-22−2222−222200022−222-223−23−2323002−22−2000000000000−226−6−66000000000000000000000000
χ644-44-4-2400-42-22−2222−222200022−222-2−232323−23002−22−2000000000000−22−666−6000000000000000000000000
χ654-44-4-2-40042-2222−2222−2204i−4i22−22-22−2i2i−2i2i00−22−220000000−2i22i2000−22i2−i2i2−i2000000000000000000000000
χ664-44-4-2-40042-2222−2222−220−4i4i22−22-222i−2i2i−2i00−22−2200000002i2−2i2000−22−i2i2−i2i2000000000000000000000000
χ674-44-4-2-40042-22−2222−222204i−4i−2222-22−2i2i−2i2i002−22−200000002i2−2i20002−2−i2i2−i2i2000000000000000000000000
χ684-44-4-2-40042-22−2222−22220−4i4i−2222-222i−2i2i−2i002−22−20000000−2i22i20002−2i2−i2i2−i2000000000000000000000000
χ694-4-4440000-4-4422−22−2222000000000000022−22−2222000000000000000000ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ470000000000000000
χ704-4-4440000-4-4422−22−2222000000000000022−22−2222000000000000000000−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ470000000000000000
χ714-4-4440000-4-44−222222−220000000000000−222222−22000000000000000000ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ470000000000000000
χ724-4-4440000-4-44−222222−220000000000000−222222−22000000000000000000−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ470000000000000000
χ7388-8-8-40-880-4440000000000000004-40000000000000000000000000000000000000000000000
χ748-8-88-4000044-442−42−42420000000000000−222222−22000000000000000000000000000000000000000000
χ758-8-88-4000044-4−424242−42000000000000022−22−2222000000000000000000000000000000000000000000

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