Finite Group Databasebeta

← Group #10951976

Character table — Group #10951976

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222444444444444666666888888888888121212121212121616161616161616161624242424243232484848
order12234468824681212161616162424881616161624681216162448484848244481616226668122448482481616624228
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111
χ5111111111111111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-111111-1-11-1111-111-1-1-1-11-1-1-1-11-11
χ6111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-111111-1-1-11-1-1-11-11-1-1111-1-111-11-1
χ7111111111111111-1-1-1-111-1-1111111111-1-11-1-1-1-1-1-1-1-1-1111-1111-111-1-111-111-1-1-11-1
χ8111111111111111-1-1-1-111-1-11111-1-1111-1-11-1-1-1-1-1-1-1-1-111-11-1-1-11-11-1-1-1-1-111111-11
χ9111111111-1-1111111111111111111-1-1-1-1-111111-1-111111-1-11-1-111-1-1-111-1-1-1-11-1-11
χ10111111111-1-11111111111111111-1-1-1-1-1-1-111111-1-11111111-111-1-1-1-1-1-1-1-1-1-11-111-1
χ11111111111-1-11111111111-1-1-1-1-1-111-1-1-1-1-11111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1111-1111-1
χ12111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111-111-1-1-1-1-1111111-1-1-11
χ13111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-1-1-1111-1-1-111-1-1-11-111-1-1-1111-1-111
χ14111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-11-1-1111-1-11111-111-111-1-1
χ15111111111-1-11111-1-1-1-111-1-1111111-1-1-1111-1-1-1-111-1-1-111-111-1-1-11-111111-1-11-11-1-1
χ16111111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1111-1-111-1-11-1-1-11-111
χ172222222-2-2222-2220000-2-2220000002-2200-2000022-2-22000000000-20000-20000000
χ182222222-2-2222-2220000-2-2-2-20000002-2200-20000-2-222-2000000000-2000020000000
χ192222222-2-2-2-22-2220000-2-222000000-22-200-20000-2-2-2-220000000002000020000000
χ202222222-2-2-2-22-2220000-2-2-2-2000000-22-200-200002222-200000000020000-20000000
χ21222-122-12222-12-1-12222-1-100000022-12-122-1-1-1-1-1000000022-1-1-12-1-1-1-100000-1-1000
χ22222-122-12222-12-1-12222-1-1000000-2-2-12-122-1-1-1-1-10000000-2-2111-21-1-1-10000011000
χ23222-122-12222-12-1-1-2-2-2-2-1-100000022-12-1-2-2-1111100000002-2-1-1-1-2-1-1110000011000
χ24222-122-12222-12-1-1-2-2-2-2-1-1000000-2-2-12-1-2-2-111110000000-2211121-11100000-1-1000
χ25222-122-122-2-2-12-1-12222-1-1000000221-21-2-2-1-1-1-1-10000000-2-2-1112-1111000001-1000
χ26222-122-122-2-2-12-1-12222-1-1000000-2-21-21-2-2-1-1-1-1-10000000221-1-1-2111100000-11000
χ27222-122-122-2-2-12-1-1-2-2-2-2-1-1000000221-2122-111110000000-22-111-2-11-1-100000-11000
χ28222-122-122-2-2-12-1-1-2-2-2-2-1-1000000-2-21-2122-1111100000002-21-1-1211-1-1000001-1000
χ2922-222-222200-2-22-20000220022222-200000-2000000000-2-2002000-20002-200000000
χ3022-222-222200-2-22-2000022002222-2200000-2000000000-2-200-20002000-2200000000
χ3122-222-222200-2-22-200002200-2-2-2-22-200000-200000000022002000-2000-2200000000
χ3222-222-222200-2-22-200002200-2-2-2-2-2200000-20000000002200-200020002-200000000
χ3322-22-222002-2-20-2222−2−2002222−2−20020-22−2022−2−22-200-22−2000000002−20002−200000
χ3422-22-222002-2-20-2222−2−200-2-2−2−2220020-22−2022−2−2-22002−22000000002−2000−2200000
χ3522-22-222002-2-20-22−2−2220022−2−2220020-2−220−2−2222-200-2−2200000000−22000−2200000
χ3622-22-222002-2-20-22−2−22200-2-222−2−20020-2−220−2−222-220022−200000000−220002−200000
χ3722-22-22200-22-20-2222−2−2002222−2−200-202−22022−2−2-2200-22−200000000−22000−2200000
χ3822-22-22200-22-20-2222−2−200-2-2−2−22200-202−22022−2−22-2002−2200000000−220002−200000
χ3922-22-22200-22-20-22−2−2220022−2−22200-2022−20−2−222-2200-2−22000000002−20002−200000
χ4022-22-22200-22-20-22−2−22200-2-222−2−200-2022−20−2−2222-20022−2000000002−2000−2200000
χ414444-4-44000040-4-4000000002222−22−2200000000000000000−222200000000000000000000
χ424444-4-44000040-4-400000000−22−2222220000000000000000022−2200000000000000000000
χ43444-244-2-4-444-2-4-2-200002200000000-2-4-20020000000000000000002000000000000
χ44444-244-2-4-4-4-4-2-4-2-200002200000000242002000000000000000000-2000000000000
χ4544-444-44-4-400-444-40000-4-4000000000000040000000000000000000000000000000
χ4644-4-24-4-244002-4-220000-2-20000004-40000020000000000000-200020000000000000
χ4744-4-24-4-244002-4-220000-2-2000000-4400000200000000000002000-20000000000000
χ4844-4-24-4-2-4-40024-220000220000000000000-200000000000000−2i32i3000000000000000
χ4944-4-24-4-2-4-40024-220000220000000000000-2000000000000002i3−2i3000000000000000
χ5044-4-2-44-2004-4202-22222−22−220000000000-20222−220−2−222000000000000000−220000000000
χ5144-4-2-44-2004-4202-2−22−2222220000000000-202−2222022−2−20000000000000002−20000000000
χ5244-4-2-44-200-44202-22222−22−22000000000020-2−22220−2−2220000000000000002−20000000000
χ5344-4-2-44-200-44202-2−22−222222000000000020-222−22022−2−2000000000000000−220000000000
χ544-40400-422−22000000ζ11−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+ζ4722−2222−222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000ζ11−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+ζ47002-200000000000000000000000
χ554-40400-422−22000000ζ11−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+ζ4722−22−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000ζ11−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+ζ4700-2200000000000000000000000
χ564-40400-422−22000000−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−ζ4722−2222−22−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000−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−ζ47002-200000000000000000000000
χ574-40400-422−22000000−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−ζ4722−22−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000−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−ζ4700-2200000000000000000000000
χ584-40400-4−2222000000ζ11−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+ζ47−222222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000ζ11−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+ζ4700-2200000000000000000000000
χ594-40400-4−2222000000ζ11−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+ζ47−2222−22222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000ζ11−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+ζ47002-200000000000000000000000
χ604-40400-4−2222000000−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−ζ47−222222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000−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−ζ4700-2200000000000000000000000
χ614-40400-4−2222000000−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−ζ47−2222−2222−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000−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−ζ47002-200000000000000000000000
χ62888-4-8-8-40000-4044000000000000000000000000000000000000000000000000000
χ638-80-400442−420000002ζ11−2ζ13−2ζ25−2ζ29+2ζ31−2ζ41+2ζ43+2ζ47−2ζ11+2ζ13+2ζ25+2ζ29−2ζ31+2ζ41−2ζ43−2ζ472ζ11−2ζ13+2ζ25−2ζ29−2ζ31+2ζ41+2ζ43−2ζ47−2ζ11+2ζ13−2ζ25+2ζ29+2ζ31−2ζ41−2ζ43+2ζ47−222200000000000000−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−ζ47000000000000000000000000000
χ648-80-400442−42000000−2ζ11+2ζ13+2ζ25+2ζ29−2ζ31+2ζ41−2ζ43−2ζ472ζ11−2ζ13−2ζ25−2ζ29+2ζ31−2ζ41+2ζ43+2ζ47−2ζ11+2ζ13−2ζ25+2ζ29+2ζ31−2ζ41−2ζ43+2ζ472ζ11−2ζ13+2ζ25−2ζ29−2ζ31+2ζ41+2ζ43−2ζ47−222200000000000000ζ11−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+ζ47000000000000000000000000000
χ658-80-4004−42420000002ζ11−2ζ13+2ζ25−2ζ29−2ζ31+2ζ41+2ζ43−2ζ47−2ζ11+2ζ13−2ζ25+2ζ29+2ζ31−2ζ41−2ζ43+2ζ47−2ζ11+2ζ13+2ζ25+2ζ29−2ζ31+2ζ41−2ζ43−2ζ472ζ11−2ζ13−2ζ25−2ζ29+2ζ31−2ζ41+2ζ43+2ζ4722−2200000000000000−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−ζ47000000000000000000000000000
χ668-80-4004−4242000000−2ζ11+2ζ13−2ζ25+2ζ29+2ζ31−2ζ41−2ζ43+2ζ472ζ11−2ζ13+2ζ25−2ζ29−2ζ31+2ζ41+2ζ43−2ζ472ζ11−2ζ13−2ζ25−2ζ29+2ζ31−2ζ41+2ζ43+2ζ47−2ζ11+2ζ13+2ζ25+2ζ29−2ζ31+2ζ41−2ζ43−2ζ4722−2200000000000000ζ11−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+ζ47000000000000000000000000000

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