Finite Group Databasebeta

← Group #10951980

Character table — Group #10951980

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222222222224444444444444466888888888888881212121212121212121616161624242424242424323232324848
order1223446881616161624681212161624244848484888681216162424244848484848482444816161616228822448161666242422
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111
χ51111111111111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1-11111111-1-1111111-1-1-1-1-111-1-1
χ71111111111111-1-1111111111111-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1111111111-1-1-1-1
χ81111111111111-1-1111111111111-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-11111
χ9111111111-1-1-1-1111111-1-111-1-1-1-111111-1-1111-1-1-1-1-1-111111-1-1-1-11-11-11-11-11-1-11-11-11-1
χ10111111111-1-1-1-1111111-1-111-1-1-1-111111-1-1111-1-1-1-1-1-111111-1-1-1-1-11-11-11-111-1-1-11-11-11
χ11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-11-1111-11-1-11
χ12111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-11111-11-111-11-1-111-11-111-1
χ13111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1111-1-1-1-11111-1-1111-1-1-1-11-1-11-11-11-1111-1-111-1
χ14111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1111-1-1-1-11111-1-1111-1-1-1-1-111-11-11-1-111-111-1-11
χ15111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-111111-1-111-11-11-1-11-1-11-11
χ16111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-11111-111-1-11-111-1-1-111-11-1
χ172222222-2-20000222-22200-2-20000222-2200-2-2-200000022-2-22000000000000-200000000
χ182222222-2-20000222-22200-2-20000-2-22-2200-2-2-2000000-2-222-2000000000000200000000
χ192222222-2-20000-2-22-22200-2-2000022-22-200-222000000-2-2-2-22000000000000200000000
χ202222222-2-20000-2-22-22200-2-20000-2-2-22-200-2220000002222-2000000000000-200000000
χ21222-122-122222222-12-1-122-1-1-1-1-1-100-12-122-1-1-1-1-1-1-1-1-100000000022220000000-1-1-1-100
χ22222-122-122222222-12-1-122-1-1-1-1-1-100-12-122-1-1-1-1-1-1-1-1-1000000000-2-2-2-20000000111100
χ23222-122-1222222-2-2-12-1-122-1-1-1-1-1-1001-21-2-2-111-1-1111100000000022-2-20000000-1-11100
χ24222-122-1222222-2-2-12-1-122-1-1-1-1-1-1001-21-2-2-111-1-11111000000000-2-222000000011-1-100
χ25222-122-122-2-2-2-222-12-1-1-2-2-1-1111100-12-1-2-2-1-1-11111110000000002-22-20000000-11-1100
χ26222-122-122-2-2-2-222-12-1-1-2-2-1-1111100-12-1-2-2-1-1-1111111000000000-22-2200000001-11-100
χ27222-122-122-2-2-2-2-2-2-12-1-1-2-2-1-11111001-2122-11111-1-1-1-10000000002-2-220000000-111-100
χ28222-122-122-2-2-2-2-2-2-12-1-1-2-2-1-11111001-2122-11111-1-1-1-1000000000-222-200000001-1-1100
χ2922-222-2222222200-2-22-2-2-22222220000000-200-2-20000000000000000022-2-2000000000
χ3022-222-2222222200-2-22-2-2-22222220000000-200-2-200000000000000000-2-222000000000
χ3122-222-2222-2-2-2-200-2-22-22222-2-2-2-20000000-20022000000000000000002-2-22000000000
χ3222-222-2222-2-2-2-200-2-22-22222-2-2-2-20000000-2002200000000000000000-222-2000000000
χ3322-22-2220022−2−22-2-20-222−20022−2−22220-22−20002−222−2−22-200-222−2−20000000002−2000000
χ3422-22-2220022−2−22-2-20-222−20022−2−2-2-220-22−20002−222−2−2-22002−2−222000000000−22000000
χ3522-22-2220022−2−2-22-20-222−20022−2−222-202−220002−2−2−222-2200-222−2−2000000000−22000000
χ3622-22-2220022−2−2-22-20-222−20022−2−2-2-2-202−220002−2−2−2222-2002−2−2220000000002−2000000
χ3722-22-22200−2−2222-2-20-22−2200−2−2222220-2−22000−22−2−2222-200-2−2−222000000000−22000000
χ3822-22-22200−2−2222-2-20-22−2200−2−222-2-220-2−22000−22−2−222-2200222−2−20000000002−2000000
χ3922-22-22200−2−222-22-20-22−2200−2−22222-2022−2000−2222−2−2-2200-2−2−2220000000002−2000000
χ4022-22-22200−2−222-22-20-22−2200−2−222-2-2-2022−2000−2222−2−22-200222−2−2000000000−22000000
χ414444-4-44002222−22−220040-4-4−2222002222−22−220000000000−2222000000000000000000000000000000
χ424444-4-4400−22−2222220040-4-422−2200−22−222222000000000022−22000000000000000000000000000000
χ43444-244-2-4-4000044-2-4-2-20022000000-2-4-20022200000000000000000000000000000000
χ44444-244-2-4-40000-4-4-2-4-2-20022000000242002-2-200000000000000000000000000000000
χ45444-2-4-4-2002222−22−2200-2022−222200−2−2220000000023−232−26−66−600000000000000000000000000
χ46444-2-4-4-2002222−22−2200-2022−222200−2−22200000000−23232−2−66−6600000000000000000000000000
χ47444-2-4-4-200−22−22222200-202222−220022−2−20000000023−23−22−66−6600000000000000000000000000
χ48444-2-4-4-200−22−22222200-202222−220022−2−200000000−2323−226−66−600000000000000000000000000
χ4944-444-44-4-4000000-444-400-4-40000000000040000000000000000000000000000000000
χ5044-4-24-4-2444444002-4-22-4-4-2-2-2-2-2-2000000020022000000000000000000000000000000
χ5144-4-24-4-244-4-4-4-4002-4-2244-2-222220000000200-2-2000000000000000000000000000000
χ5244-4-24-4-2-4-400000024-22002200000000000-2000023−23−232300000000000000000000000000
χ5344-4-24-4-2-4-400000024-22002200000000000-20000−232323−2300000000000000000000000000
χ5444-4-2-44-2002222−22−224-4202-222−2200−2−22200-20222−22000−22−2−22200000000000000000000000000
χ5544-4-2-44-2002222−22−22-44202-222−2200−2−2220020-2−2222000−2222−2−200000000000000000000000000
χ5644-4-2-44-200−22−2222224-4202-2−22220022−2−200-202−22220002−222−2−200000000000000000000000000
χ5744-4-2-44-200−22−222222-44202-2−22220022−2−20020-222−220002−2−2−22200000000000000000000000000
χ584-40400-422−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4322−2200000000000000002-20ζ11−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−ζ4700000000000000000
χ594-40400-422−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−22220000000000000000-220−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+ζ4700000000000000000
χ604-40400-422−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4322−2200000000000000002-20−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+ζ4700000000000000000
χ614-40400-422−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−22220000000000000000-220ζ11−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−ζ4700000000000000000
χ624-40400-4−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4722−220000000000000000-220ζ11−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−ζ4700000000000000000
χ634-40400-4−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−222200000000000000002-20−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+ζ4700000000000000000
χ644-40400-4−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4722−220000000000000000-220−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+ζ4700000000000000000
χ654-40400-4−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−222200000000000000002-20ζ11−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−ζ4700000000000000000
χ668-80-400442−42−4ζ25+4ζ31−4ζ41+4ζ474ζ25−4ζ31+4ζ41−4ζ474ζ11−4ζ13−4ζ29+4ζ43−4ζ11+4ζ13+4ζ29−4ζ4300000000−22222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43000000000000000000000000000000000000000000
χ678-80-400442−424ζ25−4ζ31+4ζ41−4ζ47−4ζ25+4ζ31−4ζ41+4ζ47−4ζ11+4ζ13+4ζ29−4ζ434ζ11−4ζ13−4ζ29+4ζ4300000000−2222−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43000000000000000000000000000000000000000000
χ688-80-4004−42424ζ11−4ζ13−4ζ29+4ζ43−4ζ11+4ζ13+4ζ29−4ζ434ζ25−4ζ31+4ζ41−4ζ47−4ζ25+4ζ31−4ζ41+4ζ470000000022−22−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47000000000000000000000000000000000000000000
χ698-80-4004−4242−4ζ11+4ζ13+4ζ29−4ζ434ζ11−4ζ13−4ζ29+4ζ43−4ζ25+4ζ31−4ζ41+4ζ474ζ25−4ζ31+4ζ41−4ζ470000000022−222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47000000000000000000000000000000000000000000

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