Finite Group Databasebeta

← Group #10951986

Character table — Group #10951986

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222222224444444444466668888888888121212121212121212121616161616161616161616242424243232484848
order12234468888446881212242424241616161624121216161616242422441616161616162468122424484848482488612248
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-111111-1-1-1-111-1-1-1-1-1-11
χ311111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-11
χ91111111-1-111-1-11-1111-1-111111111-1-111-1-11-11-11-111-1-1-1-11-11-11-1-111-1-1111-11-11-1-1
χ101111111-1-111-1-11-1111-1-111111111-1-1-1-1111-1-11-1111-1-1-1-1-111-11-1-1-1-11111-11-11-11-1
χ111111111-1-111-1-11-1111-1-1111111-1-1-1-111-1-11-11-11-111-1-1-1-1-11-11-11111-1-1-1-11-1-11-111
χ121111111-1-111-1-11-1111-1-1111111-1-1-1-1-1-1111-1-11-1111-1-1-1-11-1-11-111-1-111-1-1-111-11-11
χ131111111-1-111-1-11-1111-1-111-1-1-1-111-1-111-1-11-1-11-11-1-111111-11-11-1-111-1-1-1-1-111-1-111
χ141111111-1-111-1-11-1111-1-111-1-1-1-111-1-1-1-1111-11-11-1-1-11111-111-11-1-1-1-111-1-11-1-111-11
χ151111111-1-111-1-11-1111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-11-1-11111-11-11-11111-1-111-11-111-1-1
χ161111111-1-111-1-11-1111-1-111-1-1-1-1-1-1-1-1-1-1111-11-11-1-1-111111-1-11-111-1-111111-11-1-11-1
χ17222222222-2-2-2-222-22222-2-2000000-2-20000-2222220000000000000000000-2-200000
χ18222222222-2-2-2-222-22222-2-2000000-2-20000-22-2-2-2-200000000000000000002200000
χ192222222-2-2-2-2222-2-222-2-2-2-2000000220000-2-22-22-20000000000000000000-2200000
χ202222222-2-2-2-2222-2-222-2-2-2-2000000220000-2-2-22-2200000000000000000002-200000
χ21222-122-1222222-122-1-1-1-1-1-1000022-1-12222-1-1000000000022-12-1-1-1-1-1-1-10000-1-1000
χ22222-122-1222222-122-1-1-1-1-1-1000022-1-1-2-2-2-2-1-10000000000-2-2-12-1-1-11111000011000
χ23222-122-1222222-122-1-1-1-1-1-10000-2-2-1-12222-1-10000000000-2-21-2111-1-1-1-1000011000
χ24222-122-1222222-122-1-1-1-1-1-10000-2-2-1-1-2-2-2-2-1-10000000000221-211111110000-1-1000
χ25222-122-1-2-222-2-2-1-22-1-111-1-10000221122-2-2-1100000000002-2-1-2-111-1-1110000-11000
χ26222-122-1-2-222-2-2-1-22-1-111-1-100002211-2-222-110000000000-22-1-2-11111-1-100001-1000
χ27222-122-1-2-222-2-2-1-22-1-111-1-10000-2-21122-2-2-110000000000-22121-1-1-1-11100001-1000
χ28222-122-1-2-222-2-2-1-22-1-111-1-10000-2-211-2-222-1100000000002-2121-1-111-1-10000-11000
χ2922-222-22002200-20-22-2002222222-2000000-200000-2-200000020-20000002-20000000
χ3022-222-22002200-20-22-200222222-22000000-200000-2-2000000-202000000-220000000
χ3122-222-22002200-20-22-20022-2-2-2-22-2000000-2000002200000020-2000000-220000000
χ3222-222-22002200-20-22-20022-2-2-2-2-22000000-20000022000000-2020000002-20000000
χ3322-22-222220000-2-20-22220022−2−200002−22−20-22-2-222−222−2−200000002−22−2000000000
χ3422-22-222220000-2-20-22220022−2−20000−22−220-2-222-22−222−2−20000000−22−22000000000
χ3522-22-222220000-2-20-222200−2−22200002−22−20-2-222-2−22−2−22200000002−22−2000000000
χ3622-22-222220000-2-20-222200−2−2220000−22−220-22-2-22−22−2−2220000000−22−22000000000
χ3722-22-222-2-20000-220-22-2-20022−2−200002−2−220222-2-22−2−2−22200000002−2−22000000000
χ3822-22-222-2-20000-220-22-2-20022−2−20000−222−202-2-2222−2−2−2220000000−222−2000000000
χ3922-22-222-2-20000-220-22-2-200−2−22200002−2−2202-2-222−2222−2−200000002−2−22000000000
χ4022-22-222-2-20000-220-22-2-200−2−2220000−222−20222-2-2−2222−2−20000000−222−2000000000
χ414444-4-44000000400-4-400002222−22−2200000000000000−2222000000000000000000000000
χ424444-4-44000000400-4-40000−22−2222220000000000000022−22000000000000000000000000
χ43444-244-244-4-4-4-4-24-4-2-2-2-2220000002200002-2000000000000000000000000000000
χ44444-244-2-4-4-4-444-2-4-4-2-22222000000-2-2000022000000000000000000000000000000
χ4544-444-4400-4-400-4044-400-4-400000000000040000000000000000000000000000000
χ4644-4-24-4-200440020-4-2200-2-200004-400000020000000000000-202000000000000000
χ4744-4-24-4-200440020-4-2200-2-20000-440000002000000000000020-2000000000000000
χ4844-4-24-4-200-4-400204-220022000000000000-2000000000000000023−230000000000000
χ4944-4-24-4-200-4-400204-220022000000000000-20000000000000000−23230000000000000
χ5044-4-2-44-24400002-402-2-2-2000000000022−2222−220200000000000000000−22−22000000000
χ5144-4-2-44-24400002-402-2-2-20000000000−2222−222202000000000000000002−22−2000000000
χ5244-4-2-44-2-4-400002402-222000000000022−22−22220-200000000000000000−222−2000000000
χ5344-4-2-44-2-4-400002402-2220000000000−222222−220-2000000000000000002−2−22000000000
χ544-40400-4−2i22i222−222i−2i00000−2i22i222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43002i−2i000000000000ζ11+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+ζ4700000000000000000000
χ554-40400-4−2i22i222−222i−2i00000−2i22i222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43002i−2i000000000000−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−ζ4700000000000000000000
χ564-40400-4−2i22i2−2222−2i2i00000−2i22i2−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700−2i2i000000000000−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−ζ4700000000000000000000
χ574-40400-4−2i22i2−2222−2i2i00000−2i22i2−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700−2i2i000000000000ζ11+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+ζ4700000000000000000000
χ584-40400-42i2−2i222−22−2i2i000002i2−2i222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300−2i2i000000000000−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−ζ4700000000000000000000
χ594-40400-42i2−2i222−22−2i2i000002i2−2i222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300−2i2i000000000000ζ11+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+ζ4700000000000000000000
χ604-40400-42i2−2i2−22222i−2i000002i2−2i2−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47002i−2i000000000000ζ11+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+ζ4700000000000000000000
χ614-40400-42i2−2i2−22222i−2i000002i2−2i2−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47002i−2i000000000000−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−ζ4700000000000000000000
χ62888-4-8-8-4000000-40044000000000000000000000000000000000000000000000000
χ638-80-4004−4i24i242−424i−4i000002i2−2i2−2222000000−2i2i000000000000000000000000000000000000
χ648-80-4004−4i24i2−4242−4i4i000002i2−2i222−220000002i−2i000000000000000000000000000000000000
χ658-80-40044i2−4i242−42−4i4i00000−2i22i2−22220000002i−2i000000000000000000000000000000000000
χ668-80-40044i2−4i2−42424i−4i00000−2i22i222−22000000−2i2i000000000000000000000000000000000000

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