Finite Group Databasebeta

← Group #69239

Character table — Group #69239

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222444444444444444444666688881212121212121616161624242424
order12442346888812126121616161624242424484848484848484888882488441616161661224242488
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111
χ911-1-1-1111-1-111-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1i−ii−i11-1-11-1i−i1-1i−i
χ1011-1-1-1111-1-111-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i-11−iii−i11-1-1-11−ii-11−ii
χ1111-1-1-1111-1-111-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii1-1i−i−ii-1-1111-1i−i-11−ii
χ1211-1-1-1111-1-111-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11−ii−ii-1-111-11−ii1-1i−i
χ1311-1-1-1111-1-111-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i1-1−iii−i-1-1111-1−ii-11i−i
χ1411-1-1-1111-1-111-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11i−ii−i-1-111-11i−i1-1−ii
χ1511-1-1-1111-1-111-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1−ii−ii11-1-11-1−ii1-1−ii
χ1611-1-1-1111-1-111-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii-11i−i−ii11-1-1-11i−i-11i−i
χ1722222222-2-2-2-222220000-2-2-2-20000000022220000-2-2000000000000
χ1822222222-2-2-2-222220000-2-2-2-200000000-2-2-2-2000022000000000000
χ1922222-12-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222000000-1-1-1-10000
χ2022222-12-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000011110000
χ2122222-12-12222-1-1-1-1-2-2-2-2-1-1-1-111111111000022-2-2000000-1-1110000
χ2222222-12-12222-1-1-1-1-2-2-2-2-1-1-1-1111111110000-2-22200000011-1-10000
χ232222-22-22000022-2-22−22−2000022−2−222−2−22-22-20000002−22−200000000
χ242222-22-22000022-2-22−22−2000022−2−222−2−2-22-22000000−22−2200000000
χ252222-22-22000022-2-2−22−220000−2−222−2−2222-22-2000000−22−2200000000
χ262222-22-22000022-2-2−22−220000−2−222−2−222-22-220000002−22−200000000
χ2722-2-222-220000-2-22-2−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i000000−222−200000000
χ2822-2-222-220000-2-22-2−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0000002−2−2200000000
χ2922-2-222-220000-2-22-2i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i0000002−2−2200000000
χ3022-2-222-220000-2-22-2i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i000000−222−200000000
χ3122-2-2-222222-2-2-2-2-220000-2-222000000002i2i−2i−2i0000−2i2i000000000000
χ3222-2-2-222222-2-2-2-2-220000-2-22200000000−2i−2i2i2i00002i−2i000000000000
χ3322-2-2-2-12-1-2-222111-12i2i−2i−2i-1-111−i−i−i−iiiii00002-22i−2i000000-11−ii0000
χ3422-2-2-2-12-1-2-222111-12i2i−2i−2i-1-111−i−i−i−iiiii0000-22−2i2i0000001-1i−i0000
χ3522-2-2-2-12-1-2-222111-1−2i−2i2i2i-1-111iiii−i−i−i−i00002-2−2i2i000000-11i−i0000
χ3622-2-2-2-12-1-2-222111-1−2i−2i2i2i-1-111iiii−i−i−i−i0000-222i−2i0000001-1−ii0000
χ3744444-24-2-4-4-4-4-2-2-2-200002222000000000000000000000000000000
χ384444-4-2-4-20000-2-22222−2222−220000−2−222−2−2220000000000000000000000
χ394444-4-2-4-20000-2-222−2222−2222000022−2−222−2−20000000000000000000000
χ4044-4-44-2-4-2000022-22−2i22i22i2−2i20000i2i2−i2−i2−i2−i2i2i20000000000000000000000
χ4144-4-44-2-4-2000022-222i2−2i2−2i22i20000−i2−i2i2i2i2i2−i2−i20000000000000000000000
χ4244-4-4-4-24-244-4-4222-2000022-2-2000000000000000000000000000000
χ434-44i−4i040-4−2i22i222−224i−4i00000022−22−2i22i2000000000000000000000000000000
χ444-44i−4i040-42i2−2i2−22224i−4i000000−22222i2−2i2000000000000000000000000000000
χ454-44i−4i0-202−2i22i222−22−2i2i000000−22i2−i2ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ470000000000000000000000
χ464-44i−4i0-202−2i22i222−22−2i2i000000−22i2−i2−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ470000000000000000000000
χ474-44i−4i0-2022i2−2i2−2222−2i2i0000002−2−i2i2−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ430000000000000000000000
χ484-44i−4i0-2022i2−2i2−2222−2i2i0000002−2−i2i2ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ430000000000000000000000
χ494-4−4i4i040-4−2i22i2−2222−4i4i000000−2222−2i22i2000000000000000000000000000000
χ504-4−4i4i040-42i2−2i222−22−4i4i00000022−222i2−2i2000000000000000000000000000000
χ514-4−4i4i0-202−2i22i2−22222i−2i0000002−2i2−i2ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ43−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ470000000000000000000000
χ524-4−4i4i0-202−2i22i2−22222i−2i0000002−2i2−i2−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ43ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ470000000000000000000000
χ534-4−4i4i0-2022i2−2i222−222i−2i000000−22−i2i2ζ11−ζ25+ζ41−ζ43−ζ11+ζ25−ζ41+ζ43−ζ13+ζ29+ζ31−ζ47ζ13−ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ11+ζ25−ζ41−ζ43−ζ11−ζ25+ζ41+ζ430000000000000000000000
χ544-4−4i4i0-2022i2−2i222−222i−2i000000−22−i2i2−ζ11+ζ25−ζ41+ζ43ζ11−ζ25+ζ41−ζ43ζ13−ζ29−ζ31+ζ47−ζ13+ζ29+ζ31−ζ47−ζ13+ζ29−ζ31+ζ47ζ13−ζ29+ζ31−ζ47−ζ11−ζ25+ζ41+ζ43ζ11+ζ25−ζ41−ζ430000000000000000000000

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