Finite Group Databasebeta

← Group #101348

Character table — Group #101348

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444442244448888888844444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i111-111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i111-111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii111-111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii111-111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i11-1-1ii−i−i−i−iii-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1
χ172222222222222222-2-222-2-222222222-200-2000000-2-2-2-2000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-200-20000002222000000000000000000000000
χ192222222222-2-2-2-22222-2-22200000000-222-2-2-222-2-20000000000000000000000000000
χ202222222222-2-2-2-22222-2-22200000000-2-2-2-222-2-2220000000000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-200000000200200000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-20000000020020000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-22222-2-222-2-2-2-200000000200-2000000000022-2-2-2-2220000000000000000
χ2422222222-2-22222-2-222-2-2-2-200000000200-20000000000-2-22222-2-20000000000000000
χ2522222222-2-22222-2-2-2-2-2-22200000000-2222-2-2-2-2220000000000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-22200000000-2-2-222222-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i-2002000000−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i-20020000002i2i−2i−2i000000000000000000000000
χ29222-22-2-2-2220000-2-22-2002-222−2−222−2−202-20002-2002−22−22−22−22−22−20000000000000000
χ30222-22-2-2-2220000-2-22-2002-222−2−222−2−20-22000-22002−22−2−22−22−22−220000000000000000
χ31222-22-2-2-2220000-2-22-2002-2−2−222−2−22202-20002-200−22−22−22−22−22−220000000000000000
χ32222-22-2-2-2220000-2-22-2002-2−2−222−2−2220-22000-2200−22−222−22−22−22−20000000000000000
χ33222-22-2-2-2220000-2-2-2200-2222−2−222−2−200002i−2i002i−2i−22−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ34222-22-2-2-2220000-2-2-2200-2222−2−222−2−20000−2i2i00−2i2i−22−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ35222-22-2-2-2220000-2-2-2200-22−2−222−2−22200002i−2i002i−2i2−22−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ36222-22-2-2-2220000-2-2-2200-22−2−222−2−2220000−2i2i00−2i2i2−22−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ37222-22-2-2-2-2-20000222-200-22i2i2−i2−i2−i2−i2i2i200002i−2i00−2i2i−i2i2i2−i2−222−22−2−220000000000000000
χ38222-22-2-2-2-2-20000222-200-22i2i2−i2−i2−i2−i2i2i20000−2i2i002i−2i−i2i2i2−i22−2−22−222−20000000000000000
χ39222-22-2-2-2-2-20000222-200-22−i2−i2i2i2i2i2−i2−i200002i−2i00−2i2ii2−i2−i2i22−2−22−222−20000000000000000
χ40222-22-2-2-2-2-20000222-200-22−i2−i2i2i2i2i2−i2−i20000−2i2i002i−2ii2−i2−i2i2−222−22−2−220000000000000000
χ41222-22-2-2-2-2-2000022-22002-2i2i2−i2−i2−i2−i2i2i202-2000-2200i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ42222-22-2-2-2-2-2000022-22002-2i2i2−i2−i2−i2−i2i2i20-220002-200i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ43222-22-2-2-2-2-2000022-22002-2−i2−i2i2i2i2i2−i2−i202-2000-2200−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ44222-22-2-2-2-2-2000022-22002-2−i2−i2i2i2i2i2−i2−i20-220002-200−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ452-22-2-222-22i−2i2i2i−2i−2i2i−2i002-2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000001+i−1−i1−i−1+i00002−2i2−i2
χ462-22-2-222-22i−2i2i2i−2i−2i2i−2i002-2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000−1−i1+i−1+i1−i0000−22−i2i2
χ472-22-2-222-22i−2i2i2i−2i−2i2i−2i002-200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000001+i−1−i1−i−1+i0000−22−i2i2
χ482-22-2-222-22i−2i2i2i−2i−2i2i−2i002-200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000−1−i1+i−1+i1−i00002−2i2−i2
χ492-22-2-222-2−2i2i−2i−2i2i2i−2i2i002-2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000001−i−1+i1+i−1−i0000−22i2−i2
χ502-22-2-222-2−2i2i−2i−2i2i2i−2i2i002-2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000−1+i1−i−1−i1+i00002−2−i2i2
χ512-22-2-222-2−2i2i−2i−2i2i2i−2i2i002-200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000001−i−1+i1+i−1−i00002−2−i2i2
χ522-22-2-222-2−2i2i−2i−2i2i2i−2i2i002-200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000−1+i1−i−1−i1+i0000−22i2−i2
χ5344-4-4-44-44004i−4i4i−4i00000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ5444-4-4-44-44004i−4i4i−4i0000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ5544-4-4-44-4400−4i4i−4i4i00000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ5644-4-4-44-4400−4i4i−4i4i0000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ574-444-4-4-444i−4i0000−4i4i0000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ584-444-4-4-444i−4i0000−4i4i000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ594-444-4-4-44−4i4i00004i−4i0000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ604-444-4-4-44−4i4i00004i−4i000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ614-44-4-444-44i−4i−4i−4i4i4i4i−4i00-44000000000000000000000000000000000000000000000000
χ624-44-4-444-4−4i4i4i4i−4i−4i−4i4i00-44000000000000000000000000000000000000000000000000
χ634-4-4444-4-4004-4-44000000000000000000000000000000000000002i−2i2i−2i000000000000
χ644-4-4444-4-4004-4-4400000000000000000000000000000000000000−2i2i−2i2i000000000000
χ654-4-4444-4-400-444-4000000000000000000000000000000000000002i−2i−2i2i000000000000
χ664-4-4444-4-400-444-400000000000000000000000000000000000000−2i2i2i−2i000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-88-888000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.