Finite Group Databasebeta

← Group #101440

Character table — Group #101440

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1111-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11-1111-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-11-1111-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11-1111-1iiii−i−i−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11-1111-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11-1111-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11-1111-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-11-1111-1−i−i−i−iiiii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ172222222222222222-2-222-2-222222222-2-200000000-2-2-2-2000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ1922222222222-2-2-2-2222-2-22200000000-2-222-2-222-2-20000000000000000000000000000
χ2022222222222-2-2-2-2222-2-22200000000-2-2-2-222-2-2220000000000000000000000000000
χ2122222222222-2-2-2-22-2-2-2-2-2-200000000220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222222-2-2-2-22-2-2-2-2-2-20000000022000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-22222-22-2-2-22-200000000-2222-2-2-2-2220000000000000000000000000000
χ2422222222-2-2-22222-22-2-2-22-200000000-22-2-22222-2-20000000000000000000000000000
χ2522222222-2-2-22222-2-22-2-2-22000000002-200000000000022-2-2-2-2220000000000000000
χ2622222222-2-2-22222-2-22-2-2-22000000002-2000000000000-2-22222-2-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2222-222i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-22−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i000000000000000000000000
χ29222-22-2-2-222-20000-22200-2-222−2−222−2−200002-2002-22−22−22−22−22−22−20000000000000000
χ30222-22-2-2-222-20000-22200-2-222−2−222−2−20000-2200-222−22−2−22−22−22−220000000000000000
χ31222-22-2-2-222-20000-22200-2-2−2−222−2−22200002-2002-2−22−22−22−22−22−220000000000000000
χ32222-22-2-2-222-20000-22200-2-2−2−222−2−2220000-2200-22−22−222−22−22−22−20000000000000000
χ33222-22-2-2-222-20000-2-2-2002222−2−222−2−2002i−2i002i−2i00−22−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ34222-22-2-2-222-20000-2-2-2002222−2−222−2−200−2i2i00−2i2i00−22−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ35222-22-2-2-222-20000-2-2-20022−2−222−2−222002i−2i002i−2i002−22−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ36222-22-2-2-222-20000-2-2-20022−2−222−2−22200−2i2i00−2i2i002−22−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ37222-22-2-2-2-2-22000022-200-22i2i2−i2−i2−i2−i2i2i200002-200-22i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ38222-22-2-2-2-2-22000022-200-22i2i2−i2−i2−i2−i2i2i20000-22002-2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ39222-22-2-2-2-2-22000022-200-22−i2−i2i2i2i2i2−i2−i200002-200-22−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ40222-22-2-2-2-2-22000022-200-22−i2−i2i2i2i2i2−i2−i20000-22002-2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ41222-22-2-2-2-2-2200002-22002-2i2i2−i2−i2−i2−i2i2i2002i−2i00−2i2i00−i2i2i2−i2−222−22−2−220000000000000000
χ42222-22-2-2-2-2-2200002-22002-2i2i2−i2−i2−i2−i2i2i200−2i2i002i−2i00−i2i2i2−i22−2−22−222−20000000000000000
χ43222-22-2-2-2-2-2200002-22002-2−i2−i2i2i2i2i2−i2−i2002i−2i00−2i2i00i2−i2−i2i22−2−22−222−20000000000000000
χ44222-22-2-2-2-2-2200002-22002-2−i2−i2i2i2i2i2−i2−i200−2i2i002i−2i00i2−i2−i2i2−222−22−2−220000000000000000
χ452-2-2222-2-22-22-2-222-2002-2002-22-22-22-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ462-2-2222-2-22-22-2-222-2002-2002-22-22-22-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ472-2-2222-2-22-22-2-222-2002-200-22-22-22-22000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ482-2-2222-2-22-22-2-222-2002-200-22-22-22-22000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ492-2-2222-2-2-22-222-2-22002-2002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000i2−i2−i2i2−222−2
χ502-2-2222-2-2-22-222-2-22002-2002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000−i2i2i2−i22−2−22
χ512-2-2222-2-2-22-222-2-22002-200−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000i2−i2−i2i22−2−22
χ522-2-2222-2-2-22-222-2-22002-200−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000−i2i2i2−i2−222−2
χ5344-4-4-444-40004i−4i4i−4i00000000000000000000000000000000000002-22i−2i000000000000
χ5444-4-4-444-40004i−4i4i−4i0000000000000000000000000000000000000-22−2i2i000000000000
χ5544-4-4-444-4000−4i4i−4i4i00000000000000000000000000000000000002-2−2i2i000000000000
χ5644-4-4-444-4000−4i4i−4i4i0000000000000000000000000000000000000-222i−2i000000000000
χ574-44-4-44-440004i−4i−4i4i000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ584-44-4-44-440004i−4i−4i4i00000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ594-44-4-44-44000−4i4i4i−4i000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ604-44-4-44-44000−4i4i4i−4i00000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ614-4-4444-4-44-4444-4-4-400-44000000000000000000000000000000000000000000000000
χ624-4-4444-4-4-44-4-4-444400-44000000000000000000000000000000000000000000000000
χ634-4-4-44-4444-4-40000400000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-4-44-4444-4-400004000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-4-44-444-4440000-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-4-44-444-4440000-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

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