Finite Group Databasebeta

← Group #349247

Character table — Group #349247

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-22222222222-2-20000-2-200000000-2-2-2-200000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-200002200000000-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000-2-200000000222200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000220000000022-2-200000000000000000000
χ2122222222-2-2-2-222222-2-2-2000000002-20022000000-2-2222-20000-2-20000000000000000
χ2222222222-2-2-2-222222-2-2-2000000002-200-2-200000022-2-22-20000220000000000000000
χ2322222222-2-2-2-22222-22-2-200000000-22220000-2-2220000-2200-2-2000000000000000000
χ2422222222-2-2-2-22222-22-2-200000000-22-2-2000022-2-20000-220022000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-222000000002-20022000000-2-2-2-2-220000220000000000000000
χ2622222222-2-2-2-2-2-2-2-22-222000000002-200-2-20000002222-220000-2-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-222200000000-22220000-2-2-2-200002-20022000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222200000000-22-2-20000222200002-200-2-2000000000000000000
χ2922-222-2-2-222-2-20000220022-2-20000-2-22-22-22-22-2002-200000000000000000000000000
χ3022-222-2-2-222-2-20000220022-2-20000-2-2-22-222-2-2200-2200000000000000000000000000
χ3122-222-2-2-222-2-200002200-2-2220000-2-22-2-22-222-200-2200000000000000000000000000
χ3222-222-2-2-222-2-200002200-2-2220000-2-2-222-2-22-22002-200000000000000000000000000
χ3322-222-2-2-222-2-20000-2-20022-2-20000220000-22002i−2i002i−2i00002i−2i2i−2i0000000000000000
χ3422-222-2-2-222-2-20000-2-20022-2-20000220000-2200−2i2i00−2i2i0000−2i2i−2i2i0000000000000000
χ3522-222-2-2-222-2-20000-2-200-2-22200002200002-2002i−2i00−2i2i00002i−2i−2i2i0000000000000000
χ3622-222-2-2-222-2-20000-2-200-2-22200002200002-200−2i2i002i−2i0000−2i2i2i−2i0000000000000000
χ3722-222-2-2-2-2-22200002-20000002i2i−2i−2i-22002-200002i−2i-2200002i−2i−2i2i000000000000000000
χ3822-222-2-2-2-2-22200002-20000002i2i−2i−2i-2200-220000−2i2i2-200002i−2i2i−2i000000000000000000
χ3922-222-2-2-2-2-22200002-2000000−2i−2i2i2i-22002-20000−2i2i-220000−2i2i2i−2i000000000000000000
χ4022-222-2-2-2-2-22200002-2000000−2i−2i2i2i-2200-2200002i−2i2-20000−2i2i−2i2i000000000000000000
χ4122-222-2-2-2-2-2220000-220000002i2i−2i−2i2-22-20000-2200002i−2i00−2i2i00−2i2i0000000000000000
χ4222-222-2-2-2-2-2220000-220000002i2i−2i−2i2-2-2200002-20000−2i2i00−2i2i002i−2i0000000000000000
χ4322-222-2-2-2-2-2220000-22000000−2i−2i2i2i2-22-20000-220000−2i2i002i−2i002i−2i0000000000000000
χ4422-222-2-2-2-2-2220000-22000000−2i−2i2i2i2-2-2200002-200002i−2i002i−2i00−2i2i0000000000000000
χ452-22-22-22-22-22-22i2i−2i−2i002i−2i2-22-22i−2i2i−2i000000000000000000000000000000002−2i2−i22−2i2−i2
χ462-22-22-22-22-22-22i2i−2i−2i002i−2i2-22-22i−2i2i−2i00000000000000000000000000000000−22−i2i2−22−i2i2
χ472-22-22-22-22-22-22i2i−2i−2i002i−2i-22-22−2i2i−2i2i000000000000000000000000000000002−2i2−i2−22−i2i2
χ482-22-22-22-22-22-22i2i−2i−2i002i−2i-22-22−2i2i−2i2i00000000000000000000000000000000−22−i2i22−2i2−i2
χ492-22-22-22-22-22-2−2i−2i2i2i00−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000002−2−i2i22−2−i2i2
χ502-22-22-22-22-22-2−2i−2i2i2i00−2i2i2-22-2−2i2i−2i2i00000000000000000000000000000000−22i2−i2−22i2−i2
χ512-22-22-22-22-22-2−2i−2i2i2i00−2i2i-22-222i−2i2i−2i000000000000000000000000000000002−2−i2i2−22i2−i2
χ522-22-22-22-22-22-2−2i−2i2i2i00−2i2i-22-222i−2i2i−2i00000000000000000000000000000000−22i2−i22−2−i2i2
χ53444-4-44-4-400004-44-400000000000000000000000000000000000000002-22-200000000
χ54444-4-44-4-400004-44-40000000000000000000000000000000000000000-22-2200000000
χ55444-4-44-4-40000-44-4400000000000000000000000000000000000000002-2-2200000000
χ56444-4-44-4-40000-44-440000000000000000000000000000000000000000-222-200000000
χ574-444-4-4-4400004i−4i−4i4i0000000000000000000000000000000000002i−2i2-2000000000000
χ584-444-4-4-4400004i−4i−4i4i000000000000000000000000000000000000−2i2i-22000000000000
χ594-444-4-4-440000−4i4i4i−4i0000000000000000000000000000000000002i−2i-22000000000000
χ604-444-4-4-440000−4i4i4i−4i000000000000000000000000000000000000−2i2i2-2000000000000
χ614-44-44-44-4-44-444i4i−4i−4i00−4i4i000000000000000000000000000000000000000000000000
χ624-44-44-44-4-44-44−4i−4i4i4i004i−4i000000000000000000000000000000000000000000000000
χ634-4-4-444-444-4-44000000004-4-4400000000000000000000000000000000000000000000
χ644-4-4-444-444-4-4400000000-444-400000000000000000000000000000000000000000000
χ654-4-4-444-44-444-40000000000004-4-440000000000000000000000000000000000000000
χ664-4-4-444-44-444-4000000000000-444-40000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).