Finite Group Databasebeta

← Group #349306

Character table — Group #349306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222444444444444444444448888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-111
χ172222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2000000-2-20000000022000000000000000000
χ182222222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000002200000000-2-2000000000000000000
χ19222222222222-2-2-2-2-2-2222222222222-2-2000000-2-200000000-2-2000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000220000000022000000000000000000
χ2122222222-2-2-2-222-2-22-20000000022-2-22-2000022000022-2-2-2-200000000000000000000
χ2222222222-2-2-2-222-2-22-20000000022-2-22-20000-2-20000-2-2222200000000000000000000
χ2322222222-2-2-2-222-2-2-2200000000-2-222-2222220000-2-200000000-2-20000000000000000
χ2422222222-2-2-2-222-2-2-2200000000-2-222-22-2-2-2-200002200000000220000000000000000
χ2522222222-2-2-2-2-2-2222-200000000-2-2222-20000220000-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2222-200000000-2-2222-20000-2-200002222-2-200000000000000000000
χ2722222222-2-2-2-2-2-222-220000000022-2-2-2222-2-20000-2-200000000220000000000000000
χ2822222222-2-2-2-2-2-222-220000000022-2-2-22-2-22200002200000000-2-20000000000000000
χ2922-22-22-2-222-2-200002222-2-200000000-2-22-2002-22-22-2002-20000000000000000000000
χ3022-22-22-2-222-2-200002222-2-200000000-2-2-2200-222-2-2200-220000000000000000000000
χ3122-22-22-2-222-2-2000022-2-22200000000-2-22-200-22-222-200-220000000000000000000000
χ3222-22-22-2-222-2-2000022-2-22200000000-2-2-22002-2-22-22002-20000000000000000000000
χ3322-22-22-2-222-2-20000-2-222-2-20000000022002i−2i00-22002i−2i002i−2i002i−2i0000000000000000
χ3422-22-22-2-222-2-20000-2-222-2-2000000002200−2i2i00-2200−2i2i00−2i2i00−2i2i0000000000000000
χ3522-22-22-2-222-2-20000-2-2-2-2220000000022002i−2i002-200−2i2i00−2i2i002i−2i0000000000000000
χ3622-22-22-2-222-2-20000-2-2-2-222000000002200−2i2i002-2002i−2i002i−2i00−2i2i0000000000000000
χ3722-22-22-2-2-2-22200002-200002i2i−2i−2i0000-22002i−2i2-2000000-22002i−2i−2i2i0000000000000000
χ3822-22-22-2-2-2-22200002-200002i2i−2i−2i0000-2200−2i2i-220000002-2002i−2i2i−2i0000000000000000
χ3922-22-22-2-2-2-22200002-20000−2i−2i2i2i0000-22002i−2i-220000002-200−2i2i−2i2i0000000000000000
χ4022-22-22-2-2-2-22200002-20000−2i−2i2i2i0000-2200−2i2i2-2000000-2200−2i2i2i−2i0000000000000000
χ4122-22-22-2-2-2-2220000-2200002i2i−2i−2i00002-22-2000000-22−2i2i002i−2i−2i2i000000000000000000
χ4222-22-22-2-2-2-2220000-2200002i2i−2i−2i00002-2-220000002-22i−2i00−2i2i−2i2i000000000000000000
χ4322-22-22-2-2-2-2220000-220000−2i−2i2i2i00002-22-2000000-222i−2i00−2i2i2i−2i000000000000000000
χ4422-22-22-2-2-2-2220000-220000−2i−2i2i2i00002-2-220000002-2−2i2i002i−2i2i−2i000000000000000000
χ452-2-222-22-22-22-20000002i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000000002−2i2−i2i2−i22−2
χ462-2-222-22-22-22-20000002i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000−22−i2i2−i2i2−22
χ472-2-222-22-22-22-20000002i−2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000000002−2−i2i2i2−i2−22
χ482-2-222-22-22-22-20000002i−2i2i−2i-22-22−2i2i−2i2i000000000000000000000000000000−22i2−i2−i2i22−2
χ492-2-222-22-22-22-2000000−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000002−2−i2i2−i2i22−2
χ502-2-222-22-22-22-2000000−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000000000−22i2−i2i2−i2−22
χ512-2-222-22-22-22-2000000−2i2i−2i2i-22-222i−2i2i−2i0000000000000000000000000000002−2i2−i2−i2i2−22
χ522-2-222-22-22-22-2000000−2i2i−2i2i-22-222i−2i2i−2i000000000000000000000000000000−22−i2i2i2−i22−2
χ53444-44-4-4-400004-40000000000000000000000000000000000000000002-22-200000000
χ54444-44-4-4-400004-4000000000000000000000000000000000000000000-22-2200000000
χ55444-44-4-4-40000-440000000000000000000000000000000000000000002-2-2200000000
χ56444-44-4-4-40000-44000000000000000000000000000000000000000000-222-200000000
χ574-444-4-4-444-4-440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ584-444-4-4-444-4-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ594-444-4-4-44-444-400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ604-444-4-4-44-444-40000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-44-4-444-40000004i−4i0000000000000000000000000000000000002-22i−2i000000000000
χ624-44-4-444-40000004i−4i000000000000000000000000000000000000-22−2i2i000000000000
χ634-44-4-444-4000000−4i4i0000000000000000000000000000000000002-2−2i2i000000000000
χ644-44-4-444-4000000−4i4i000000000000000000000000000000000000-222i−2i000000000000
χ654-4-444-44-4-44-44000000000000004i−4i−4i4i00000000000000000000000000000000000000
χ664-4-444-44-4-44-4400000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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