Finite Group Databasebeta

← Group #349229

Character table — Group #349229

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-22222222222-2-20000-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-222-2-2-2-2-2-20000-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000022-2-2220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200002222-2-20000000000000000000000000000
χ2122222222-2-2-2-222222-20000-2-200002-200222-2000000-2-2000022-2-20000000000000000
χ2222222222-2-2-2-222222-20000-2-200002-200-2-22-2000000220000-2-2220000000000000000
χ2322222222-2-2-2-22222-220000-2-20000-222200-220000-2-20022-2-200000000000000000000
χ2422222222-2-2-2-22222-220000-2-20000-22-2-200-2200002200-2-22200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-200002200002-20022-22000000-2-20000-2-2220000000000000000
χ2622222222-2-2-2-2-2-2-2-22-200002200002-200-2-2-2200000022000022-2-20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-220000220000-2222002-20000-2-200-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-220000220000-22-2-2002-20000220022-2-200000000000000000000
χ2922-22-22-2-222-2-200002222-2-2000000-2-22-22-2002-2002-22-2000000000000000000000000
χ3022-22-22-2-222-2-200002222-2-2000000-2-2-22-22002-200-22-22000000000000000000000000
χ3122-22-22-2-222-2-2000022-2-222000000-2-22-2-2200-22002-2-22000000000000000000000000
χ3222-22-22-2-222-2-2000022-2-222000000-2-2-222-200-2200-222-2000000000000000000000000
χ3322-22-22-2-222-2-20000-2-222-2-200000022000000-220000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ3422-22-22-2-222-2-20000-2-222-2-200000022000000-22000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3522-22-22-2-222-2-20000-2-2-2-222000000220000002-20000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ3622-22-22-2-222-2-20000-2-2-2-222000000220000002-2000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ3722-22-22-2-2-2-22200002-20000002i2i−2i−2i-22002-200002i−2i00-222i−2i−2i2i00000000000000000000
χ3822-22-22-2-2-2-22200002-20000002i2i−2i−2i-2200-2200002i−2i002-2−2i2i2i−2i00000000000000000000
χ3922-22-22-2-2-2-22200002-2000000−2i−2i2i2i-22002-20000−2i2i00-22−2i2i2i−2i00000000000000000000
χ4022-22-22-2-2-2-22200002-2000000−2i−2i2i2i-2200-220000−2i2i002-22i−2i−2i2i00000000000000000000
χ4122-22-22-2-2-2-2220000-220000002i2i−2i−2i2-22-2000000−2i2i-220000002i−2i−2i2i0000000000000000
χ4222-22-22-2-2-2-2220000-220000002i2i−2i−2i2-2-22000000−2i2i2-2000000−2i2i2i−2i0000000000000000
χ4322-22-22-2-2-2-2220000-22000000−2i−2i2i2i2-22-20000002i−2i-22000000−2i2i2i−2i0000000000000000
χ4422-22-22-2-2-2-2220000-22000000−2i−2i2i2i2-2-220000002i−2i2-20000002i−2i−2i2i0000000000000000
χ452-2-2-2-22222-2-2222-2-2002-22-22-22-22-2000000000000000000000000000000002−22−22−22−2
χ462-2-2-2-22222-2-2222-2-2002-22-22-22-22-200000000000000000000000000000000−22−22−22−22
χ472-2-2-2-22222-2-2222-2-200-22-222-2-22-22000000000000000000000000000000002−22−2−22−22
χ482-2-2-2-22222-2-2222-2-200-22-222-2-22-2200000000000000000000000000000000−22−222−22−2
χ492-2-2-2-22222-2-22-2-222002-22-2-22-22-22000000000000000000000000000000002−2−222−2−22
χ502-2-2-2-22222-2-22-2-222002-22-2-22-22-2200000000000000000000000000000000−222−2−222−2
χ512-2-2-2-22222-2-22-2-22200-22-22-222-22-2000000000000000000000000000000002−2−22−222−2
χ522-2-2-2-22222-2-22-2-22200-22-22-222-22-200000000000000000000000000000000−222−22−2−22
χ5344-4-44-44-400004i−4i4i−4i00000000000000000000000000000000000000002i−2i2-200000000
χ5444-4-44-44-400004i−4i4i−4i0000000000000000000000000000000000000000−2i2i-2200000000
χ5544-4-44-44-40000−4i4i−4i4i00000000000000000000000000000000000000002i−2i-2200000000
χ5644-4-44-44-40000−4i4i−4i4i0000000000000000000000000000000000000000−2i2i2-200000000
χ574-444-4-44-400004i−4i−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ584-444-4-44-400004i−4i−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ594-444-4-44-40000−4i4i4i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ604-444-4-44-40000−4i4i4i−4i000000000000000000000000000000000000-222i−2i000000000000
χ614-44-444-4-44-44-40000004-4-440000000000000000000000000000000000000000000000
χ624-44-444-4-44-44-4000000-444-40000000000000000000000000000000000000000000000
χ634-44-444-4-4-44-440000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-44-444-4-4-44-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ654-4-4-4-4444-444-444-4-4000000-4400000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-4-4-4440000004-400000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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