Finite Group Databasebeta

← Group #396456

Character table — Group #396456

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444488888888888888888888888888881616161616161616161616161616
order12222222224444444444444444222244444444444444448888888844444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1
χ11111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ12111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1
χ17222222-2-2-2-2222-22-2-2-22222-2-2-2-2000000000000000000000000000000002i−2i00002i−2i00
χ18222222-2-2-2-2222-22-2-2-22222-2-2-2-200000000000000000000000000000000−2i2i0000−2i2i00
χ19222222-2-2-2-2222-22-2-2-2-2-2-2-22222000000000000000000000000000000002i−2i0000−2i2i00
χ20222222-2-2-2-2222-22-2-2-2-2-2-2-2222200000000000000000000000000000000−2i2i00002i−2i00
χ21222222-2-2-2-2-2-2-22-2222000000002200-2-200000022-2-20000000022-2-200000000000000
χ22222222-2-2-2-2-2-2-22-2222000000002200-2-2000000-2-22200000000-2-22200000000000000
χ23222222-2-2-2-2-2-2-22-222200000000-2-2002200000022-2-200000000-2-22200000000000000
χ24222222-2-2-2-2-2-2-22-222200000000-2-20022000000-2-2220000000022-2-200000000000000
χ252222-2-22-22-22-2-2-2222-222-2-222-2-2002200-2-200002-22-200000000000000000000000000
χ262222-2-22-22-22-2-2-2222-222-2-222-2-200-2-200220000-22-2200000000000000000000000000
χ272222-2-22-22-22-2-2-2222-2-2-222-2-222002200-2-20000-22-2200000000000000000000000000
χ282222-2-22-22-22-2-2-2222-2-2-222-2-22200-2-2002200002-22-200000000000000000000000000
χ292222-2-2-22-222-2-222-2-2222-2-2-2-222000000000000000022-2-200000000000000002-20000
χ302222-2-2-22-222-2-222-2-2222-2-2-2-2220000000000000000-2-2220000000000000000-220000
χ312222-2-2-22-222-2-222-2-22-2-22222-2-2000000000000000022-2-20000000000000000-220000
χ322222-2-2-22-222-2-222-2-22-2-22222-2-20000000000000000-2-22200000000000000002-20000
χ332222-2-2-22-22-222-2-222-2000000000000000022-2-22-2-22000022-2-2000000000000000000
χ342222-2-2-22-22-222-2-222-2000000000000000022-2-2-222-20000-2-222000000000000000000
χ352222-2-2-22-22-222-2-222-20000000000000000-2-2222-2-220000-2-222000000000000000000
χ362222-2-2-22-22-222-2-222-20000000000000000-2-222-222-2000022-2-2000000000000000000
χ3722-2-22-222-2-222-22-22-2-2000000002-22-22-22-20000000000002-22-2000000000000000000
χ3822-2-22-222-2-222-22-22-2-2000000002-2-222-2-22000000000000-22-22000000000000000000
χ3922-2-22-222-2-222-22-22-2-200000000-222-2-222-2000000000000-22-22000000000000000000
χ4022-2-22-222-2-222-22-22-2-200000000-22-22-22-220000000000002-22-2000000000000000000
χ4122-2-22-222-2-2-2-22-22-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002i−2i000000002-2
χ4222-2-22-222-2-2-2-22-22-2222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000−2i2i00000000-22
χ4322-2-22-222-2-2-2-22-22-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000002i−2i00000000-22
χ4422-2-22-222-2-2-2-22-22-222−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000−2i2i000000002-2
χ4522-2-22-2-2-222-2-22222-2-22i−2i2i−2i−2i2i−2i2i2-200-22002i−2i2i−2i000000000000000000000000000000
χ4622-2-22-2-2-222-2-22222-2-22i−2i2i−2i−2i2i−2i2i-22002-200−2i2i−2i2i000000000000000000000000000000
χ4722-2-22-2-2-222-2-22222-2-2−2i2i−2i2i2i−2i2i−2i2-200-2200−2i2i−2i2i000000000000000000000000000000
χ4822-2-22-2-2-222-2-22222-2-2−2i2i−2i2i2i−2i2i−2i-22002-2002i−2i2i−2i000000000000000000000000000000
χ4922-2-2-222-2-222-22-2-22-2200000000002-200-222i−2i−2i2i0000000000002i−2i2i−2i00000000000000
χ5022-2-2-222-2-222-22-2-22-2200000000002-200-22−2i2i2i−2i000000000000−2i2i−2i2i00000000000000
χ5122-2-2-222-2-222-22-2-22-220000000000-22002-22i−2i−2i2i000000000000−2i2i−2i2i00000000000000
χ5222-2-2-222-2-222-22-2-22-220000000000-22002-2−2i2i2i−2i0000000000002i−2i2i−2i00000000000000
χ5322-2-2-222-2-22-22-222-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000002i−2i00002-2000000
χ5422-2-2-222-2-22-22-222-22-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000−2i2i0000-22000000
χ5522-2-2-222-2-22-22-222-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000002i−2i0000-22000000
χ5622-2-2-222-2-22-22-222-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000−2i2i00002-2000000
χ5722-2-2-22-222-2-22-2-222-222i−2i−2i2i−2i2i2i−2i000000000000000000002-2-222i−2i−2i2i00000000000000
χ5822-2-2-22-222-2-22-2-222-222i−2i−2i2i−2i2i2i−2i00000000000000000000-222-2−2i2i2i−2i00000000000000
χ5922-2-2-22-222-2-22-2-222-22−2i2i2i−2i2i−2i−2i2i000000000000000000002-2-22−2i2i2i−2i00000000000000
χ6022-2-2-22-222-2-22-2-222-22−2i2i2i−2i2i−2i−2i2i00000000000000000000-222-22i−2i−2i2i00000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ624444-4-44-44-4-4444-4-4-4400000000000000000000000000000000000000000000000000
χ6344-4-44-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-44-444-4-44-400000000000000000000000000000000000000000000000000
χ658-88-800000000000000000000000000000000000000004i−4i0000000000000000000000
χ668-88-80000000000000000000000000000000000000000−4i4i0000000000000000000000
χ678-8-88000000000000000000000000000000000000004i−4i000000000000000000000000
χ688-8-8800000000000000000000000000000000000000−4i4i000000000000000000000000

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