Finite Group Databasebeta

← Group #419340

Character table — Group #419340

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422224444444444448888888888884444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ511111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1
χ9111111111111111111-1-111-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111
χ11111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ12111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111
χ172222222222-2-2-2-2-2-2-2-22-2002-2000000000000002i2i−2i−2i0000000000002i−2i000000
χ182222222222-2-2-2-2-2-2-2-22-2002-200000000000000−2i−2i2i2i000000000000−2i2i000000
χ192222222222-2-2-2-2-2-2-2-2-2200-22000000000000002i2i−2i−2i000000000000−2i2i000000
χ202222222222-2-2-2-2-2-2-2-2-2200-2200000000000000−2i−2i2i2i0000000000002i−2i000000
χ21222222-2-2-2-22-22-2-2-222002-2002-2000022-2-20000000000000000000000002-200
χ22222222-2-2-2-22-22-2-2-222002-2002-20000-2-222000000000000000000000000-2200
χ23222222-2-2-2-22-22-2-2-22200-2200-22000022-2-2000000000000000000000000-2200
χ24222222-2-2-2-22-22-2-2-22200-2200-220000-2-2220000000000000000000000002-200
χ252222-2-222-2-2-2-2222-22-2002-200-2222-2-200000000000000000000002-200000000
χ262222-2-222-2-2-2-2222-22-2002-200-22-2-2220000000000000000000000-2200000000
χ272222-2-222-2-2-2-2222-22-200-22002-222-2-20000000000000000000000-2200000000
χ282222-2-222-2-2-2-2222-22-200-22002-2-2-22200000000000000000000002-200000000
χ292222-2-2-2-2222-2-222-2-222200-2-200000000000000000022-2-200000000002-20000
χ302222-2-2-2-2222-2-222-2-222200-2-2000000000000000000-2-2220000000000-220000
χ312222-2-2-2-2222-2-222-2-22-2-2002200000000000000000022-2-20000000000-220000
χ322222-2-2-2-2222-2-222-2-22-2-20022000000000000000000-2-22200000000002-20000
χ332222-2-2-2-222-222-2-222-22-222-22-2-2000000000000000000002-200000000000000
χ342222-2-2-2-222-222-2-222-22-2-2-2-222200000000000000000000-2200000000000000
χ352222-2-2-2-222-222-2-222-2-22222-2-2-200000000000000000000-2200000000000000
χ362222-2-2-2-222-222-2-222-2-22-2-22-222000000000000000000002-200000000000000
χ3722-2-22-22-22-2-22-22-2-222000000002i−2i2i−2i0000000000002-22-200002i−2i0000000000
χ3822-2-22-22-22-2-22-22-2-222000000002i−2i2i−2i000000000000-22-220000−2i2i0000000000
χ3922-2-22-22-22-2-22-22-2-22200000000−2i2i−2i2i0000000000002-22-20000−2i2i0000000000
χ4022-2-22-22-22-2-22-22-2-22200000000−2i2i−2i2i000000000000-22-2200002i−2i0000000000
χ4122-2-2-222-2-222-2-22-222-2000000002i−2i−2i2i000022-2-22i−2i2i−2i00000000000000000000
χ4222-2-2-222-2-222-2-22-222-2000000002i−2i−2i2i0000-2-222−2i2i−2i2i00000000000000000000
χ4322-2-2-222-2-222-2-22-222-200000000−2i2i2i−2i000022-2-2−2i2i−2i2i00000000000000000000
χ4422-2-2-222-2-222-2-22-222-200000000−2i2i2i−2i0000-2-2222i−2i2i−2i00000000000000000000
χ4522-2-2-222-2-22-222-22-2-220000000000002i−2i2i−2i00002-2-220000000000000000002i−2i
χ4622-2-2-222-2-22-222-22-2-220000000000002i−2i2i−2i0000-222-2000000000000000000−2i2i
χ4722-2-2-222-2-22-222-22-2-22000000000000−2i2i−2i2i00002-2-22000000000000000000−2i2i
χ4822-2-2-222-2-22-222-22-2-22000000000000−2i2i−2i2i0000-222-20000000000000000002i−2i
χ4922-2-2-22-222-2-2-222-22-220000000000002i−2i−2i2i000000002-2-22002i−2i000000000000
χ5022-2-2-22-222-2-2-222-22-220000000000002i−2i−2i2i00000000-222-200−2i2i000000000000
χ5122-2-2-22-222-2-2-222-22-22000000000000−2i2i2i−2i000000002-2-2200−2i2i000000000000
χ5222-2-2-22-222-2-2-222-22-22000000000000−2i2i2i−2i00000000-222-2002i−2i000000000000
χ53444444-4-4-4-4-44-4444-4-400000000000000000000000000000000000000000000
χ544444-4-444-4-444-4-4-44-4400000000000000000000000000000000000000000000
χ5544-4-44-44-44-44-44-444-4-400000000000000000000000000000000000000000000
χ5644-4-44-4-44-444444-4-4-4-400000000000000000000000000000000000000000000
χ5744-4-44-4-44-44-4-4-4-4444400000000000000000000000000000000000000000000
χ5844-4-4-44-444-444-4-44-44-400000000000000000000000000000000000000000000
χ598-88-80000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ608-88-8000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ618-8-880000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ628-8-88000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000

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