Finite Group Databasebeta

← Group #453897

Character table — Group #453897

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12442222222444444444444444448888888888888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ9111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ10111111111111111111-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ11111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ12111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-111-1-1
χ172222222-2-2-2-2-2-222-2-22000000000022-2-2000000002i2i−2i−2i000000002i−2i00000000
χ182222222-2-2-2-2-2-222-2-22000000000022-2-200000000−2i−2i2i2i00000000−2i2i00000000
χ192222222-2-2-2-2-2-222-2-220000000000-2-222000000002i2i−2i−2i00000000−2i2i00000000
χ202222222-2-2-2-2-2-222-2-220000000000-2-22200000000−2i−2i2i2i000000002i−2i00000000
χ2122222-2-222-2-22-22-22-2-22222-2-22i2i−2i−2i000000000000000000002i−2i000000000000
χ2222222-2-222-2-22-22-22-2-22222-2-2−2i−2i2i2i00000000000000000000−2i2i000000000000
χ2322222-2-222-2-22-22-22-2-2-2-2-2-2222i2i−2i−2i00000000000000000000−2i2i000000000000
χ2422222-2-222-2-22-22-22-2-2-2-2-2-222−2i−2i2i2i000000000000000000002i−2i000000000000
χ252222-22-22-22-222-22-2-2-20000000000000022-2-22i2i−2i−2i00000000000000002i−2i0000
χ262222-22-22-22-222-22-2-2-20000000000000022-2-2−2i−2i2i2i0000000000000000−2i2i0000
χ272222-22-22-22-222-22-2-2-200000000000000-2-2222i2i−2i−2i0000000000000000−2i2i0000
χ282222-22-22-22-222-22-2-2-200000000000000-2-222−2i−2i2i2i00000000000000002i−2i0000
χ2922-2-22222222-2-2-2-2-2-2-20000002-22-20000000000002i−2i2i−2i00000000000000002i−2i
χ3022-2-22222222-2-2-2-2-2-2-20000002-22-2000000000000−2i2i−2i2i0000000000000000−2i2i
χ3122-2-22222222-2-2-2-2-2-2-2000000-22-220000000000002i−2i2i−2i0000000000000000−2i2i
χ3222-2-22222222-2-2-2-2-2-2-2000000-22-22000000000000−2i2i−2i2i00000000000000002i−2i
χ3322-2-2222-2-2-2-222-2-222-20000000000000000002-22-22-2-222-20000000000000000
χ3422-2-2222-2-2-2-222-2-222-20000000000000000002-22-2-222-2-220000000000000000
χ3522-2-2222-2-2-2-222-2-222-2000000000000000000-22-222-2-22-220000000000000000
χ3622-2-2222-2-2-2-222-2-222-2000000000000000000-22-22-222-22-20000000000000000
χ3722-2-22-2-222-2-2-22-22-2220000002i−2i−2i2i00002i−2i2i−2i00000000000000000000002-200
χ3822-2-22-2-222-2-2-22-22-2220000002i−2i−2i2i0000−2i2i−2i2i0000000000000000000000-2200
χ3922-2-22-2-222-2-2-22-22-222000000−2i2i2i−2i00002i−2i2i−2i0000000000000000000000-2200
χ4022-2-22-2-222-2-2-22-22-222000000−2i2i2i−2i0000−2i2i−2i2i00000000000000000000002-200
χ4122-2-2-22-2-22-22222-2-2-2222-2-22-20000000000002i−2i−2i2i00000000002i−2i0000000000
χ4222-2-2-22-2-22-22222-2-2-2222-2-22-2000000000000−2i2i2i−2i0000000000−2i2i0000000000
χ4322-2-2-22-2-22-22222-2-2-22-2-222-220000000000002i−2i−2i2i0000000000−2i2i0000000000
χ4422-2-2-22-2-22-22222-2-2-22-2-222-22000000000000−2i2i2i−2i00000000002i−2i0000000000
χ4522-2-2-2-222-2-22-22222-2-200000000002i−2i2i−2i2i−2i−2i2i0000000000000000002-2000000
χ4622-2-2-2-222-2-22-22222-2-200000000002i−2i2i−2i−2i2i2i−2i000000000000000000-22000000
χ4722-2-2-2-222-2-22-22222-2-20000000000−2i2i−2i2i2i−2i−2i2i000000000000000000-22000000
χ4822-2-2-2-222-2-22-22222-2-20000000000−2i2i−2i2i−2i2i2i−2i0000000000000000002-2000000
χ4922-2-2-2-22-222-22-222-22-222-2-2-2200002i−2i−2i2i000000000000002i−2i00000000000000
χ5022-2-2-2-22-222-22-222-22-222-2-2-220000−2i2i2i−2i00000000000000−2i2i00000000000000
χ5122-2-2-2-22-222-22-222-22-2-2-2222-200002i−2i−2i2i00000000000000−2i2i00000000000000
χ5222-2-2-2-22-222-22-222-22-2-2-2222-20000−2i2i2i−2i000000000000002i−2i00000000000000
χ5344444-4-4-4-444-444-4-44-400000000000000000000000000000000000000000000
χ544444-44-4-44-44-4-4-4444-400000000000000000000000000000000000000000000
χ554444-4-444-4-444-4-4-4-44400000000000000000000000000000000000000000000
χ564444-4-44-444-4-44-4-44-4400000000000000000000000000000000000000000000
χ5744-4-44-4-4-4-4444-4-444-4400000000000000000000000000000000000000000000
χ5844-4-4-44-44-44-4-4-44-444400000000000000000000000000000000000000000000
χ598-88i−8i000000000000004-44i−4i0000000000000000000000000000000000000000
χ608-88i−8i00000000000000-44−4i4i0000000000000000000000000000000000000000
χ618-8−8i8i000000000000004-4−4i4i0000000000000000000000000000000000000000
χ628-8−8i8i00000000000000-444i−4i0000000000000000000000000000000000000000

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