Finite Group Databasebeta

← Group #317371

Character table — Group #317371

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888822224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-11111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ17222222222-2-2-2222-2-2-222-2-200002-222-2-2000000000000002-200000000000000
χ18222222222-2-2-2222-2-2-222-2-200002-2-2-22200000000000000-2200000000000000
χ19222222222-2-2-2222-2-2-2-2-2220000-2222-2-200000000000000-2200000000000000
χ20222222222-2-2-2222-2-2-2-2-2220000-22-2-222000000000000002-200000000000000
χ2122222222-2222-2-2-22-2-222222222-2-2000022-2-2-2-2000000000000000000000000
χ2222222222-2222-2-2-22-2-22222-2-2-2-2-2-20000-2-22222000000000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-22222220000-2-222-2-2000000000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-2-2-2-2-222000022-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-2200000000002i2i−2i−2i0000000000000000002i−2i
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-220000000000−2i−2i2i2i000000000000000000−2i2i
χ2722222222-2-2-2-2-2-2-2-222-2-22200002-200000000002i2i−2i−2i000000000000000000−2i2i
χ2822222222-2-2-2-2-2-2-2-222-2-22200002-20000000000−2i−2i2i2i0000000000000000002i−2i
χ2922-2-222-2-2022-2000-2002-22-222-2-20000002-2000000000000000000i2−i2i2−i2i2−i2i2−i200
χ3022-2-222-2-2022-2000-2002-22-222-2-20000002-2000000000000000000−i2i2−i2i2−i2i2−i2i200
χ3122-2-222-2-2022-2000-2002-22-2-2-222000000-22000000000000000000i2−i2i2−i2−i2i2−i2i200
χ3222-2-222-2-2022-2000-2002-22-2-2-222000000-22000000000000000000−i2i2−i2i2i2−i2i2−i200
χ3322-2-222-2-2022-2000-200-22-2222-2-2000000-22000000000000000000i2−i2−i2i2i2−i2−i2i200
χ3422-2-222-2-2022-2000-200-22-2222-2-2000000-22000000000000000000−i2i2i2−i2−i2i2i2−i200
χ3522-2-222-2-2022-2000-200-22-22-2-2220000002-2000000000000000000i2−i2−i2i2−i2i2i2−i200
χ3622-2-222-2-2022-2000-200-22-22-2-2220000002-2000000000000000000−i2i2i2−i2i2−i2−i2i200
χ3722-2-2-2-22222-22-2-22-22-200002i−2i2i−2i00000000002i−2i0000002-2002i−2i000000000000
χ3822-2-2-2-22222-22-2-22-22-200002i−2i2i−2i00000000002i−2i000000-2200−2i2i000000000000
χ3922-2-2-2-22222-22-2-22-22-20000−2i2i−2i2i0000000000−2i2i0000002-200−2i2i000000000000
χ4022-2-2-2-22222-22-2-22-22-20000−2i2i−2i2i0000000000−2i2i000000-22002i−2i000000000000
χ4122-2-2-2-222-22-2222-2-2-2200002i−2i2i−2i0000000000−2i2i00002-20000002i−2i0000000000
χ4222-2-2-2-222-22-2222-2-2-2200002i−2i2i−2i0000000000−2i2i0000-22000000−2i2i0000000000
χ4322-2-2-2-222-22-2222-2-2-220000−2i2i−2i2i00000000002i−2i00002-2000000−2i2i0000000000
χ4422-2-2-2-222-22-2222-2-2-220000−2i2i−2i2i00000000002i−2i0000-220000002i−2i0000000000
χ454444-4-4-4-404-4-400040000004i−4i−4i4i000000000000000000000000000000000000
χ464444-4-4-4-404-4-40004000000−4i4i4i−4i000000000000000000000000000000000000
χ474444-4-4-4-40-444000-40000000000000000004-400000000000000000000000000
χ484444-4-4-4-40-444000-4000000000000000000-4400000000000000000000000000
χ4944-4-444-4-40-4-440004004-4-440000000000000000000000000000000000000000
χ5044-4-444-4-40-4-44000400-444-40000000000000000000000000000000000000000
χ5144-4-4-4-4444-44-4-4-444-4400000000000000000000000000000000000000000000
χ5244-4-4-4-444-4-44-444-444-400000000000000000000000000000000000000000000
χ534-44-44-44-440004-4-4000000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-44-44-44-440004-4-400000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-44-44-44-4-4000-4440000000000000000000000022−22−222200000000000000000000
χ564-44-44-44-4-4000-44400000000000000000000000−222222−2200000000000000000000
χ574-4-44-444-44000-44-40000000000000004i−4i000000000000000000000000000000
χ584-4-44-444-44000-44-4000000000000000−4i4i000000000000000000000000000000
χ594-4-44-444-4-40004-4400000000000004-400000000000000000000000000000000
χ604-4-44-444-4-40004-440000000000000-4400000000000000000000000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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