Finite Group Databasebeta

← Group #316638

Character table — Group #316638

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888244444888888888822244444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111-1-1-1-111-111-1111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-111-1-1-111-1-1-1-11111-1-111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1
χ91111111111111111-1-111-1-11111-111-11111-1-11111-1-1-111-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111-111-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ111111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ121111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-111-111-1-111-1-1-1-111-111-111-1-1-1-1-1-1-1-1111111
χ141111111111111111-1-111-1-1-1-1-1-1-111-111-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-11111
χ17222222222-222-2-22-222-2-2-2-20000222-2-2-20000000000-20020000000000000000
χ18222222222-222-2-22-222-2-2-2-200002-2-2-2220000000000200-20000000000000000
χ19222222222-222-2-22-2-2-2-2-2220000-2222-2-20000000000200-20000000000000000
χ20222222222-222-2-22-2-2-2-2-2220000-2-2-22220000000000-20020000000000000000
χ2122222222-22-2-222-2222-2-2222222-200-200-2-2220000-2-200000000000000000000
χ2222222222-22-2-222-2222-2-222-2-2-2-2-200-20022-2-200002200000000000000000000
χ2322222222-22-2-222-22-2-2-2-2-2-22222200200-2-2-2-200002200000000000000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2-2-220020022220000-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-20020000002i2i−2i−2i00000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-2002000000−2i−2i2i2i0000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000200-20000002i2i−2i−2i0000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000200-2000000−2i−2i2i2i00000000000000002i−2i0000
χ2922-2-222-2-20-200220-22i−2i002i−2i2i2i−2i−2i000000002-200000000000000002−22−200i2−i2i2−i2
χ3022-2-222-2-20-200220-22i−2i002i−2i2i2i−2i−2i000000002-20000000000000000−22−2200−i2i2−i2i2
χ3122-2-222-2-20-200220-22i−2i002i−2i−2i−2i2i2i00000000-2200000000000000002−2−2200i2−i2−i2i2
χ3222-2-222-2-20-200220-22i−2i002i−2i−2i−2i2i2i00000000-220000000000000000−222−200−i2i2i2−i2
χ3322-2-222-2-20-200220-2−2i2i00−2i2i2i2i−2i−2i00000000-2200000000000000002−2−2200−i2i2i2−i2
χ3422-2-222-2-20-200220-2−2i2i00−2i2i2i2i−2i−2i00000000-220000000000000000−222−200i2−i2−i2i2
χ3522-2-222-2-20-200220-2−2i2i00−2i2i−2i−2i2i2i000000002-200000000000000002−22−200−i2i2−i2i2
χ3622-2-222-2-20-200220-2−2i2i00−2i2i−2i−2i2i2i000000002-20000000000000000−22−2200i2−i2i2−i2
χ372-22-22-22-222-2-22-22-2002-2002i−2i2i−2i0000002i−2i0000000000002i−2i2-2000000000000
χ382-22-22-22-222-2-22-22-2002-2002i−2i2i−2i0000002i−2i000000000000−2i2i-22000000000000
χ392-22-22-22-222-2-22-22-2002-200−2i2i−2i2i000000−2i2i0000000000002i−2i-22000000000000
χ402-22-22-22-222-2-22-22-2002-200−2i2i−2i2i000000−2i2i000000000000−2i2i2-2000000000000
χ412-22-22-22-2-22222-2-2-200-22002i−2i2i−2i000000−2i2i0000000002-2000002i−2i0000000000
χ422-22-22-22-2-22222-2-2-200-22002i−2i2i−2i000000−2i2i000000000-2200000−2i2i0000000000
χ432-22-22-22-2-22222-2-2-200-2200−2i2i−2i2i0000002i−2i0000000002-200000−2i2i0000000000
χ442-22-22-22-2-22222-2-2-200-2200−2i2i−2i2i0000002i−2i000000000-22000002i−2i0000000000
χ454444-4-4-4-4404-400-400000000000000000000022−2222−220000000000000000000000
χ464444-4-4-4-4404-400-4000000000000000000000−2222−22220000000000000000000000
χ474444-4-4-4-4-40-440040000000000000000000002i2−2i2−2i22i20000000000000000000000
χ484444-4-4-4-4-40-44004000000000000000000000−2i22i22i2−2i20000000000000000000000
χ4944-4-444-4-40400-4-4044i−4i00−4i4i0000000000000000000000000000000000000000
χ5044-4-444-4-40400-4-404−4i4i004i−4i0000000000000000000000000000000000000000
χ514-44-44-44-44-4-4-4-444400-44000000000000000000000000000000000000000000
χ524-44-44-44-4-4-444-44-44004-4000000000000000000000000000000000000000000
χ534-44-4-44-4440-4400-40000000000004i−4i000000000000000000000000000000000
χ544-44-4-44-4440-4400-4000000000000−4i4i000000000000000000000000000000000
χ554-44-4-44-44-404-40040000000000000004-4000000000000000000000000000000
χ564-44-4-44-44-404-4004000000000000000-44000000000000000000000000000000
χ574-4-444-4-440400-440-40000000000000000000000004i−4i00000000000000000000
χ584-4-444-4-440400-440-4000000000000000000000000−4i4i00000000000000000000
χ594-4-444-4-440-4004-4040000004-4-44000000000000000000000000000000000000
χ604-4-444-4-440-4004-404000000-444-4000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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