Finite Group Databasebeta

← Group #318318

Character table — Group #318318

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888824444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-1111111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-111-1-11111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1111111-111-111-1-1-1-1111111-11111-1-1-1-1-111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1111111-111-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-111-1111111-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-11-1-111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111111-1-111-1-1-1-1-1-111
χ172222222222-2-22-2-2222-2-2-2-20000-2222-2-2000000000020000-200000000000000
χ182222222222-2-22-2-2222-2-2-2-20000-2-2-22220000000000-20000200000000000000
χ192222222222-2-22-2-22-2-222-2-20000222-2-2-20000000000-20000200000000000000
χ202222222222-2-22-2-22-2-222-2-200002-2-2-222000000000020000-200000000000000
χ2122222222-2-222-222-22222-2-22222-200-20022-2-2-2-2000000000000000000000000
χ2222222222-2-222-222-22222-2-2-2-2-2-2-200-200-2-22222000000000000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222200200-2-222-2-2000000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-2-220020022-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000200-2000000002i2i−2i−2i0000000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000200-200000000−2i−2i2i2i000000000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000-2002000000002i2i−2i−2i000000000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000-200200000000−2i−2i2i2i0000000000002i−2i000000
χ2922-2-22-22-2002-202-202i−2i2i−2i002i2i−2i−2i0000002-2000000000000000000i2−i2002−22−2i2−i2
χ3022-2-22-22-2002-202-202i−2i2i−2i002i2i−2i−2i0000002-2000000000000000000−i2i200−22−22−i2i2
χ3122-2-22-22-2002-202-202i−2i2i−2i00−2i−2i2i2i000000-22000000000000000000i2−i2002−2−22−i2i2
χ3222-2-22-22-2002-202-202i−2i2i−2i00−2i−2i2i2i000000-22000000000000000000−i2i200−222−2i2−i2
χ3322-2-22-22-2002-202-20−2i2i−2i2i002i2i−2i−2i000000-22000000000000000000i2−i200−222−2−i2i2
χ3422-2-22-22-2002-202-20−2i2i−2i2i002i2i−2i−2i000000-22000000000000000000−i2i2002−2−22i2−i2
χ3522-2-22-22-2002-202-20−2i2i−2i2i00−2i−2i2i2i0000002-2000000000000000000i2−i200−22−22i2−i2
χ3622-2-22-22-2002-202-20−2i2i−2i2i00−2i−2i2i2i0000002-2000000000000000000−i2i2002−22−2−i2i2
χ372-2-22-2-22222-2-2-222-200002-22-22-200000000002-2000002i−2i2i−2i000000000000000
χ382-2-22-2-22222-2-2-222-200002-22-22-200000000002-200000−2i2i−2i2i000000000000000
χ392-2-22-2-22222-2-2-222-200002-2-22-220000000000-22000002i−2i−2i2i000000000000000
χ402-2-22-2-22222-2-2-222-200002-2-22-220000000000-2200000−2i2i2i−2i000000000000000
χ412-2-22-2-222-2-2-2-222220000-222-22-20000000000-2200000000002-22-20000000000
χ422-2-22-2-222-2-2-2-222220000-222-22-20000000000-220000000000-22-220000000000
χ432-2-22-2-222-2-2-2-222220000-22-22-2200000000002-200000000002-2-220000000000
χ442-2-22-2-222-2-2-2-222220000-22-22-2200000000002-20000000000-222-20000000000
χ4544-44-44-4-44-400400-4000000000000000000000022−2222−2200000000000000000000
χ4644-44-44-4-44-400400-40000000000000000000000−2222−222200000000000000000000
χ4744-44-44-4-4-4400-400400000000000000000000002i2−2i2−2i22i200000000000000000000
χ4844-44-44-4-4-4400-40040000000000000000000000−2i22i22i2−2i200000000000000000000
χ4944-4-44-44-400-440-4404i−4i−4i4i000000000000000000000000000000000000000000
χ5044-4-44-44-400-440-440−4i4i4i−4i000000000000000000000000000000000000000000
χ514-4444-4-4-44-400-4004000000000000004i−4i000000000000000000000000000000
χ524-4444-4-4-44-400-400400000000000000−4i4i000000000000000000000000000000
χ534-4444-4-4-4-4400400-4000000000004-4000000000000000000000000000000000
χ544-4444-4-4-4-4400400-400000000000-44000000000000000000000000000000000
χ554-44-4-444-4004-40-4400000000000000000004i−4i00000000000000000000000000
χ564-44-4-444-4004-40-440000000000000000000−4i4i00000000000000000000000000
χ574-44-4-444-400-4404-400000004i−4i−4i4i000000000000000000000000000000000000
χ584-44-4-444-400-4404-40000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-44-4-4444444-4-4-4-40000-440000000000000000000000000000000000000000
χ604-4-44-4-444-4-4444-4-4400004-40000000000000000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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