Finite Group Databasebeta

← Group #293719

Character table — Group #293719

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444442244444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111
χ4111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-11-11111-1-1
χ51111111111111111111111-1-11-1-11111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111
χ71111111111111111111111-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1
χ81111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1-1-111
χ91111111111111111-1-1-1-11111-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1111-1
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1111-1-1-11
χ131111111111111111-1-1-1-111-1-1-11111-1111111-1-1-1-11111-1-1-1-1-111-1-1-11-1-1-111-11
χ141111111111111111-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-1-11111-111-1-1-11-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1111-1
χ1722222222222-2-2-2-2222-2-2-2-20020022-2-2-20000000000000000-20000002000000
χ1822222222222-2-2-2-2222-2-2-2-200200-2-2-22200000000000000002000000-2000000
χ1922222222222-2-2-2-22-2-222-2-200-200222-2-200000000000000002000000-2000000
χ2022222222222-2-2-2-22-2-222-2-200-200-2-22220000000000000000-20000002000000
χ2122222222-2-2-22222-22222-2-222-22200-2000000000000000000000-200-20000000
χ2222222222-2-2-22222-22222-2-2-2-2-2-2-200-200000000000000000000020020000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2222-2-2002000000000000000000000-20020000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2222002000000000000000000000200-20000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200-20000200000000000000000002-202-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200-2000020000000000000000000-220-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220020000-200000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220020000-20000000000000000000-2202-200000000
χ2922-2-22-2-220002-22-202i−2i2i−2i002-202i−2i000000000000022−2−2i2i2−i2−i2000000002−2i2−i200
χ3022-2-22-2-220002-22-202i−2i2i−2i002-202i−2i0000000000000−2−222−i2−i2i2i200000000−22−i2i200
χ3122-2-22-2-220002-22-202i−2i2i−2i00-220−2i2i000000000000022−2−2i2i2−i2−i200000000−22−i2i200
χ3222-2-22-2-220002-22-202i−2i2i−2i00-220−2i2i0000000000000−2−222−i2−i2i2i2000000002−2i2−i200
χ3322-2-22-2-220002-22-20−2i2i−2i2i002-20−2i2i000000000000022−2−2−i2−i2i2i2000000002−2−i2i200
χ3422-2-22-2-220002-22-20−2i2i−2i2i002-20−2i2i0000000000000−2−222i2i2−i2−i200000000−22i2−i200
χ3522-2-22-2-220002-22-20−2i2i−2i2i00-2202i−2i000000000000022−2−2−i2−i2i2i200000000−22i2−i200
χ3622-2-22-2-220002-22-20−2i2i−2i2i00-2202i−2i0000000000000−2−222i2i2−i2−i2000000002−2−i2i200
χ372-22-2-22-2222-22-2-22-200002-2000002i−2i02i−2i22-2-200002i−2i2i−2i000000000000000000
χ382-22-2-22-2222-22-2-22-200002-2000002i−2i02i−2i-2-2220000−2i2i−2i2i000000000000000000
χ392-22-2-22-2222-22-2-22-200002-200000−2i2i0−2i2i22-2-20000−2i2i−2i2i000000000000000000
χ402-22-2-22-2222-22-2-22-200002-200000−2i2i0−2i2i-2-22200002i−2i2i−2i000000000000000000
χ412-22-2-22-2222-2-222-2-20000-22000002i−2i0−2i2i000022-2-200002i−2i2i−2i00000000000000
χ422-22-2-22-2222-2-222-2-20000-22000002i−2i0−2i2i0000-2-2220000−2i2i−2i2i00000000000000
χ432-22-2-22-2222-2-222-2-20000-2200000−2i2i02i−2i000022-2-20000−2i2i−2i2i00000000000000
χ442-22-2-22-2222-2-222-2-20000-2200000−2i2i02i−2i0000-2-22200002i−2i2i−2i00000000000000
χ4544-44-44-4-44-440000-4000000000000000022−2222−2200000000000000000000000000
χ4644-44-44-4-44-440000-40000000000000000−2222−222200000000000000000000000000
χ4744-44-44-4-4-44-400004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4844-44-44-4-4-44-40000400000000000000000000−2i22i2−2i22i20000000000000000000000
χ4944-4-44-4-44000-44-4404i−4i−4i4i000000000000000000000000000000000000000000
χ5044-4-44-4-44000-44-440−4i4i4i−4i000000000000000000000000000000000000000000
χ514-44-4-44-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ524-44-4-44-44-4-44-444-4400004-40000000000000000000000000000000000000000
χ534-4-44-4-44400044-4-400000000000000000000000002i2−2i2−2i22i2000000000000000000
χ544-4-44-4-44400044-4-40000000000000000000000000−2i22i22i2−2i2000000000000000000
χ554-4-44-4-444000-4-4440000000000000000000000000000022−22−222200000000000000
χ564-4-44-4-444000-4-44400000000000000000000000000000−222222−2200000000000000
χ574-4-4-4444-44-4-400004000000000000000022−22−222200000000000000000000000000
χ584-4-4-4444-44-4-4000040000000000000000−222222−2200000000000000000000000000
χ594-4-4-4444-4-4440000-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-4-4444-4-4440000-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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