Finite Group Databasebeta

← Group #318878

Character table — Group #318878

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888822444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-1111111-1-1-1-111-111-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111111-1-1
χ91111111111111111-1-111-1-11111-111-11111-1-1-1-1111111-111-1-1-1-1-111-1-111-1-1-1-1
χ101111111111111111-1-111-1-11111-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ111111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111
χ121111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-111-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-111-111-1-11111-1-111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1-1-111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-111
χ172222222222-2-22-2-2222-2-2-2-20000222-2-2-2000000000000-200200000000000000
χ182222222222-2-22-2-2222-2-2-2-200002-2-2-222000000000000200-200000000000000
χ192222222222-2-22-2-22-2-2-2-2220000-2222-2-2000000000000200-200000000000000
χ202222222222-2-22-2-22-2-2-2-2220000-2-2-2222000000000000-200200000000000000
χ2122222222-2-222-222-222-2-2222222-200-200-2-222-2-2000000000000000000000000
χ2222222222-2-222-222-222-2-222-2-2-2-2-200-20022-2-222000000000000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-22222200200-2-2-2-222000000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-2-22002002222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-2002000000002i2i−2i−2i0000000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-200200000000−2i−2i2i2i000000000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000200-2000000002i2i−2i−2i000000000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000200-200000000−2i−2i2i2i0000000000002i−2i000000
χ29222-2-22-2-22222-2-2-2-2002-20022-2-20000002-2000000002-202-2000000000000000
χ30222-2-22-2-22222-2-2-2-2002-20022-2-20000002-200000000-220-22000000000000000
χ31222-2-22-2-22222-2-2-2-2002-200-2-222000000-22000000002-20-22000000000000000
χ32222-2-22-2-22222-2-2-2-2002-200-2-222000000-2200000000-2202-2000000000000000
χ33222-2-22-2-2-2-2222-2-2200-220022-2-2000000-22000000000000002i−2i2i−2i0000000000
χ34222-2-22-2-2-2-2222-2-2200-220022-2-2000000-2200000000000000−2i2i−2i2i0000000000
χ35222-2-22-2-2-2-2222-2-2200-2200-2-2220000002-2000000000000002i−2i−2i2i0000000000
χ36222-2-22-2-2-2-2222-2-2200-2200-2-2220000002-200000000000000−2i2i2i−2i0000000000
χ3722-22-2-22-2002-202-202i−2i002i−2i2i−2i2i−2i000000002-20000000000000000i2−i2002−2i2−i22−2
χ3822-22-2-22-2002-202-202i−2i002i−2i2i−2i2i−2i000000002-20000000000000000−i2i200−22−i2i2−22
χ3922-22-2-22-2002-202-202i−2i002i−2i−2i2i−2i2i00000000-220000000000000000i2−i200−22−i2i22−2
χ4022-22-2-22-2002-202-202i−2i002i−2i−2i2i−2i2i00000000-220000000000000000−i2i2002−2i2−i2−22
χ4122-22-2-22-2002-202-20−2i2i00−2i2i2i−2i2i−2i00000000-220000000000000000i2−i2002−2−i2i2−22
χ4222-22-2-22-2002-202-20−2i2i00−2i2i2i−2i2i−2i00000000-220000000000000000−i2i200−22i2−i22−2
χ4322-22-2-22-2002-202-20−2i2i00−2i2i−2i2i−2i2i000000002-20000000000000000i2−i200−22i2−i2−22
χ4422-22-2-22-2002-202-20−2i2i00−2i2i−2i2i−2i2i000000002-20000000000000000−i2i2002−2−i2i22−2
χ45444-4-44-4-444-4-4-444-400-44000000000000000000000000000000000000000000
χ46444-4-44-4-4-4-4-4-44444004-4000000000000000000000000000000000000000000
χ4744-44-4-44-400-440-4404i−4i00−4i4i0000000000000000000000000000000000000000
χ4844-44-4-44-400-440-440−4i4i004i−4i0000000000000000000000000000000000000000
χ4944-4-44-4-44004-40-4400000004i−4i−4i4i000000000000000000000000000000000000
χ5044-4-44-4-44004-40-440000000−4i4i4i−4i000000000000000000000000000000000000
χ5144-4-44-4-4400-4404-40000000000000000000004i−4i000000000000000000000000
χ5244-4-44-4-4400-4404-4000000000000000000000−4i4i000000000000000000000000
χ534-4444-4-4-44-400400-4000000000000000000000022−2222−2200000000000000000000
χ544-4444-4-4-44-400400-40000000000000000000000−2222−222200000000000000000000
χ554-4444-4-4-4-4400-400400000000000000000000002i2−2i2−2i22i200000000000000000000
χ564-4444-4-4-4-4400-40040000000000000000000000−2i22i22i2−2i200000000000000000000
χ574-44-4-4-4444-400-4004000000000000004-4000000000000000000000000000000
χ584-44-4-4-4444-400-400400000000000000-44000000000000000000000000000000
χ594-44-4-4-444-4400400-4000000000004i−4i000000000000000000000000000000000
χ604-44-4-4-444-4400400-400000000000−4i4i000000000000000000000000000000000
χ618-8-88-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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