Finite Group Databasebeta

← Group #252517

Character table — Group #252517

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444448888888824444444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1111111111-1-11-1-11-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-111111111111-1-1-11-1-11-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111-1-11-1-11-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-11111
χ91111111111111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-11-1-11-11-111-1-111-1-111-1-1
χ101111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111-11-1-11-11-1-1-111-1-111-1-111
χ111111111111111-1-1-1-1-1-111111-1-11111-11111-1-1-1-11-1-11-1-1-1111-1-1-1-111-1-111
χ121111111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-111111-1-11-1-1-11-1-11111-1-111-1-1
χ131111111111111-1-1-1-1-1-1111-1-111-1-1-1-1-11111-1-1-1-11-11-1-1111-1-111-1-11111-1-1
χ141111111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-111111-11-1-111111-1-111-1-1-1-111
χ151111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-11111-1-1-1-1-111111-1-1-1-11111-1-1-1-111
χ161111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-11111-111111-1-111-1-1-1-11111-1-1
χ17222222222222-22222-2-2-2-2-200220022-200000000000-200-20000000000000
χ18222222222222-22222-2-2-2-2-200-2-200-2-2-20000000000020020000000000000
χ19222222222222-2-2-2-2-222-2-2-2002200-2-2200000000000200-20000000000000
χ20222222222222-2-2-2-2-222-2-2-200-2-20022200000000000-20020000000000000
χ2122222222-2-2-2-2222-2-222-2-222200-2-200-20000000000200-200000000000000
χ2222222222-2-2-2-2222-2-222-2-22-2-2002200-20000000000-200200000000000000
χ2322222222-2-2-2-22-2-222-2-2-2-222200-2-20020000000000-200200000000000000
χ2422222222-2-2-2-22-2-222-2-2-2-22-2-200220020000000000200-200000000000000
χ2522222222-2-2-2-2-222-2-2-2-222-2000000002000000002-200200-2000000000000
χ2622222222-2-2-2-2-222-2-2-2-222-200000000200000000-2200-2002000000000000
χ2722222222-2-2-2-2-2-2-2222222-200000000-2000000002200-200-2000000000000
χ2822222222-2-2-2-2-2-2-2222222-200000000-200000000-2-2002002000000000000
χ29222-2-22-2-2-2-22202-22-200000002i−2i002i−2i022−2−222−2−20000000000000000i2−i2i2−i2
χ30222-2-22-2-2-2-22202-22-200000002i−2i002i−2i0−2−222−2−2220000000000000000−i2i2−i2i2
χ31222-2-22-2-2-2-22202-22-20000000−2i2i00−2i2i022−2−222−2−20000000000000000−i2i2−i2i2
χ32222-2-22-2-2-2-22202-22-20000000−2i2i00−2i2i0−2−222−2−2220000000000000000i2−i2i2−i2
χ33222-2-22-2-2-2-2220-22-2200000002i−2i00−2i2i022−2−2−2−2220000000000000000i2−i2−i2i2
χ34222-2-22-2-2-2-2220-22-2200000002i−2i00−2i2i0−2−22222−2−20000000000000000−i2i2i2−i2
χ35222-2-22-2-2-2-2220-22-220000000−2i2i002i−2i022−2−2−2−2220000000000000000−i2i2i2−i2
χ36222-2-22-2-2-2-2220-22-220000000−2i2i002i−2i0−2−22222−2−20000000000000000i2−i2−i2i2
χ372-2-22-22-222-22-220000002-2-22i−2i002i−2i00000002i−2i2i−2i00000000002-200000000
χ382-2-22-22-222-22-220000002-2-22i−2i002i−2i0000000−2i2i−2i2i0000000000-2200000000
χ392-2-22-22-222-22-220000002-2-2−2i2i00−2i2i00000002i−2i2i−2i0000000000-2200000000
χ402-2-22-22-222-22-220000002-2-2−2i2i00−2i2i0000000−2i2i−2i2i00000000002-200000000
χ412-2-22-22-22-22-222000000-22-22i−2i00−2i2i0002i−2i2i−2i0000000000002-20000000000
χ422-2-22-22-22-22-222000000-22-22i−2i00−2i2i000−2i2i−2i2i000000000000-220000000000
χ432-2-22-22-22-22-222000000-22-2−2i2i002i−2i0002i−2i2i−2i000000000000-220000000000
χ442-2-22-22-22-22-222000000-22-2−2i2i002i−2i000−2i2i−2i2i0000000000002-20000000000
χ45444-4-44-4-444-4-404-4-44000000000000000000000000000000000000000000
χ46444-4-44-4-444-4-40-444-4000000000000000000000000000000000000000000
χ4744-4-44-4-440000000004-4000000000000000000000000000000002i−2i2i−2i0000
χ4844-4-44-4-440000000004-400000000000000000000000000000000−2i2i−2i2i0000
χ4944-4-44-4-44000000000-44000000000000000000000000000000002i−2i−2i2i0000
χ5044-4-44-4-44000000000-4400000000000000000000000000000000−2i2i2i−2i0000
χ514-4-44-44-444-44-4-4000000-4440000000000000000000000000000000000000
χ524-4-44-44-44-44-44-40000004-440000000000000000000000000000000000000
χ534-4-4-4444-44-4-4400000000000000000002i2−2i2−2i22i2000000000000000000000000
χ544-4-4-4444-44-4-440000000000000000000−2i22i22i2−2i2000000000000000000000000
χ554-4-4-4444-4-444-4000000000000000000000002i2−2i2−2i22i200000000000000000000
χ564-4-4-4444-4-444-400000000000000000000000−2i22i22i2−2i200000000000000000000
χ5788-88-8-88-8000000000000000000000000000000000000000000000000000
χ588-8888-8-8-8000000000000000000000000000000000000000000000000000
χ598-88-8-8-888000000000000000000000000000000000000000000000000000

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