Finite Group Databasebeta

← Group #279367

Character table — Group #279367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442222444444444444888888884444488888888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ91111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ172222222222-2-22-2-222222-2-2-2-2-2-222-2-22200000000-222-2-200000000000000000000000000
χ182222222222-2-22-2-222222-2-2-2-2-2-2-2-222-2-2000000002-2-22200000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2222222-2-22200000000-2-2-22200000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-22222-2-222-2-200000000222-2-200000000000000000000000000
χ2122222222-2-222-222-20000-2-200002222-2-222222222-20000-2-20000-2-2000000000000000000
χ2222222222-2-222-222-20000-2-200002222-2-2-2-2-2-2-2-2-2-2-2000022000022000000000000000000
χ2322222222-2-222-222-20000-2-20000-2-2-2-2222222-2-2-2-220000-2-2000022000000000000000000
χ2422222222-2-222-222-20000-2-20000-2-2-2-222-2-2-2-2222220000220000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022000022-2-2-2-20000000020000002i2i−2i−2i002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2000022000022-2-2-2-2000000002000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-20000220000-2-2222200000000-20000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-20000220000-2-2222200000000-2000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ29222-22-2-2-22-2222-2-2-222-2-22-222-2-200000000000000000000000000000002-2002-200000000
χ30222-22-2-2-22-2222-2-2-222-2-22-222-2-20000000000000000000000000000000-2200-2200000000
χ31222-22-2-2-22-2222-2-2-2-2-2222-2-2-22200000000000000000000000000000002-200-2200000000
χ32222-22-2-2-22-2222-2-2-2-2-2222-2-2-2220000000000000000000000000000000-22002-200000000
χ33222-22-2-2-22-2-2-2222-222-2-2-22-2-2220000000000000000000000000000000002i−2i002i−2i000000
χ34222-22-2-2-22-2-2-2222-222-2-2-22-2-222000000000000000000000000000000000−2i2i00−2i2i000000
χ35222-22-2-2-22-2-2-2222-2-2-222-2222-2-20000000000000000000000000000000002i−2i00−2i2i000000
χ36222-22-2-2-22-2-2-2222-2-2-222-2222-2-2000000000000000000000000000000000−2i2i002i−2i000000
χ3722-2-2-22-222200-200-20000002i−2i2i−2i2-2002-222−2−222−2−20002i−2i2−2i2−i2i2−i22−2i2−i2i2−i200000000000000
χ3822-2-2-22-222200-200-20000002i−2i2i−2i2-2002-2−2−222−2−2220002i−2i−22−i2i2−i2i2−22−i2i2−i2i200000000000000
χ3922-2-2-22-222200-200-20000002i−2i2i−2i-2200-2222−2−2−2−222000−2i2i2−2i2−i2i2−i2−22−i2i2−i2i200000000000000
χ4022-2-2-22-222200-200-20000002i−2i2i−2i-2200-22−2−22222−2−2000−2i2i−22−i2i2−i2i22−2i2−i2i2−i200000000000000
χ4122-2-2-22-222200-200-2000000−2i2i−2i2i2-2002-222−2−222−2−2000−2i2i2−2−i2i2−i2i22−2−i2i2−i2i200000000000000
χ4222-2-2-22-222200-200-2000000−2i2i−2i2i2-2002-2−2−222−2−222000−2i2i−22i2−i2i2−i2−22i2−i2i2−i200000000000000
χ4322-2-2-22-222200-200-2000000−2i2i−2i2i-2200-2222−2−2−2−2220002i−2i2−2−i2i2−i2i2−22i2−i2i2−i200000000000000
χ4422-2-2-22-222200-200-2000000−2i2i−2i2i-2200-22−2−22222−2−20002i−2i−22i2−i2i2−i22−2−i2i2−i2i200000000000000
χ4522-2-2-22-22-2-20020022-22-20000002-200-2222−2−222−2−202-200−222−2−22−222−2−2200000000000000
χ4622-2-2-22-22-2-20020022-22-20000002-200-22−2−222−2−22202-2002−2−222−22−2−222−200000000000000
χ4722-2-2-22-22-2-20020022-22-2000000-22002-222−2−2−2−2220-2200−222−2−222−2−222−200000000000000
χ4822-2-2-22-22-2-20020022-22-2000000-22002-2−2−22222−2−20-22002−2−222−2−222−2−2200000000000000
χ4922-2-2-22-22-2-2002002-22-220000002-200-2222−2−222−2−20-2200−22−222−2−22−222−200000000000000
χ5022-2-2-22-22-2-2002002-22-220000002-200-22−2−222−2−2220-22002−22−2−222−22−2−2200000000000000
χ5122-2-2-22-22-2-2002002-22-22000000-22002-222−2−2−2−22202-200−22−222−22−22−2−2200000000000000
χ5222-2-2-22-22-2-2002002-22-22000000-22002-2−2−22222−2−202-2002−22−2−22−22−222−200000000000000
χ53444-44-4-4-4-4444-4-4-440000-440000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-44-4-4-444400004-40000000000000000000000000000000000000000000000000
χ5544-44-4-44-44-400-40040000004i−4i−4i4i000000000000000000000000000000000000000000000
χ5644-44-4-44-44-400-4004000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ5744-44-4-44-4-4400400-44-4-44000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-4400400-4-444-4000000000000000000000000000000000000000000000000000
χ594-44-4-4-444000000000000000000004-40022−2222−2222−2222−220000000000000000000000000000000
χ604-44-4-4-444000000000000000000004-400−2222−2222−2222−22220000000000000000000000000000000
χ614-44-4-4-44400000000000000000000-440022−2222−22−2222−22220000000000000000000000000000000
χ624-44-4-4-44400000000000000000000-4400−2222−222222−2222−220000000000000000000000000000000
χ634-4-444-4-44004-404-40000000000000000000004-4-440000000000000000000000000000000
χ644-4-444-4-44004-404-4000000000000000000000-444-40000000000000000000000000000000
χ654-4-444-4-4400-440-44000000000000000004-4-4400000000000000000000000000000000000
χ664-4-444-4-4400-440-4400000000000000000-444-400000000000000000000000000000000000
χ674-4-4-4444-4004-40-4400000000000000000000000000000000000000000000000000002i2−2i200
χ684-4-4-4444-4004-40-440000000000000000000000000000000000000000000000000000−2i22i200
χ694-4-4-4444-400-4404-4000000000000000000000000000000000000000000000000002i2−2i20000
χ704-4-4-4444-400-4404-400000000000000000000000000000000000000000000000000−2i22i20000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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