Finite Group Databasebeta

← Group #124792

Character table — Group #124792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order1222224444444444444444888888888822224444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000
χ2122-2-22-222-2-2000000002i2i−2i−2i2i−2i2i−2i2-20000002-22i−2i000000000000000000
χ2222-2-22-222-2-2000000002i2i−2i−2i2i−2i2i−2i2-2000000-22−2i2i000000000000000000
χ2322-2-22-222-2-2000000002i2i−2i−2i−2i2i−2i2i-2200002-200002i−2i0000000000000000
χ2422-2-22-222-2-2000000002i2i−2i−2i−2i2i−2i2i-220000-220000−2i2i0000000000000000
χ2522-2-22-222-2-200000000−2i−2i2i2i2i−2i2i−2i-2200002-20000−2i2i0000000000000000
χ2622-2-22-222-2-200000000−2i−2i2i2i2i−2i2i−2i-220000-2200002i−2i0000000000000000
χ2722-2-22-222-2-200000000−2i−2i2i2i−2i2i−2i2i2-20000002-2−2i2i000000000000000000
χ2822-2-22-222-2-200000000−2i−2i2i2i−2i2i−2i2i2-2000000-222i−2i000000000000000000
χ2922-2-22-2-2-22222-2-22i2i−2i−2i2i−2i2i−2i000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ3022-2-22-2-2-22222-2-22i2i−2i−2i2i−2i2i−2i00000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ3122-2-22-2-2-22222-2-2−2i−2i2i2i−2i2i−2i2i000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ3222-2-22-2-2-22222-2-2−2i−2i2i2i−2i2i−2i2i00000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ3322-2-22-2-2-222-2-2222i2i−2i−2i−2i2i−2i2i000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ3422-2-22-2-2-222-2-2222i2i−2i−2i−2i2i−2i2i00000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ3522-2-22-2-2-222-2-222−2i−2i2i2i2i−2i2i−2i000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ3622-2-22-2-2-222-2-222−2i−2i2i2i2i−2i2i−2i00000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ3722-2-2-222-22-200002-22-2000022-2-2002-20000000000i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-2-222-22-200002-22-2000022-2-2002-20000000000−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-2-222-22-200002-22-20000-2-22200-2200000000002−2−222−2−2200000000
χ4022-2-2-222-22-200002-22-20000-2-22200-220000000000−222−2−222−200000000
χ4122-2-2-222-22-20000-22-22000022-2-200-220000000000i2−i2−i2i2−i2i2i2−i200000000
χ4222-2-2-222-22-20000-22-22000022-2-200-220000000000−i2i2i2−i2i2−i2−i2i200000000
χ4322-2-2-222-22-20000-22-220000-2-222002-200000000002−22−2−22−2200000000
χ4422-2-2-222-22-20000-22-220000-2-222002-20000000000−22−222−22−200000000
χ45444444-4-4-4-4000000004-4-440000000000000000000000000000000000
χ46444444-4-4-4-400000000-444-40000000000000000000000000000000000
χ474444-4-44-4-440000000000004i−4i−4i4i000000000000000000000000000000
χ484444-4-44-4-44000000000000−4i4i4i−4i000000000000000000000000000000
χ494444-4-4-444-400004i−4i−4i4i00000000000000000000000000000000000000
χ504444-4-4-444-40000−4i4i4i−4i00000000000000000000000000000000000000
χ5144-4-4-44-44-44000000000000000000004-4000000000000000000000000
χ5244-4-4-44-44-4400000000000000000000-44000000000000000000000000
χ538-88-80000004-44-4000000000000000000000000000000000000000000
χ548-88-8000000-44-44000000000000000000000000000000000000000000
χ558-8-880000004-4-44000000000000000000000000000000000000000000
χ568-8-88000000-444-4000000000000000000000000000000000000000000

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