Finite Group Databasebeta

← Group #125008

Character table — Group #125008

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444442222224444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-222-2-20000-2-222000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-222220000-2-2-2-2000000000000000000000000
χ19222222222222-2-22222-2-2-2-22222-2-2220000-2-2-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-222222222-2-2-2-20000-2-222000000000000000000000000
χ21222-2-2-22-22-22-20000002i2i−2i−2i22-2-200000000002i−2i00000000000000002−22−2i2−i2i2−i2
χ22222-2-2-22-22-22-20000002i2i−2i−2i22-2-200000000002i−2i0000000000000000−22−22−i2i2−i2i2
χ23222-2-2-22-22-22-20000002i2i−2i−2i-2-2220000000000−2i2i0000000000000000i2−i2−i2i2−222−2
χ24222-2-2-22-22-22-20000002i2i−2i−2i-2-2220000000000−2i2i0000000000000000−i2i2i2−i22−2−22
χ25222-2-2-22-22-22-2000000−2i−2i2i2i22-2-20000000000−2i2i00000000000000002−22−2−i2i2−i2i2
χ26222-2-2-22-22-22-2000000−2i−2i2i2i22-2-20000000000−2i2i0000000000000000−22−22i2−i2i2−i2
χ27222-2-2-22-22-22-2000000−2i−2i2i2i-2-22200000000002i−2i0000000000000000i2−i2−i2i22−2−22
χ28222-2-2-22-22-22-2000000−2i−2i2i2i-2-22200000000002i−2i0000000000000000−i2i2i2−i2−222−2
χ2922-222-2-2-22-2-222i−2i000000002i−2i2i−2i2i−2i0000002-2002i2i−2i−2i002-20000000000000000
χ3022-222-2-2-22-2-222i−2i000000002i−2i2i−2i2i−2i0000002-200−2i−2i2i2i00-220000000000000000
χ3122-222-2-2-22-2-222i−2i00000000−2i2i−2i2i2i−2i0022-2-2-220000002i−2i000000000000000000
χ3222-222-2-2-22-2-222i−2i00000000−2i2i−2i2i2i−2i00-2-222-22000000−2i2i000000000000000000
χ3322-222-2-2-22-2-22−2i2i000000002i−2i2i−2i−2i2i0022-2-2-22000000−2i2i000000000000000000
χ3422-222-2-2-22-2-22−2i2i000000002i−2i2i−2i−2i2i00-2-222-220000002i−2i000000000000000000
χ3522-222-2-2-22-2-22−2i2i00000000−2i2i−2i2i−2i2i0000002-2002i2i−2i−2i00-220000000000000000
χ3622-222-2-2-22-2-22−2i2i00000000−2i2i−2i2i−2i2i0000002-200−2i−2i2i2i002-20000000000000000
χ3722-2-2-22-22-2-2222200002-22-20000-2-22-20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-2-22-22-2-2222200002-22-20000-2-22-20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-2-22-22-2-222220000-22-220000-2-2-220000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4022-2-2-22-22-2-222220000-22-220000-2-2-220000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4122-2-2-22-22-2-222-2-200002-22-2000022-2200000000000000002−2−222−2−2200000000
χ4222-2-2-22-22-2-222-2-200002-22-2000022-220000000000000000−222−2−222−200000000
χ4322-2-2-22-22-2-222-2-20000-22-220000222-200000000000000002−2−22−222−200000000
χ4422-2-2-22-22-2-222-2-20000-22-220000222-20000000000000000−222−22−2−2200000000
χ4544444444-4-4-4-40044-4-400000000000000000000000000000000000000000000
χ4644444444-4-4-4-400-4-44400000000000000000000000000000000000000000000
χ47444-4-4-44-4-44-444i−4i000000000000−4i4i0000000000000000000000000000000000
χ48444-4-4-44-4-44-44−4i4i0000000000004i−4i0000000000000000000000000000000000
χ4944-444-4-4-4-444-40000004i−4i−4i4i0000000000000000000000000000000000000000
χ5044-444-4-4-4-444-4000000−4i4i4i−4i0000000000000000000000000000000000000000
χ5144-4-4-44-4444-4-400000000004i−4i−4i4i000000000000000000000000000000000000
χ5244-4-4-44-4444-4-40000000000−4i4i4i−4i000000000000000000000000000000000000
χ534-444-44-4-4000000004i−4i0000000000002-22-200002i−2i2i−2i00000000000000000000
χ544-444-44-4-4000000004i−4i000000000000-22-220000−2i2i−2i2i00000000000000000000
χ554-444-44-4-400000000−4i4i0000000000002-22-20000−2i2i−2i2i00000000000000000000
χ564-444-44-4-400000000−4i4i000000000000-22-2200002i−2i2i−2i00000000000000000000
χ574-4-44-4-4440000004-4000000000000002-2-2200002-2-2200000000000000000000
χ584-4-44-4-4440000004-400000000000000-222-20000-222-200000000000000000000
χ594-4-44-4-444000000-44000000000000002-2-220000-222-200000000000000000000
χ604-4-44-4-444000000-4400000000000000-222-200002-2-2200000000000000000000
χ618-88-88-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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