Finite Group Databasebeta

← Group #147997

Character table — Group #147997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222222222444444442222444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-22222-20000-2-20000-2-22200000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000022000022-2-200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2222222220000220000-2-2-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2222-2-2-2-220000-2-20000222200000000000000000000
χ21222-22-2-2-22-22-222-2-222-2-222-20000-222-2-200000000002-2000000000000000000
χ22222-22-2-2-22-22-222-2-222-2-222-20000-2-2-2220000000000-22000000000000000000
χ23222-22-2-2-22-22-222-2-2-2-222-2-220000222-2-20000000000-22000000000000000000
χ24222-22-2-2-22-22-222-2-2-2-222-2-2200002-2-22200000000002-2000000000000000000
χ25222-22-2-2-22-22-2-2-22222-2-2-2-22000020000002i2i−2i−2i0000002i−2i0000000000000000
χ26222-22-2-2-22-22-2-2-22222-2-2-2-2200002000000−2i−2i2i2i000000−2i2i0000000000000000
χ27222-22-2-2-22-22-2-2-222-2-22222-20000-20000002i2i−2i−2i000000−2i2i0000000000000000
χ28222-22-2-2-22-22-2-2-222-2-22222-20000-2000000−2i−2i2i2i0000002i−2i0000000000000000
χ292-2-222-22-2-2-2222-22-22-22-22-220000-200000000000000000000002i−2i2i−2i00000000
χ302-2-222-22-2-2-2222-22-22-22-22-220000-20000000000000000000000−2i2i−2i2i00000000
χ312-2-222-22-2-2-2222-22-2-22-22-22-20000200000000000000000000002-2-2200000000
χ322-2-222-22-2-2-2222-22-2-22-22-22-2000020000000000000000000000-222-200000000
χ332-2-222-22-2-2-222-22-222-22-2-22-2000020000000000000000002-22-2000000000000
χ342-2-222-22-2-2-222-22-222-22-2-22-200002000000000000000000-22-22000000000000
χ352-2-222-22-2-2-222-22-22-22-222-220000-20000000000000000002i−2i−2i2i000000000000
χ362-2-222-22-2-2-222-22-22-22-222-220000-2000000000000000000−2i2i2i−2i000000000000
χ372-2-2-222-22-222-22-2-222-2-222-2-2000020000000000000000000000000000002-22-2
χ382-2-2-222-22-222-22-2-222-2-222-2-200002000000000000000000000000000000-22-22
χ392-2-2-222-22-222-22-2-22-222-2-2220000-20000000000000000000000000000002i−2i−2i2i
χ402-2-2-222-22-222-22-2-22-222-2-2220000-2000000000000000000000000000000−2i2i2i−2i
χ412-2-2-222-22-222-2-222-22-2-22-2220000-2000000000000000000000000002i−2i2i−2i0000
χ422-2-2-222-22-222-2-222-22-2-22-2220000-200000000000000000000000000−2i2i−2i2i0000
χ432-2-2-222-22-222-2-222-2-222-22-2-200002000000000000000000000000002-2-220000
χ442-2-2-222-22-222-2-222-2-222-22-2-20000200000000000000000000000000-222-20000
χ4544444444-4-4-4-40000000000044-4-400000000000000000000000000000000000
χ4644444444-4-4-4-400000000000-4-44400000000000000000000000000000000000
χ47444-44-4-4-4-44-44000000000000000000000000004i−4i0000000000000000000000
χ48444-44-4-4-4-44-4400000000000000000000000000−4i4i0000000000000000000000
χ4944-44-44-4-4000000000000000004i−4i02-22-2002i−2i2i−2i000000000000000000000000
χ5044-44-44-4-4000000000000000004i−4i0-22-2200−2i2i−2i2i000000000000000000000000
χ5144-44-44-4-400000000000000000−4i4i02-22-200−2i2i−2i2i000000000000000000000000
χ5244-44-44-4-400000000000000000−4i4i0-22-22002i−2i2i−2i000000000000000000000000
χ5344-4-4-4-4440000000000000004-40002-2-22002-2-22000000000000000000000000
χ5444-4-4-4-4440000000000000004-4000-222-200-222-2000000000000000000000000
χ5544-4-4-4-444000000000000000-440002-2-2200-222-2000000000000000000000000
χ5644-4-4-4-444000000000000000-44000-222-2002-2-22000000000000000000000000
χ574-4-444-44-444-4-400000000000000000000000000004i−4i00000000000000000000
χ584-4-444-44-444-4-40000000000000000000000000000−4i4i00000000000000000000
χ594-4-4-444-444-4-44000000000000000000004-40000000000000000000000000000
χ604-4-4-444-444-4-4400000000000000000000-440000000000000000000000000000
χ618-888-8-8-88000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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