Finite Group Databasebeta

← Group #351523

Character table — Group #351523

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442244444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ511111111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-11
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-11-11
χ121111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-111-1-1-1-1111-11-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-11111-1-1-11-11
χ17222222222-2-2-2-222222-2-22222-2-2-2-2-2-200000000222-2-2-2000000000000000000000000
χ18222222222-2-2-2-222222-2-2-2-2-2-2-2-2222200000000-2-22-222000000000000000000000000
χ19222222222-2-2-2-2222-2-2222222-2-2-2-2-2-200000000-2-2-2222000000000000000000000000
χ20222222222-2-2-2-2222-2-222-2-2-2-2-2-222220000000022-22-2-2000000000000000000000000
χ2122222222-22222-2-2-222220000-2-200002222222200-2-200-2-2-2-200000000000000000000
χ2222222222-22222-2-2-222220000-2-20000-2-2-2-2-2-2-2-200-2-200222200000000000000000000
χ2322222222-22222-2-2-2-2-2-2-20000-2-200002222-2-2-2-2002200-2-22200000000000000000000
χ2422222222-22222-2-2-2-2-2-2-20000-2-20000-2-2-2-2222200220022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200002200000000000000-220000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-200002200000000000000-22000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222000022000000000000002-20000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222000022000000000000002-2000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-22-2-222-2222-2-2-2-2200002i2i−2i−2i2-22i2i−2i−2i00002i2i−2i−2i000000002i−2i00002-22-2000000000000
χ302-22-2-222-2222-2-2-2-2200002i2i−2i−2i2-22i2i−2i−2i0000−2i−2i2i2i00000000−2i2i0000-22-22000000000000
χ312-22-2-222-2222-2-2-2-220000−2i−2i2i2i2-2−2i−2i2i2i00002i2i−2i−2i000000002i−2i0000-22-22000000000000
χ322-22-2-222-2222-2-2-2-220000−2i−2i2i2i2-2−2i−2i2i2i0000−2i−2i2i2i00000000−2i2i00002-22-2000000000000
χ332-22-2-222-22-2-222-2-2200002i2i−2i−2i-22−2i−2i2i2i22-2-200000000002-2002i−2i2i−2i0000000000000000
χ342-22-2-222-22-2-222-2-2200002i2i−2i−2i-22−2i−2i2i2i-2-2220000000000-2200−2i2i−2i2i0000000000000000
χ352-22-2-222-22-2-222-2-220000−2i−2i2i2i-222i2i−2i−2i22-2-200000000002-200−2i2i−2i2i0000000000000000
χ362-22-2-222-22-2-222-2-220000−2i−2i2i2i-222i2i−2i−2i-2-2220000000000-22002i−2i2i−2i0000000000000000
χ372-22-2-222-2-222-2-222-200000000-22000000002i2i−2i−2i2i−2i002i−2i00−2i2i2-2-220000000000000000
χ382-22-2-222-2-222-2-222-200000000-22000000002i2i−2i−2i−2i2i00−2i2i00−2i2i-222-20000000000000000
χ392-22-2-222-2-222-2-222-200000000-2200000000−2i−2i2i2i2i−2i002i−2i002i−2i-222-20000000000000000
χ402-22-2-222-2-222-2-222-200000000-2200000000−2i−2i2i2i−2i2i00−2i2i002i−2i2-2-220000000000000000
χ412-22-2-222-2-2-2-22222-2000000002-2000022-2-200002i−2i00−2i2i-220000002i−2i−2i2i000000000000
χ422-22-2-222-2-2-2-22222-2000000002-2000022-2-20000−2i2i002i−2i-22000000−2i2i2i−2i000000000000
χ432-22-2-222-2-2-2-22222-2000000002-20000-2-22200002i−2i00−2i2i2-2000000−2i2i2i−2i000000000000
χ442-22-2-222-2-2-2-22222-2000000002-20000-2-2220000−2i2i002i−2i2-20000002i−2i−2i2i000000000000
χ454444-4-4-4-404-44-400000000000000000000000000000000000000000000022−2200000000
χ464444-4-4-4-404-44-4000000000000000000000000000000000000000000000−222200000000
χ474444-4-4-4-40-44-44000000000000000000000000000000000000000000000000022−220000
χ484444-4-4-4-40-44-440000000000000000000000000000000000000000000000000−22220000
χ4944-4-444-4-4400004-4-400004-44-400000000000000000000000000000000000000000000
χ5044-4-444-4-4400004-4-40000-44-4400000000000000000000000000000000000000000000
χ5144-4-444-4-4-40000-44400000000004i−4i4i−4i00000000000000000000000000000000000000
χ5244-4-444-4-4-40000-4440000000000−4i4i−4i4i00000000000000000000000000000000000000
χ5344-4-4-4-44400000000004i−4i00000000002i2−2i22i2−2i222−2222−22000000000000000000000000000000
χ5444-4-4-4-44400000000004i−4i0000000000−2i22i2−2i22i2−2222−2222000000000000000000000000000000
χ5544-4-4-4-4440000000000−4i4i00000000002i2−2i22i2−2i2−2222−2222000000000000000000000000000000
χ5644-4-4-4-4440000000000−4i4i0000000000−2i22i2−2i22i222−2222−22000000000000000000000000000000
χ574-44-44-4-4404-4-44000000000000000000000000000000000000000000000002i2−2i2000000
χ584-44-44-4-4404-4-4400000000000000000000000000000000000000000000000−2i22i2000000
χ594-44-44-4-440-444-400000000000000000000000000000000000000000002i2−2i20000000000
χ604-44-44-4-440-444-40000000000000000000000000000000000000000000−2i22i20000000000
χ614-4-444-44-4000000004-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ624-4-444-44-4000000004-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ634-4-444-44-400000000-440000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ644-4-444-44-400000000-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ654-4-44-44-4440000-44-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ664-4-44-44-4440000-44-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ674-4-44-44-44-400004-4400000000004-4-4400000000000000000000000000000000000000
χ684-4-44-44-44-400004-440000000000-444-400000000000000000000000000000000000000

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