Finite Group Databasebeta

← Group #351621

Character table — Group #351621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888244444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ12111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-2-2-22-2-22222-2-2-2-2220000-2-2000022-2-200000000000000000000
χ1822222222222-2-2-2-22-2-22222-2-2-2-2-2-20000220000-2-22200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-22222220000-2-20000-2-22200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-22222-2-2000022000022-2-200000000000000000000
χ2122222222-2-2-22222-2-2-2000000002-222222-2-2-2-2-2000000000000000000000000
χ2222222222-2-2-22222-2-2-2000000002-2-2-2-2-22-22222000000000000000000000000
χ2322222222-2-2-22222-2-2-200000000-2222-2-2-22-2-222000000000000000000000000
χ2422222222-2-2-22222-2-2-200000000-22-2-222-2222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000000002-20000-22000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222000000002-20000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2200002-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2200002-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-222-2-22-2-222-2-222-20000000000002i−2i00002i−2i2i−2i2i−2i2-22-20000000000000000
χ3022-2-222-2-22-2-222-2-222-20000000000002i−2i00002i−2i−2i2i−2i2i-22-220000000000000000
χ3122-2-222-2-22-2-222-2-222-2000000000000−2i2i0000−2i2i2i−2i2i−2i-22-220000000000000000
χ3222-2-222-2-22-2-222-2-222-2000000000000−2i2i0000−2i2i−2i2i−2i2i2-22-20000000000000000
χ3322-2-222-2-22-2-2-2-2222-2200000000002i−2i00002i−2i002i−2i−2i2i00002-22-2000000000000
χ3422-2-222-2-22-2-2-2-2222-2200000000002i−2i00002i−2i00−2i2i2i−2i0000-22-22000000000000
χ3522-2-222-2-22-2-2-2-2222-220000000000−2i2i0000−2i2i002i−2i−2i2i0000-22-22000000000000
χ3622-2-222-2-22-2-2-2-2222-220000000000−2i2i0000−2i2i00−2i2i2i−2i00002-22-2000000000000
χ3722-2-222-2-2-22222-2-2-2-2222-2-222-2-200002i−2i0000−2i2i000000002i−2i−2i2i000000000000
χ3822-2-222-2-2-22222-2-2-2-2222-2-222-2-20000−2i2i00002i−2i00000000−2i2i2i−2i000000000000
χ3922-2-222-2-2-22222-2-2-2-22-2-222-2-22200002i−2i0000−2i2i00000000−2i2i2i−2i000000000000
χ4022-2-222-2-2-22222-2-2-2-22-2-222-2-2220000−2i2i00002i−2i000000002i−2i−2i2i000000000000
χ4122-2-222-2-2-222-2-222-22-222-2-2-2-222002i−2i0000−2i2i0000002i−2i−2i2i0000000000000000
χ4222-2-222-2-2-222-2-222-22-222-2-2-2-22200−2i2i00002i−2i000000−2i2i2i−2i0000000000000000
χ4322-2-222-2-2-222-2-222-22-2-2-22222-2-2002i−2i0000−2i2i000000−2i2i2i−2i0000000000000000
χ4422-2-222-2-2-222-2-222-22-2-2-22222-2-200−2i2i00002i−2i0000002i−2i−2i2i0000000000000000
χ45444-4-4-44-444-40000-4000000000000000000000000000000000000000022−220000
χ46444-4-4-44-444-40000-40000000000000000000000000000000000000000−22220000
χ47444-4-4-44-4-4-44000040000000000000000000000000000000000002i2−2i200000000
χ48444-4-4-44-4-4-4400004000000000000000000000000000000000000−2i22i200000000
χ4944-44-4-4-444-440000-4000000000000000000000000000000000022−220000000000
χ5044-44-4-4-444-440000-40000000000000000000000000000000000−22220000000000
χ5144-44-4-4-44-44-400004000000000000000000000000000000000000002i2−2i2000000
χ5244-44-4-4-44-44-40000400000000000000000000000000000000000000−2i22i2000000
χ534-44-44-4-440004-44-40002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ544-44-44-4-440004-44-4000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ554-44-44-4-44000-44-440002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ564-44-44-4-44000-44-44000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ574-4-444-44-40004-4-440002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ584-4-444-44-40004-4-44000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ594-4-444-44-4000-444-40002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ604-4-444-44-4000-444-4000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8-8888000000000000000000000000000000000000000000000000000000

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