Finite Group Databasebeta

← Group #295709

Character table — Group #295709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888822244444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111
χ511111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1
χ711111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1
χ811111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1-1-111
χ91111111111111111-1-1-1-111-111-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1111-1-11-1
χ101111111111111111-1-1-1-111-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-111-11
χ111111111111111111-1-1-1-111-111-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-11-1-1-111-11
χ121111111111111111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-1-11111-111-1-1-11-111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11111-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11111-1-1-1111-1
χ172222222222-2-222-2-222-2-2-2-2222-200-2-2000000000000000000-20020000000000
χ182222222222-2-222-2-222-2-2-2-22-2-2-20022000000000000000000200-20000000000
χ192222222222-2-222-2-2-2-222-2-2-222200-2-2000000000000000000200-20000000000
χ202222222222-2-222-2-2-2-222-2-2-2-2-220022000000000000000000-20020000000000
χ2122222222-2-222-2-2222222-2-2-200-22200220000000000000000000000-2-2000000
χ2222222222-2-222-2-2222222-2-2-200-2-2-200-2-2000000000000000000000022000000
χ2322222222-2-222-2-222-2-2-2-2-2-220022200-2-200000000000000000000002-2000000
χ2422222222-2-222-2-222-2-2-2-2-2-22002-2-200220000000000000000000000-22000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2002000000000000000000000002-202-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-200200000000000000000000000-220-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222200-2000000000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222200-200000000000000000000000-2202-200000000
χ2922-22-22-2-2-2-22-2222-200002-202i−2i0002i−2i00000022-2-200002i2i−2i−2i00000000000000
χ3022-22-22-2-2-2-22-2222-200002-202i−2i0002i−2i000000-2-2220000−2i−2i2i2i00000000000000
χ3122-22-22-2-2-2-22-2222-200002-20−2i2i000−2i2i00000022-2-20000−2i−2i2i2i00000000000000
χ3222-22-22-2-2-2-22-2222-200002-20−2i2i000−2i2i000000-2-22200002i2i−2i−2i00000000000000
χ3322-22-22-2-2-2-2-2222-220000-2202i−2i000−2i2i0022-2-200002i2i−2i−2i000000000000000000
χ3422-22-22-2-2-2-2-2222-220000-2202i−2i000−2i2i00-2-2220000−2i−2i2i2i000000000000000000
χ3522-22-22-2-2-2-2-2222-220000-220−2i2i0002i−2i0022-2-20000−2i−2i2i2i000000000000000000
χ3622-22-22-2-2-2-2-2222-220000-220−2i2i0002i−2i00-2-22200002i2i−2i−2i000000000000000000
χ372-222-2-22-2002-200-222i−2i2i−2i0000002-2002i−2i00000000i2−i2i2−i22−22−200000000i2−i22−200
χ382-222-2-22-2002-200-222i−2i2i−2i0000002-2002i−2i00000000−i2i2−i2i2−22−2200000000−i2i2−2200
χ392-222-2-22-2002-200-222i−2i2i−2i000000-2200−2i2i00000000i2−i2i2−i22−22−200000000−i2i2−2200
χ402-222-2-22-2002-200-222i−2i2i−2i000000-2200−2i2i00000000−i2i2−i2i2−22−2200000000i2−i22−200
χ412-222-2-22-2002-200-22−2i2i−2i2i0000002-200−2i2i00000000i2−i2i2−i2−22−2200000000i2−i2−2200
χ422-222-2-22-2002-200-22−2i2i−2i2i0000002-200−2i2i00000000−i2i2−i2i22−22−200000000−i2i22−200
χ432-222-2-22-2002-200-22−2i2i−2i2i000000-22002i−2i00000000i2−i2i2−i2−22−2200000000−i2i22−200
χ442-222-2-22-2002-200-22−2i2i−2i2i000000-22002i−2i00000000−i2i2−i2i22−22−200000000i2−i2−2200
χ45444-44-4-4-44-4004-4000000000000000000000022−2222−220000000000000000000000
χ46444-44-4-4-44-4004-40000000000000000000000−2222−22220000000000000000000000
χ47444-44-4-4-4-4400-4400000000000000000022−2222−2200000000000000000000000000
χ48444-44-4-4-4-4400-44000000000000000000−2222−222200000000000000000000000000
χ4944-44-44-4-4444-4-4-44-40000-440000000000000000000000000000000000000000
χ5044-44-44-4-444-44-4-4-4400004-40000000000000000000000000000000000000000
χ5144-4-4-4-4444-400-4400000000000000000022−22−222200000000000000000000000000
χ5244-4-4-4-4444-400-44000000000000000000−222222−2200000000000000000000000000
χ5344-4-4-4-444-44004-4000000000000000000000022−22−22220000000000000000000000
χ5444-4-4-4-444-44004-40000000000000000000000−222222−220000000000000000000000
χ554-444-4-44-400-44004-44i−4i−4i4i000000000000000000000000000000000000000000
χ564-444-4-44-400-44004-4−4i4i4i−4i000000000000000000000000000000000000000000
χ574-4-444-4-44004400-4-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-4-444-4-44004400-4-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-4-444-4-4400-4-4004400000000000000000000000022−22−2222000000000000000000
χ604-4-444-4-4400-4-40044000000000000000000000000−222222−22000000000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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