Finite Group Databasebeta

← Group #293156

Character table — Group #293156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1111-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111
χ511111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111
χ611111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111-1-1
χ711111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-111-11111-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-11-1
χ101111111111111111-1-1-1-111-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-11
χ111111111111111111-1-1-1-111-111-1-1-111111111-1-1-1-11111-1-1-1-111-11-1-1-1-1-1-111-11
χ121111111111111111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-1-1111111-11-1-1-1-111-1-11-1
χ131111111111111111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1111-1
χ172222222222-2-2-222-222-2-2-2-222200-2-2-200000000000000000000-200200000000
χ182222222222-2-2-222-222-2-2-2-22-2-200-22200000000000000000000200-200000000
χ192222222222-2-2-222-2-2-222-2-2-222002-2-200000000000000000000200-200000000
χ202222222222-2-2-222-2-2-222-2-2-2-2-20022200000000000000000000-200200000000
χ2122222222-2-2222-2-222222-2-2-20022-200220000000000000000000-2-2000000000
χ2222222222-2-2222-2-222222-2-2-200-2-2-200-2-2000000000000000000022000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-220022200-2-200000000000000000002-2000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2200-2-2200220000000000000000000-22000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-200002000000000000000000002-200002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-20000200000000000000000000-220000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222220000-2000000000000000000002-20000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222220000-200000000000000000000-2200002-2000000
χ292-222-2-22-22-222-22-2-20000-2202i−2i0002i−2i002i2i−2i−2i000022-2-2000000000000000000
χ302-222-2-22-22-222-22-2-20000-2202i−2i0002i−2i00−2i−2i2i2i0000-2-222000000000000000000
χ312-222-2-22-22-222-22-2-20000-220−2i2i000−2i2i002i2i−2i−2i0000-2-222000000000000000000
χ322-222-2-22-22-222-22-2-20000-220−2i2i000−2i2i00−2i−2i2i2i000022-2-2000000000000000000
χ332-222-2-22-22-2-2-222-2200002-202i−2i000−2i2i00000022-2-200002i2i−2i−2i00000000000000
χ342-222-2-22-22-2-2-222-2200002-202i−2i000−2i2i000000-2-2220000−2i−2i2i2i00000000000000
χ352-222-2-22-22-2-2-222-2200002-20−2i2i0002i−2i00000022-2-20000−2i−2i2i2i00000000000000
χ362-222-2-22-22-2-2-222-2200002-20−2i2i0002i−2i000000-2-22200002i2i−2i−2i00000000000000
χ372-2-222-2-22002-2200-22-22-2000002-20002-200000000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i200
χ382-2-222-2-22002-2200-22-22-2000002-20002-200000000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i200
χ392-2-222-2-22002-2200-22-22-200000-22000-2200000000i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i200
χ402-2-222-2-22002-2200-22-22-200000-22000-2200000000−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i200
χ412-2-222-2-22002-2200-2-22-22000002-2000-2200000000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i200
χ422-2-222-2-22002-2200-2-22-22000002-2000-2200000000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i200
χ432-2-222-2-22002-2200-2-22-2200000-220002-200000000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i200
χ442-2-222-2-22002-2200-2-22-2200000-220002-200000000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i200
χ45444-44-4-4-44-4000-440000000000000000022−2222−2200000000000000000000000000
χ46444-44-4-4-44-4000-4400000000000000000−2222−222200000000000000000000000000
χ47444-44-4-4-4-440004-400000000000000000000022−2222−220000000000000000000000
χ48444-44-4-4-4-440004-4000000000000000000000−2222−22220000000000000000000000
χ4944-44-44-4-4004-4-40040000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5044-44-44-4-4004-4-4004000000000000000000000000−2i22i22i2−2i2000000000000000000
χ5144-44-44-4-400-44400-4000000000000000000000000000022−22−222200000000000000
χ5244-44-44-4-400-44400-40000000000000000000000000000−222222−2200000000000000
χ534-444-4-44-4-4444-4-44-400004-40000000000000000000000000000000000000000
χ544-444-4-44-4-44-4-44-4440000-440000000000000000000000000000000000000000
χ554-44-4-44-4444000-4-4000000000000000002i2−2i2−2i22i200000000000000000000000000
χ564-44-4-44-4444000-4-400000000000000000−2i22i22i2−2i200000000000000000000000000
χ574-44-4-44-44-4-40004400000000000000000000022−22−22220000000000000000000000
χ584-44-4-44-44-4-400044000000000000000000000−222222−220000000000000000000000
χ594-4-444-4-4400-44-40044-4-44000000000000000000000000000000000000000000
χ604-4-444-4-4400-44-4004-444-4000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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