Finite Group Databasebeta

← Group #256285

Character table — Group #256285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444442244444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11-1-1-1-1111111111-11-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111-1-1-1-11-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-11111-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-11111-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-111-1-11111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111-11111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-111-1-111-11111-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-111-11111-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ151111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111111-1-111-1-1-1-111
χ172222222222-2-222-2-22222-2-20000-20000-22222000000000-20-200000000000000
χ182222222222-2-222-2-22222-2-20000-20000-2-2-2-2-200000000020200000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2000020000222-2-2000000000-20200000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-20000200002-2-22200000000020-200000000000000
χ2122222222-2-222-2-22222-2-2-2-222-2-2-20000200000000000020-2000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-222-200002000000000000-202000000000000000
χ2322222222-2-222-2-222-2-222-2-2222220000-2000000000000-20-2000000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2-2-220000-2000000000000202000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000222-2-2-200000000000000002-2000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200002-2-222-20000000000000000-22000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000-222-2-220000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000-2-2-222200000000000000002-2000000000000
χ292-2222-2-2-2-2-20022002-22-20000000000002i−2i2i−2i22−2−222−2−200000000000000i2−i2i2−i2
χ302-2222-2-2-2-2-20022002-22-20000000000002i−2i2i−2i−2−222−2−22200000000000000−i2i2−i2i2
χ312-2222-2-2-2-2-20022002-22-2000000000000−2i2i−2i2i22−2−222−2−200000000000000−i2i2−i2i2
χ322-2222-2-2-2-2-20022002-22-2000000000000−2i2i−2i2i−2−222−2−22200000000000000i2−i2i2−i2
χ332-2222-2-2-2-2-2002200-22-220000000000002i−2i−2i2i22−2−2−2−22200000000000000−i2i2i2−i2
χ342-2222-2-2-2-2-2002200-22-220000000000002i−2i−2i2i−2−22222−2−200000000000000i2−i2−i2i2
χ352-2222-2-2-2-2-2002200-22-22000000000000−2i2i2i−2i22−2−2−2−22200000000000000i2−i2−i2i2
χ362-2222-2-2-2-2-2002200-22-22000000000000−2i2i2i−2i−2−22222−2−200000000000000−i2i2i2−i2
χ372-2-22-222-22-22-22-22-200002-2000002-22-20000000002i−2i2i−2i000000002i−2i00000000
χ382-2-22-222-22-22-22-22-200002-2000002-22-2000000000−2i2i−2i2i00000000−2i2i00000000
χ392-2-22-222-22-22-22-22-200002-200000-22-220000000002i−2i2i−2i00000000−2i2i00000000
χ402-2-22-222-22-22-22-22-200002-200000-22-22000000000−2i2i−2i2i000000002i−2i00000000
χ412-2-22-222-2-22-22-22-2200002-2000002-2-22000002i−2i2i−2i00000000002i−2i0000000000
χ422-2-22-222-2-22-22-22-2200002-2000002-2-2200000−2i2i−2i2i0000000000−2i2i0000000000
χ432-2-22-222-2-22-22-22-2200002-200000-222-2000002i−2i2i−2i0000000000−2i2i0000000000
χ442-2-22-222-2-22-22-22-2200002-200000-222-200000−2i2i−2i2i00000000002i−2i0000000000
χ45444-4-4-44-4004400-4-40000004-400000000000000000000000000000000000000
χ46444-4-4-44-4004400-4-4000000-4400000000000000000000000000000000000000
χ47444-4-4-44-400-4-40044000000004i−4i000000000000000000000000000000000000
χ48444-4-4-44-400-4-4004400000000−4i4i000000000000000000000000000000000000
χ4944-44-4-4-444-400-4400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5044-44-4-4-444-400-440000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5144-44-4-4-44-44004-4000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5244-44-4-4-44-44004-400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ534-4444-4-4-44400-4-4004-4-44000000000000000000000000000000000000000000
χ544-4444-4-4-44400-4-400-444-4000000000000000000000000000000000000000000
χ554-4-44-444-44-4-444-4-440000-440000000000000000000000000000000000000000
χ564-4-44-444-4-444-4-444-40000-440000000000000000000000000000000000000000
χ574-4-4-44-444004-400-44000000000000000000000000000000000000000022−220000
χ584-4-4-44-444004-400-440000000000000000000000000000000000000000−22220000
χ594-4-4-44-44400-44004-40000000000000000000000000000000000000022−22000000
χ604-4-4-44-44400-44004-400000000000000000000000000000000000000−2222000000
χ6188-8-888-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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