Finite Group Databasebeta

← Group #321801

Character table — Group #321801

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222222244444488888888888888888816161616161616161616161632323232
order12222222444444444444444488888888888888882444888888882444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-11-11
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-11-11
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-111-1-11-1-11
χ172222222222-2-2-222-22222-2-2-2-200000000000000002-22-2000000000000
χ182222222222-2-2-222-22222-2-2-2-20000000000000000-22-22000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-22200000000000000002-2-22000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2220000000000000000-222-2000000000000
χ2122222222-2-2222-2-2222-2-2-2-22-222-2-22200000000-2-20000000000000000
χ2222222222-2-2222-2-2222-2-2-2-22-2-2-222-2-200000000220000000000000000
χ2322222222-2-2222-2-22-2-222-2-2-2222-2-2-2-200000000220000000000000000
χ2422222222-2-2222-2-22-2-222-2-2-22-2-2222200000000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-220000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-2-2-2-2-222-2-222-22000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-20000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2000000000000000000000000−2i2i2i−2i0000
χ292-2-2-2-22222-22-2-22-2200002-20000002-2000022-2-22-200002-20000000000
χ302-2-2-2-22222-22-2-22-2200002-20000002-20000-2-2222-20000-220000000000
χ312-2-2-2-22222-22-2-22-2200002-2000000-22000022-2-2-220000-220000000000
χ322-2-2-2-22222-22-2-22-2200002-2000000-220000-2-222-2200002-20000000000
χ332-2-2-2-2222-222-2-2-2220000-220000002-222-2-20000-220000002-200000000
χ342-2-2-2-2222-222-2-2-2220000-220000002-2-2-2220000-22000000-2200000000
χ352-2-2-2-2222-222-2-2-2220000-22000000-2222-2-200002-2000000-2200000000
χ362-2-2-2-2222-222-2-2-2220000-22000000-22-2-22200002-20000002-200000000
χ37444-4-44-4-40044-400-40000000000000022−2222−220000000000000000000000
χ38444-4-44-4-40044-400-400000000000000−2222−22220000000000000000000000
χ39444-4-44-4-400-4-440040000000000000000002i2−2i22i2−2i2000000000000000000
χ40444-4-44-4-400-4-44004000000000000000000−2i22i2−2i22i2000000000000000000
χ4144-44-4-44-444000-4-404-44-4000000000000000000000000000000000000
χ4244-44-4-44-444000-4-40-44-44000000000000000000000000000000000000
χ4344-44-4-44-4-4-40004404-4-44000000000000000000000000000000000000
χ4444-44-4-44-4-4-4000440-444-4000000000000000000000000000000000000
χ454-44-44-44-44-4000-440000000002i2−2i22i2−2i20000000000000000000000000000
χ464-44-44-44-44-4000-44000000000−2i22i2−2i22i20000000000000000000000000000
χ474-44-44-44-4-440004-40000000002i2−2i2−2i22i20000000000000000000000000000
χ484-44-44-44-4-440004-4000000000−2i22i22i2−2i20000000000000000000000000000
χ494-4-4444-4-4004-4400-40000000000000022−22−22220000000000000000000000
χ504-4-4444-4-4004-4400-400000000000000−222222−220000000000000000000000
χ514-4-4444-4-400-44-40040000000000000000002i2−2i2−2i22i2000000000000000000
χ524-4-4444-4-400-44-4004000000000000000000−2i22i22i2−2i2000000000000000000
χ534-4-4-4-44444-4-4444-4-40000-440000000000000000000000000000000000
χ544-4-4-4-4444-44-444-44-400004-40000000000000000000000000000000000
χ5588-8-88-8-88000000000000000000000000000000000000000000000000
χ568-888-8-8-88000000000000000000000000000000000000000000000000

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