Finite Group Databasebeta

← Group #325545

Character table — Group #325545

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444444448888444444888888888888888888448888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11
χ71111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-111-1-11-1-11
χ81111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-111-1
χ91111111111111111-1-111-1-11111-11111-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ101111111111111111-1-111-1-11111-11111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-11111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1111-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ17222222222-2-222-2-2222-2-2220000-222-2-2-20000000000000000002-20000000000
χ18222222222-2-222-2-2222-2-2220000-2-2-222-2000000000000000000-220000000000
χ19222222222-2-222-2-22-2-2-2-2-2-20000222-2-22000000000000000000-220000000000
χ20222222222-2-222-2-22-2-2-2-2-2-200002-2-22220000000000000000002-20000000000
χ2122222222-222-2-222-222-2-2-2-22222-20000222-2-20000-2-200000000000000000000
χ2222222222-222-2-222-222-2-2-2-2-2-2-2-2-200002-2-22200002200000000000000000000
χ2322222222-222-2-222-2-2-2-2-222222220000-2-2-2220000-2-200000000000000000000
χ2422222222-222-2-222-2-2-2-2-222-2-2-2-220000-222-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000020000-200000000002i2i−2i−2i000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000020000-20000000000−2i−2i2i2i00000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000-20000200000000002i2i−2i−2i00000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000-2000020000000000−2i−2i2i2i000000002i−2i000000
χ2922-2-222-2-22-2-2-2-2222002-20022-2-200000000002i2i−2i−2i2-200000000002i−2i00000000
χ3022-2-222-2-22-2-2-2-2222002-20022-2-20000000000−2i−2i2i2i2-20000000000−2i2i00000000
χ3122-2-222-2-22-2-2-2-2222002-200-2-22200000000002i2i−2i−2i-220000000000−2i2i00000000
χ3222-2-222-2-22-2-2-2-2222002-200-2-2220000000000−2i−2i2i2i-2200000000002i−2i00000000
χ3322-2-222-2-2-2-2-22222-200-220022-2-200000000000000-2200002i2i−2i−2i0000002i−2i0000
χ3422-2-222-2-2-2-2-22222-200-220022-2-200000000000000-220000−2i−2i2i2i000000−2i2i0000
χ3522-2-222-2-2-2-2-22222-200-2200-2-222000000000000002-200002i2i−2i−2i000000−2i2i0000
χ3622-2-222-2-2-2-2-22222-200-2200-2-222000000000000002-20000−2i−2i2i2i0000002i−2i0000
χ37444-4-4-44-404-4004-4000000000000000000000000000000022−2222−22000000000000
χ38444-4-4-44-404-4004-40000000000000000000000000000000−2222−2222000000000000
χ39444-4-4-44-40-4400-4400000000000000000000022−2222−220000000000000000000000
χ40444-4-4-44-40-4400-44000000000000000000000−2222−22220000000000000000000000
χ4144-44-4-4-4404-400-440000000000000000000002i2−2i2−2i22i20000000000000000000000
χ4244-44-4-4-4404-400-44000000000000000000000−2i22i22i2−2i20000000000000000000000
χ4344-44-4-4-440-44004-400000000000000000000000000000002i2−2i2−2i22i2000000000000
χ4444-44-4-4-440-44004-40000000000000000000000000000000−2i22i22i2−2i2000000000000
χ4544-4-444-4-4444-4-4-4-4400-44000000000000000000000000000000000000000000
χ4644-4-444-4-4-44444-4-4-4004-4000000000000000000000000000000000000000000
χ474-4444-4-4-4000000004-4000022−2222−2200000022−220000000000000000000000000000
χ484-4444-4-4-4000000004-40000−2222−2222000000−22220000000000000000000000000000
χ494-4444-4-4-400000000-44000022−2222−22000000−22220000000000000000000000000000
χ504-4444-4-4-400000000-440000−2222−222200000022−220000000000000000000000000000
χ514-44-4-44-444004-400-4000000000000000000000000002i2−2i22i2−2i20000000000000000
χ524-44-4-44-444004-400-400000000000000000000000000−2i22i2−2i22i20000000000000000
χ534-44-4-44-44-400-440040000000000000000000000000022−22−22220000000000000000
χ544-44-4-44-44-400-4400400000000000000000000000000−222222−220000000000000000
χ554-4-44-444-4400-4400-400000000000004-40000000000000000000000000000000
χ564-4-44-444-4400-4400-40000000000000-440000000000000000000000000000000
χ574-4-44-444-4-4004-4004000000000004i−4i000000000000000000000000000000000
χ584-4-44-444-4-4004-400400000000000−4i4i000000000000000000000000000000000
χ594-4-4-44-4440000000000004-422−22−22220000000022−2200000000000000000000000000
χ604-4-4-44-4440000000000004-4−222222−2200000000−222200000000000000000000000000
χ614-4-4-44-444000000000000-4422−22−222200000000−222200000000000000000000000000
χ624-4-4-44-444000000000000-44−222222−220000000022−2200000000000000000000000000

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