Finite Group Databasebeta

← Group #312959

Character table — Group #312959

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-111111-11-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-11-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-111-1-111111-1-1-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-11-1-1-11111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11-1-1111-11-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-11111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111111-1-1-1-1-11-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-11-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-111111-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-111111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-11-1111-1-1-1-1-11
χ17222222222-22-22-22-20000-2-22222222200-2-2000000000000-200000-2000000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-20000000000002000002000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-20022000000000000200000-2000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-2220022000000000000-2000002000000000
χ2122222222-22-22-22-222222-2-200000000-2-200220000-2-200000000020-200000000
χ2222222222-22-22-22-222222-2-200000000-2-200-2-2000022000000000-20200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002200220000-2-2000000000-20200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000002200-2-200002200000000020-200000000
χ2522-2-2-2-22222-2-222-2-22i2i−2i−2i-222i2i−2i−2i00002i−2i2i−2i0022-2-20000000000000000000000
χ2622-2-2-2-22222-2-222-2-22i2i−2i−2i-22−2i−2i2i2i00002i−2i−2i2i00-2-2220000000000000000000000
χ2722-2-2-2-22222-2-222-2-2−2i−2i2i2i-222i2i−2i−2i0000−2i2i2i−2i00-2-2220000000000000000000000
χ2822-2-2-2-22222-2-222-2-2−2i−2i2i2i-22−2i−2i2i2i0000−2i2i−2i2i0022-2-20000000000000000000000
χ2922-2-2-2-2222-2-222-2-2200002-22i2i−2i−2i000000−2i2i00000000000002i−2i2-200000000000
χ3022-2-2-2-2222-2-222-2-2200002-22i2i−2i−2i000000−2i2i0000000000000−2i2i-2200000000000
χ3122-2-2-2-2222-2-222-2-2200002-2−2i−2i2i2i0000002i−2i00000000000002i−2i-2200000000000
χ3222-2-2-2-2222-2-222-2-2200002-2−2i−2i2i2i0000002i−2i0000000000000−2i2i2-200000000000
χ3322-2-2-2-222-222-2-222-22i2i−2i−2i2-200000000−2i2i00000000002i2i−2i−2i00000000002-20000
χ3422-2-2-2-222-222-2-222-22i2i−2i−2i2-200000000−2i2i0000000000−2i−2i2i2i0000000000-220000
χ3522-2-2-2-222-222-2-222-2−2i−2i2i2i2-2000000002i−2i00000000002i2i−2i−2i0000000000-220000
χ3622-2-2-2-222-222-2-222-2−2i−2i2i2i2-2000000002i−2i0000000000−2i−2i2i2i00000000002-20000
χ3744444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ384444-4-4-4-440-40-40400000000000004-400000000000000000000000000000000
χ394444-4-4-4-440-40-4040000000000000-4400000000000000000000000000000000
χ404444-4-4-4-4-404040-4000000000000000000000000000000000000000000022−2200
χ414444-4-4-4-4-404040-40000000000000000000000000000000000000000000−222200
χ4244-4-444-4-44040-40-4000000000004-40000000000000000000000000000000000
χ4344-4-444-4-44040-40-400000000000-440000000000000000000000000000000000
χ4444-4-444-4-4-40-404040000000000000000000000000000000000000002i2−2i2000000
χ4544-4-444-4-4-40-40404000000000000000000000000000000000000000−2i22i2000000
χ4644-4-4-4-444-4-444-4-4440000-440000000000000000000000000000000000000000
χ474-44-44-4-44040-40-404000000000000000000002i2−2i22i2−2i20000000000000000000000
χ484-44-44-4-44040-40-40400000000000000000000−2i22i2−2i22i20000000000000000000000
χ494-44-44-4-440-404040-44i−4i4i−4i000000000000000000000000000000000000000000
χ504-44-44-4-440-404040-4−4i4i−4i4i000000000000000000000000000000000000000000
χ514-44-4-444-40000000000000022−2222−22000000000000002i2−2i22i−2i2i−2i0000000000000000
χ524-44-4-444-40000000000000022−2222−2200000000000000−2i22i2−2i2i−2i2i0000000000000000
χ534-44-4-444-400000000000000−2222−2222000000000000002i2−2i2−2i2i−2i2i0000000000000000
χ544-44-4-444-400000000000000−2222−222200000000000000−2i22i22i−2i2i−2i0000000000000000
χ554-4-444-44-4000000000000002i2−2i2−2i22i2000000002i2−2i20000002-2-220000000000000000
χ564-4-444-44-4000000000000002i2−2i2−2i22i200000000−2i22i2000000-222-20000000000000000
χ574-4-444-44-400000000000000−2i22i22i2−2i2000000002i2−2i2000000-222-20000000000000000
χ584-4-444-44-400000000000000−2i22i22i2−2i200000000−2i22i20000002-2-220000000000000000
χ594-4-44-44-4404040-40-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-44-44-4404040-40-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-4-44-44-440-40-404044-4-44000000000000000000000000000000000000000000
χ624-4-44-44-440-40-40404-444-4000000000000000000000000000000000000000000

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