Finite Group Databasebeta

← Group #313049

Character table — Group #313049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882224444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-1-11-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1111111-1-1-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-11111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-11-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-11111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-11-1-11-111-1-111-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-111-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1111-1-1-1-111111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1111-1-1-1-1-11
χ17222222222-22-22-22-2-22222-200000000-2-222000000-2-200000020000-200000000
χ18222222222-22-22-22-2-22222-200000000-2-2-2-200000022000000-20000200000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000000002222000000-2-2000000-20000200000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000000022-2-20000002200000020000-200000000
χ2122222222-22-22-22-22-20000-22222222200000000-2-2000000000-200-2000000000
χ2222222222-22-22-22-22-20000-22222-2-2-2-200000000-2-20000000002002000000000
χ2322222222-22-22-22-22-20000-2-2-2-2-222-2-20000000022000000000200-2000000000
χ2422222222-22-22-22-22-20000-2-2-2-2-2-2-2220000000022000000000-2002000000000
χ2522-22-2-2-2222-2-222-2-2-22i2i−2i−2i22i2i−2i−2i00002i−2i0022-2-22i−2i0000000000000000000000
χ2622-22-2-2-2222-2-222-2-2-22i2i−2i−2i2−2i−2i2i2i00002i−2i00-2-222−2i2i0000000000000000000000
χ2722-22-2-2-2222-2-222-2-2-2−2i−2i2i2i22i2i−2i−2i0000−2i2i00-2-2222i−2i0000000000000000000000
χ2822-22-2-2-2222-2-222-2-2-2−2i−2i2i2i2−2i−2i2i2i0000−2i2i0022-2-2−2i2i0000000000000000000000
χ2922-22-2-2-222-2-222-2-2222i2i−2i−2i-200000000−2i2i00000000002i2i−2i−2i00000000002-20000
χ3022-22-2-2-222-2-222-2-2222i2i−2i−2i-200000000−2i2i0000000000−2i−2i2i2i0000000000-220000
χ3122-22-2-2-222-2-222-2-222−2i−2i2i2i-2000000002i−2i00000000002i2i−2i−2i0000000000-220000
χ3222-22-2-2-222-2-222-2-222−2i−2i2i2i-2000000002i−2i0000000000−2i−2i2i2i00000000002-20000
χ3322-22-2-2-22-222-2-222-220000-22i2i−2i−2i000000000000−2i2i0000002-2002i−2i0000000000
χ3422-22-2-2-22-222-2-222-220000-22i2i−2i−2i000000000000−2i2i000000-2200−2i2i0000000000
χ3522-22-2-2-22-222-2-222-220000-2−2i−2i2i2i0000000000002i−2i0000002-200−2i2i0000000000
χ3622-22-2-2-22-222-2-222-220000-2−2i−2i2i2i0000000000002i−2i000000-22002i−2i0000000000
χ3744444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ38444-44-4-4-44040-40-4004-44-400000000000000000000000000000000000000000
χ39444-44-4-4-44040-40-400-44-4400000000000000000000000000000000000000000
χ40444-44-4-4-4-40-4040400000000000000000002i2−2i22i2−2i2000000000000000000000000
χ41444-44-4-4-4-40-404040000000000000000000−2i22i2−2i22i2000000000000000000000000
χ4244-44-4-4-44-4-444-4-444-4000040000000000000000000000000000000000000000
χ4344-4-4-444-440-40-404004i−4i−4i4i00000000000000000000000000000000000000000
χ4444-4-4-444-440-40-40400−4i4i4i−4i00000000000000000000000000000000000000000
χ4544-4-4-444-4-404040-400000000000000000002i2−2i2−2i22i2000000000000000000000000
χ4644-4-4-444-4-404040-40000000000000000000−2i22i22i2−2i2000000000000000000000000
χ474-444-4-44-4000000000000002i2−2i22i2−2i20000002i2−2i2000000002-22-20000000000000000
χ484-444-4-44-4000000000000002i2−2i22i2−2i2000000−2i22i200000000-22-220000000000000000
χ494-444-4-44-400000000000000−2i22i2−2i22i20000002i2−2i200000000-22-220000000000000000
χ504-444-4-44-400000000000000−2i22i2−2i22i2000000−2i22i2000000002-22-20000000000000000
χ514-44-4-44-4404040-40-400000000004i−4i0000000000000000000000000000000000
χ524-44-4-44-4404040-40-40000000000−4i4i0000000000000000000000000000000000
χ534-44-4-44-440-40-404040000000000000000000000000000000000000022−22000000
χ544-44-4-44-440-40-4040400000000000000000000000000000000000000−2222000000
χ554-4-4444-4-40000000000000022−22−2222000000000000002i2−2i22i−2i−2i2i0000000000000000
χ564-4-4444-4-40000000000000022−22−222200000000000000−2i22i2−2i2i2i−2i0000000000000000
χ574-4-4444-4-400000000000000−222222−22000000000000002i2−2i2−2i2i2i−2i0000000000000000
χ584-4-4444-4-400000000000000−222222−2200000000000000−2i22i22i−2i−2i2i0000000000000000
χ594-4-4-44-444040-40-4040000000000004-400000000000000000000000000000000
χ604-4-4-44-444040-40-404000000000000-4400000000000000000000000000000000
χ614-4-4-44-4440-404040-400000000000000000000000000000000000000000022−2200
χ624-4-4-44-4440-404040-4000000000000000000000000000000000000000000−222200

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