Finite Group Databasebeta

← Group #10641

Character table — Group #10641

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37
size1111222222224448888888888888888161616161616
order1222224444444442244888888888888448888
χ11111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ7111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ92222222-2-2222-2-2-222-2-2000000000000000000
χ102222222-2-2222-2-2-2-2-222000000000000000000
χ11222222-222-2-2-2-22-20000000000000000002i−2i00
χ12222222-222-2-2-2-22-2000000000000000000−2i2i00
χ13222222-2-2-2-2-2-22-22000000000000000000002i−2i
χ14222222-2-2-2-2-2-22-2200000000000000000000−2i2i
χ152222-2-22222-2-22-2-200000000000000002i−2i0000
χ162222-2-22222-2-22-2-20000000000000000−2i2i0000
χ172222-2-22-2-22-2-2-222000000002i2i−2i−2i0000000000
χ182222-2-22-2-22-2-2-22200000000−2i−2i2i2i0000000000
χ192222-2-2-222-222-2-2200000000000022-2-2000000
χ202222-2-2-222-222-2-22000000000000-2-222000000
χ212222-2-2-2-2-2-22222-200002i2i−2i−2i00000000000000
χ222222-2-2-2-2-2-22222-20000−2i−2i2i2i00000000000000
χ2322-2-22-2-20022-20002-200i2−i2i2−i20000i2−i2i2−i2000000
χ2422-2-22-2-20022-20002-200−i2i2−i2i20000−i2i2−i2i2000000
χ2522-2-22-2-20022-2000-2200i2−i2i2−i20000−i2i2−i2i2000000
χ2622-2-22-2-20022-2000-2200−i2i2−i2i20000i2−i2i2−i2000000
χ2722-2-2-22200-22-2000002i−2i2−2−220000i2−i2−i2i2000000
χ2822-2-2-22200-22-2000002i−2i−222−20000−i2i2i2−i2000000
χ2922-2-2-22200-22-200000−2i2i2−2−220000−i2i2i2−i2000000
χ3022-2-2-22200-22-200000−2i2i−222−20000i2−i2−i2i2000000
χ3144-4-44-4400-4-440000000000000000000000000
χ3244-4-4-44-4004-440000000000000000000000000
χ334-44-40004i−4i000000000000002ζ−2ζ2ζ3−2ζ30000000000
χ344-44-40004i−4i00000000000000−2ζ2ζ−2ζ32ζ30000000000
χ354-44-4000−4i4i000000000000002ζ3−2ζ32ζ−2ζ0000000000
χ364-44-4000−4i4i00000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ378-8-88000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.