Finite Group Databasebeta

← Group #166017

Character table — Group #166017

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1111-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-11-11-11-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-11-11-11-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-11-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1111-1-11-1111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1111-1-11-11-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-111-1-1-111-111-1-1-11-111-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-111-1-1-111-111-1-1-11-111-1-1-11111-1-111-1-1-1-111
χ17222222222222222-2-22-2-20000-20022-200220000-2-20000000000000000
χ18222222222222222-2-22-2-20000-200-2-2-200-2-20000220000000000000000
χ19222222222222-2-2-22-2-22-20000-2220022200-2-200000000000000000000
χ20222222222222-2-2-22-2-22-20000-2-2-2002-2-2002200000000000000000000
χ21222222222222-2-2-2-22-2-22222220000-2000000-2-2000000000000000000
χ22222222222222-2-2-2-22-2-22-2-2-2-220000-200000022000000000000000000
χ2322222222-2-2-2-222-22-2-22-2000022200-2-2-200-2200000000000000000000
χ2422222222-2-2-2-222-22-2-22-200002-2-200-222002-200000000000000000000
χ2522222222-2-2-2-222-2-22-2-2222-2-2-200002000000-22000000000000000000
χ2622222222-2-2-2-222-2-22-2-22-2-222-2000020000002-2000000000000000000
χ2722222222-2-2-2-2-2-22-2-22-2-2000020022200-2-20000-220000000000000000
χ2822222222-2-2-2-2-2-22-2-22-2-20000200-2-22002200002-20000000000000000
χ292-2-2222-2-222-2-22-2-20020000000002i−2i0002i−2i0000000000i2−i2i2−i22−22−20000
χ302-2-2222-2-222-2-22-2-20020000000002i−2i0002i−2i0000000000−i2i2−i2i2−22−220000
χ312-2-2222-2-222-2-22-2-2002000000000−2i2i000−2i2i0000000000i2−i2i2−i2−22−220000
χ322-2-2222-2-222-2-22-2-2002000000000−2i2i000−2i2i0000000000−i2i2−i2i22−22−20000
χ332-2-2222-2-2-2-222-22-20020000000002i−2i000−2i2i0000000000i2−i2−i2i22−2−220000
χ342-2-2222-2-2-2-222-22-20020000000002i−2i000−2i2i0000000000−i2i2i2−i2−222−20000
χ352-2-2222-2-2-2-222-22-2002000000000−2i2i0002i−2i0000000000i2−i2−i2i2−222−20000
χ362-2-2222-2-2-2-222-22-2002000000000−2i2i0002i−2i0000000000−i2i2i2−i22−2−220000
χ374444-4-4-4-44-44-400000000000000000000000000000000000000002-22-2
χ384444-4-4-4-44-44-40000000000000000000000000000000000000000-22-22
χ394444-4-4-4-4-44-4400000000000000000000000000000000000000002-2-22
χ404444-4-4-4-4-44-440000000000000000000000000000000000000000-222-2
χ4144-4-44-44-40000000400-40000004-400000000000000000000000000000
χ4244-4-44-44-40000000400-4000000-4400000000000000000000000000000
χ4344-4-44-44-40000000-4004000000000004i−4i000000000000000000000000
χ4444-4-44-44-40000000-400400000000000−4i4i000000000000000000000000
χ4544-4-4-44-4400000000400-4004i−4i00000000000000000000000000000000
χ4644-4-4-44-4400000000400-400−4i4i00000000000000000000000000000000
χ4744-4-4-44-4400000000-40044-40000000000000000000000000000000000
χ4844-4-4-44-4400000000-4004-440000000000000000000000000000000000
χ494-4-4444-4-444-4-4-44400-400000000000000000000000000000000000000
χ504-4-4444-4-4-4-4444-4400-400000000000000000000000000000000000000
χ514-4-44-4-4444-4-4400000000000000000000000000002-22-2000000000000
χ524-4-44-4-4444-4-440000000000000000000000000000-22-22000000000000
χ534-4-44-4-444-444-400000000000000000000000000002-2-22000000000000
χ544-4-44-4-444-444-40000000000000000000000000000-222-2000000000000
χ558-88-88-8-88000000000000000000000000000000000000000000000000
χ568-88-8-888-8000000000000000000000000000000000000000000000000

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