Finite Group Databasebeta

← Group #168491

Character table — Group #168491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-11-1-1-11111-11-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-1-1-1-1-11-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-11-1-1-1-1
χ911111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-11111-1-1-1-11-1-11-11-111-1-11-1111-1-1
χ1011111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-11111-1-1-1-1-11-1-11-11-1-11111-1-1-111
χ1111111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-11-11-1-1-1111-11-1-111
χ1211111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-11111-11-1-11-1111-1-111-111-1-1
χ1311111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1111-1111-1-1-1-1-1-1-111
χ1411111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-11-1-1-111-11111-1-1
χ1511111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-11-1111-11-1-111-1-1-111-1-1
χ1611111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-1-111-1-11-111-1-1-111-1-111
χ172222222222222-2-2-2-2-222-2-22-20000000000000000000000002-2-200000020000
χ182222222222222-2-2-2-2-222-2-22-2000000000000000000000000-222000000-20000
χ19222222222222-222-2-22-2-2-2-2-2200000000000000000000220-200000000-200000
χ20222222222222-222-2-22-2-2-2-2-2200000000000000000000-2-20200000000200000
χ21222222222222-2-2-222-2-2-222-2-22222000000000000000000-200000000-2000000
χ22222222222222-2-2-222-2-2-222-2-2-2-2-2-20000000000000000002000000002000000
χ2322222222-2-2-2-222222-2-2-2-2-22-200000000000000000000000022-2000000-20000
χ2422222222-2-2-2-222222-2-2-2-2-22-2000000000000000000000000-2-2200000020000
χ2522222222-2-2-2-2-222-2-2-22222-2-222-2-2000000000000000000200000000-2000000
χ2622222222-2-2-2-2-222-2-2-22222-2-2-2-222000000000000000000-2000000002000000
χ2722222222-2-2-2-2-2-2-222222-2-2-22000000000000000000002-20-200000000200000
χ2822222222-2-2-2-2-2-2-222222-2-2-2200000000000000000000-220200000000-200000
χ2922-2-2-22-222i2i−2i−2i0002i−2i0002-2002i−2i2-2i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000000000
χ3022-2-2-22-222i2i−2i−2i0002i−2i0002-2002i−2i2-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000000000
χ3122-2-2-22-222i2i−2i−2i0002i−2i0002-200−2i2i-22i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000000000
χ3222-2-2-22-222i2i−2i−2i0002i−2i0002-200−2i2i-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000000000
χ3322-2-2-22-22−2i−2i2i2i000−2i2i0002-2002i−2i-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000000000
χ3422-2-2-22-22−2i−2i2i2i000−2i2i0002-2002i−2i-22−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000000000
χ3522-2-2-22-22−2i−2i2i2i000−2i2i0002-200−2i2i2-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000000000
χ3622-2-2-22-22−2i−2i2i2i000−2i2i0002-200−2i2i2-2−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000000000
χ374444-4-4-4-4000004-40000000000000000000002-22-22-22-2000000000000000000
χ384444-4-4-4-4000004-4000000000000000000000-22-22-22-22000000000000000000
χ394444-4-4-4-400000-440000000000000000000002-22-2-22-22000000000000000000
χ404444-4-4-4-400000-44000000000000000000000-22-222-22-2000000000000000000
χ4144-4-44-44-4000000000400000-400000000000022−22−22220000000000000000000000
χ4244-4-44-44-4000000000400000-4000000000000−222222−220000000000000000000000
χ4344-4-44-44-4000000000-400000400000000000000002i2−2i2−2i22i2000000000000000000
χ4444-4-44-44-4000000000-40000040000000000000000−2i22i22i2−2i2000000000000000000
χ4544-4-4-44-444i4i−4i−4i000−4i4i000-440000000000000000000000000000000000000000
χ4644-4-4-44-44−4i−4i4i4i0004i−4i000-440000000000000000000000000000000000000000
χ474-44-444-4-400004000000000-40000022−2222−22000000000000000000000000000000
χ484-44-444-4-400004000000000-400000−2222−2222000000000000000000000000000000
χ494-44-444-4-40000-400000000040000000002i2−2i22i2−2i200000000000000000000000000
χ504-44-444-4-40000-40000000004000000000−2i22i2−2i22i200000000000000000000000000
χ514-44-4-4-4444i−4i4i−4i0000000000000000000000000000000000000002i−2i2-20000000
χ524-44-4-4-4444i−4i4i−4i000000000000000000000000000000000000000−2i2i-220000000
χ534-44-4-4-444−4i4i−4i4i0000000000000000000000000000000000000002i−2i-220000000
χ544-44-4-4-444−4i4i−4i4i000000000000000000000000000000000000000−2i2i2-20000000
χ554-4-444-4-444-4-4400000000000000000000000000000000000000000000002i−2i2i−2i
χ564-4-444-4-444-4-440000000000000000000000000000000000000000000000−2i2i−2i2i
χ574-4-444-4-44-444-400000000000000000000000000000000000000000000002i−2i−2i2i
χ584-4-444-4-44-444-40000000000000000000000000000000000000000000000−2i2i2i−2i
χ594-4-44-444-400000000004-4000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ604-4-44-444-400000000004-400000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ614-4-44-444-40000000000-44000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-4-44-444-40000000000-4400000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000

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