Finite Group Databasebeta

← Group #166421

Character table — Group #166421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444442244444448888888822224444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-1111-1-11-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-111-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11-11111-1-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-111111-1-1-111-1-11-111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-1-11111-11-1-11-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-11-1-11-11-1-111111-1-111-1-1
χ1311111111-1-1-1-1-1-11-1-111111-1-111-111-1-11111-1-1-1-11-1-1-1-1-111-111111-1-1-1-111
χ1411111111-1-1-1-1-1-11-1-111111-1-111-111-1-1-1-1-1-111111-111-1-111-11-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-11-1-111111-1-111-1-1-1111111-1-1-1-1-11-1-1-11-111-111-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-111111-1-111-1-1-111-1-1-1-11111-1111-11-111-1-1-111-1-1-1-111
χ1722222222222222-2-2-22-2-2-220000-2222200000000-2-2000000000000000000
χ1822222222222222-2-2-22-2-2-220000-2-2-2-2-20000000022000000000000000000
χ19222222222222-2-22-2-2-2-2-22-20000200000000000000000220-2-20000000000
χ20222222222222-2-22-2-2-2-2-22-20000200000000000000000-2-20220000000000
χ21222222222222-2-2-222-222-2-222-2-2-20000000000000000-2002000000000000
χ22222222222222-2-2-222-222-2-2-2-222-20000000000000000200-2000000000000
χ2322222222-2-2-2-222222-2-2-22-20000-2000000000000000002-20-220000000000
χ2422222222-2-2-2-222222-2-2-22-20000-200000000000000000-2202-20000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2222220000000000000000-200-2000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2200000000000000002002000000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-220000222-2-200000000-22000000000000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-2200002-2-222000000002-2000000000000000000
χ292-222-2-22-222-2-22-20002000-2000002i−2i2i−2i22−2−222−2−2000000000000i2−i2i2−i20000
χ302-222-2-22-222-2-22-20002000-2000002i−2i2i−2i−2−222−2−222000000000000−i2i2−i2i20000
χ312-222-2-22-222-2-22-20002000-200000−2i2i−2i2i22−2−222−2−2000000000000−i2i2−i2i20000
χ322-222-2-22-222-2-22-20002000-200000−2i2i−2i2i−2−222−2−222000000000000i2−i2i2−i20000
χ332-222-2-22-2-2-222-220002000-2000002i−2i−2i2i22−2−2−2−222000000000000i2−i2−i2i20000
χ342-222-2-22-2-2-222-220002000-2000002i−2i−2i2i−2−22222−2−2000000000000−i2i2i2−i20000
χ352-222-2-22-2-2-222-220002000-200000−2i2i2i−2i22−2−2−2−222000000000000−i2i2i2−i20000
χ362-222-2-22-2-2-222-220002000-200000−2i2i2i−2i−2−22222−2−2000000000000i2−i2−i2i20000
χ37444-4-44-4-400000004i−4i000000000000002-22-22i−2i2i−2i00000000000000000000
χ38444-4-44-4-400000004i−4i00000000000000-22-22−2i2i−2i2i00000000000000000000
χ39444-4-44-4-40000000−4i4i000000000000002-22-2−2i2i−2i2i00000000000000000000
χ40444-4-44-4-40000000−4i4i00000000000000-22-222i−2i2i−2i00000000000000000000
χ4144-4-4-4-4444-44-400000000000000000000000000000000000000000002-22-2
χ4244-4-4-4-4444-44-40000000000000000000000000000000000000000000-22-22
χ4344-4-4-4-444-44-4400000000000000000000000000000000000000000002-2-22
χ4444-4-4-4-444-44-440000000000000000000000000000000000000000000-222-2
χ454-444-4-44-444-4-4-44000-400040000000000000000000000000000000000000
χ464-444-4-44-4-4-4444-4000-400040000000000000000000000000000000000000
χ474-44-44-4-44000000400000-4000000000000002i2−2i2−2i22i200000000000000000000
χ484-44-44-4-44000000400000-400000000000000−2i22i22i2−2i200000000000000000000
χ494-44-44-4-44000000-4000004000000000022−22−2222000000000000000000000000
χ504-44-44-4-44000000-40000040000000000−222222−22000000000000000000000000
χ514-4-44-44-4400000000004-400004-4000000000000000000000000000000000
χ524-4-44-44-4400000000004-40000-44000000000000000000000000000000000
χ534-4-44-44-440000000000-44004-400000000000000000000000000000000000
χ544-4-44-44-440000000000-4400-4400000000000000000000000000000000000
χ554-4-4-4444-44-4-44000000000000000000000000000002-20000002-200000000
χ564-4-4-4444-44-4-4400000000000000000000000000000-22000000-2200000000
χ574-4-4-4444-4-444-4000000000000000000000000000002-2000000-2200000000
χ584-4-4-4444-4-444-400000000000000000000000000000-220000002-200000000
χ5988-888-8-8-8000000000000000000000000000000000000000000000000000

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