Finite Group Databasebeta

← Group #166949

Character table — Group #166949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444442244444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-111-1-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-11-1-111111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-111111-1-111-1-11-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1-11111111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-11-1-1-111111-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-11-11-1-111-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-111111-11-1-1-1-1-1111111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111111-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-11111-1111111-1-1-1-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-222-22222-200000000000000-20000-2000000000000
χ1822222222222222-2-2-2-2-222-2-2-2-2-2-200000000000000200002000000000000
χ19222222222222-2-2222-2-2-2-220000-222-2-200000000-22000000000000000000
χ20222222222222-2-2222-2-2-2-220000-2-2-222000000002-2000000000000000000
χ21222222222222-2-2-2-2-222-2-2-2000020000000000000002-20002-20000000000
χ22222222222222-2-2-2-2-222-2-2-200002000000000000000-22000-220000000000
χ2322222222-2-2-2-22222-222-2-2-20000-20000000000000002-2000-220000000000
χ2422222222-2-2-2-22222-222-2-2-20000-2000000000000000-220002-20000000000
χ2522222222-2-2-2-222-2-22-2-2-2-2200002222200000000-2-2000000000000000000
χ2622222222-2-2-2-222-2-22-2-2-2-2200002-2-2-2-20000000022000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-222-222-2-220000000000000020000-2000000000000
χ2822222222-2-2-2-2-2-222-2-2-222-2-2-222200000000000000-200002000000000000
χ292-2-2222-2-22i2i−2i−2i2i−2i000002-202-22i−2i0000022−2−2i2i2−i2−i20000000000002−2i2−i20000
χ302-2-2222-2-22i2i−2i−2i2i−2i000002-202-22i−2i00000−2−222−i2−i2i2i2000000000000−22−i2i20000
χ312-2-2222-2-22i2i−2i−2i2i−2i000002-20-22−2i2i0000022−2−2i2i2−i2−i2000000000000−22−i2i20000
χ322-2-2222-2-22i2i−2i−2i2i−2i000002-20-22−2i2i00000−2−222−i2−i2i2i20000000000002−2i2−i20000
χ332-2-2222-2-2−2i−2i2i2i−2i2i000002-202-2−2i2i0000022−2−2−i2−i2i2i20000000000002−2−i2i20000
χ342-2-2222-2-2−2i−2i2i2i−2i2i000002-202-2−2i2i00000−2−222i2i2−i2−i2000000000000−22i2−i20000
χ352-2-2222-2-2−2i−2i2i2i−2i2i000002-20-222i−2i0000022−2−2−i2−i2i2i2000000000000−22i2−i20000
χ362-2-2222-2-2−2i−2i2i2i−2i2i000002-20-222i−2i00000−2−222i2i2−i2−i20000000000002−2−i2i20000
χ3744-44-4-44-40000000004-400000000000000002i2−2i22i2−2i200000000000000000000
χ3844-44-4-44-40000000004-40000000000000000−2i22i2−2i22i200000000000000000000
χ3944-44-4-44-4000000000-440000000000002i2−2i22i2−2i2000000000000000000000000
χ4044-44-4-44-4000000000-44000000000000−2i22i2−2i22i2000000000000000000000000
χ4144-4-44-4-444i−4i4i−4i000000000000000000000000000000002i−2i0002-200000000
χ4244-4-44-4-444i−4i4i−4i00000000000000000000000000000000−2i2i000-2200000000
χ4344-4-44-4-44−4i4i−4i4i000000000000000000000000000000002i−2i000-2200000000
χ4444-4-44-4-44−4i4i−4i4i00000000000000000000000000000000−2i2i0002-200000000
χ454-444-4-4-440000004i−4i0000000000000002i−2i−2i2i2-2-2200000000000000000000
χ464-444-4-4-440000004i−4i000000000000000−2i2i2i−2i-222-200000000000000000000
χ474-444-4-4-44000000−4i4i0000000000000002i−2i−2i2i-222-200000000000000000000
χ484-444-4-4-44000000−4i4i000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ494-44-44-44-44-4-4400000000000000000000000000000000000000000002i−2i2i−2i
χ504-44-44-44-44-4-440000000000000000000000000000000000000000000−2i2i−2i2i
χ514-44-44-44-4-444-400000000000000000000000000000000000000000002i−2i−2i2i
χ524-44-44-44-4-444-40000000000000000000000000000000000000000000−2i2i2i−2i
χ534-4-4444-4-44i4i−4i−4i−4i4i00000-4400000000000000000000000000000000000000
χ544-4-4444-4-4−4i−4i4i4i4i−4i00000-4400000000000000000000000000000000000000
χ554-4-4-4-44440000000040000-4000004i−4i000000000000000000000000000000
χ564-4-4-4-44440000000040000-400000−4i4i000000000000000000000000000000
χ574-4-4-4-444400000000-40000400000004-40000000000000000000000000000
χ584-4-4-4-444400000000-4000040000000-440000000000000000000000000000
χ59888-8-88-8-8000000000000000000000000000000000000000000000000000

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