Finite Group Databasebeta

← Group #168447

Character table — Group #168447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888222444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-11-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111-11-1-11111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-1111-11-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1111-1-1-11-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-11-1-1-11-11-11111
χ911111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-11-1-1-111-111-1-1
χ1011111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-11-1-111
χ1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-1111-1-1
χ1211111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1111-111-1-1-111
χ1311111111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111111-1-1-111-1-1
χ1511111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-11-1111-1-11-1-1-1-1-111
χ1611111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11-111-1-111-1-11111-1-1
χ17222222222222222-2-2-2-2-2-2-22-200000000000000000000002000-200020-200000
χ18222222222222222-2-2-2-2-2-2-22-20000000000000000000000-20002000-20200000
χ19222222222222-2-2-22-2-222-2-2-22000000000000000000000002200-200000-20000
χ20222222222222-2-2-22-2-222-2-2-2200000000000000000000000-2-20020000020000
χ21222222222222-2-2-2-222-2-222-2-22222000000000000000000000-200000-2000000
χ22222222222222-2-2-2-222-2-222-2-2-2-2-2-20000000000000000000002000002000000
χ2322222222-2-2-2-222-2222-2-2-2-2-22000000000000000000000002-200-20000020000
χ2422222222-2-2-2-222-2222-2-2-2-2-2200000000000000000000000-2200200000-20000
χ2522222222-2-2-2-222-2-2-2-22222-2-222-2-2000000000000000000000200000-2000000
χ2622222222-2-2-2-222-2-2-2-22222-2-2-2-222000000000000000000000-2000002000000
χ2722222222-2-2-2-2-2-22-22222-2-22-2000000000000000000000020002000-20-200000
χ2822222222-2-2-2-2-2-22-22222-2-22-20000000000000000000000-2000-200020200000
χ29222-2-2-2-222i2i−2i−2i00002i−2i002-2002i−2i2-222−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000000000
χ30222-2-2-2-222i2i−2i−2i00002i−2i002-2002i−2i2-2−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000000000
χ31222-2-2-2-222i2i−2i−2i00002i−2i002-200−2i2i-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000000000
χ32222-2-2-2-222i2i−2i−2i00002i−2i002-200−2i2i-22−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000000000
χ33222-2-2-2-22−2i−2i2i2i0000−2i2i002-2002i−2i-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000000000
χ34222-2-2-2-22−2i−2i2i2i0000−2i2i002-2002i−2i-22−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000000000
χ35222-2-2-2-22−2i−2i2i2i0000−2i2i002-200−2i2i2-222−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000000000
χ36222-2-2-2-22−2i−2i2i2i0000−2i2i002-200−2i2i2-2−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000000000
χ37444-4-4-4-444i4i−4i−4i0000−4i4i00-440000000000000000000000000000000000000000
χ38444-4-4-4-44−4i−4i4i4i00004i−4i00-440000000000000000000000000000000000000000
χ3944-444-4-4-400000040000000-4000000000000022−2222−220000000000000000000000
χ4044-444-4-4-400000040000000-40000000000000−2222−22220000000000000000000000
χ4144-444-4-4-4000000-400000004000000000000000002i2−2i22i2−2i2000000000000000000
χ4244-444-4-4-4000000-40000000400000000000000000−2i22i2−2i22i2000000000000000000
χ4344-4-4-444-400004-400000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4444-4-4-444-400004-40000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4544-4-4-444-40000-4400000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ4644-4-4-444-40000-440000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ474-444-4-44-44-44-400000000000000000000000000000000000000000000002i−2i2i−2i
χ484-444-4-44-44-44-40000000000000000000000000000000000000000000000−2i2i−2i2i
χ494-444-4-44-4-44-4400000000000000000000000000000000000000000000002i−2i−2i2i
χ504-444-4-44-4-44-440000000000000000000000000000000000000000000000−2i2i2i−2i
χ514-44-444-4-44i−4i−4i4i000000000000000000000000000000002-20000002i−2i00000000
χ524-44-444-4-44i−4i−4i4i00000000000000000000000000000000-22000000−2i2i00000000
χ534-44-444-4-4−4i4i4i−4i000000000000000000000000000000002-2000000−2i2i00000000
χ544-44-444-4-4−4i4i4i−4i00000000000000000000000000000000-220000002i−2i00000000
χ554-4-44-44-44000000040000000-4000000002i2−2i22i2−2i200000000000000000000000000
χ564-4-44-44-44000000040000000-400000000−2i22i2−2i22i200000000000000000000000000
χ574-4-44-44-440000000-400000004000022−2222−22000000000000000000000000000000
χ584-4-44-44-440000000-4000000040000−2222−2222000000000000000000000000000000
χ594-4-4-44-44400000000004-4000000002-2-222-2-2200000000000000000000000000
χ604-4-4-44-44400000000004-400000000-222-2-222-200000000000000000000000000
χ614-4-4-44-4440000000000-44000000002-2-22-222-200000000000000000000000000
χ624-4-4-44-4440000000000-4400000000-222-22-2-2200000000000000000000000000

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