Finite Group Databasebeta

← Group #168221

Character table — Group #168221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888222224444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-11-1-11-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-111-111-1-11-1-1-111-1-1
χ1011111111-1-1-1-11-1-11-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-1-1-111-1111-1-111
χ1111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11-111-1-111
χ1211111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-111-11-1-111-1-1
χ1311111111-1-1-1-11-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-11-1-1111-11111-1-1
χ1411111111-1-1-1-11-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-11-1-1-1-111
χ1511111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-11-1111-1-1111-1-1-1-1-111
χ1611111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1-111111-1-1
χ172222222222222-2-2-2-2-222-2-22-222220000000000000000-20000-2000000000000
χ182222222222222-2-2-2-2-222-2-22-2-2-2-2-20000000000000000200002000000000000
χ19222222222222-222-2-2-2-2-222-2-2000000000000000000000000002-22-200000000
χ20222222222222-222-2-2-2-2-222-2-200000000000000000000000000-22-2200000000
χ21222222222222-2-2-2222-2-2-2-2-220000000000000000000002-20000000-22000000
χ22222222222222-2-2-2222-2-2-2-2-22000000000000000000000-2200000002-2000000
χ2322222222-2-2-2-2222-222-2-2-2-22-222-2-20000000000000000-200002000000000000
χ2422222222-2-2-2-2222-222-2-2-2-22-2-2-222000000000000000020000-2000000000000
χ2522222222-2-2-2-2-2222-2-222-2-2-22000000000000000000000220000000-2-2000000
χ2622222222-2-2-2-2-2222-2-222-2-2-22000000000000000000000-2-2000000022000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000-222-200000000
χ29222-2-2-2-2222-2-22000002-200-202i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000
χ30222-2-2-2-2222-2-22000002-200-202i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000
χ31222-2-2-2-2222-2-22000002-200-20−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000
χ32222-2-2-2-2222-2-22000002-200-20−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000
χ33222-2-2-2-22-2-222200000-2200-202i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000
χ34222-2-2-2-22-2-222200000-2200-202i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000
χ35222-2-2-2-22-2-222200000-2200-20−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000
χ36222-2-2-2-22-2-222200000-2200-20−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000
χ37444-4-4-4-4444-4-4-400000-44004000000000000000000000000000000000000000
χ38444-4-4-4-44-4-444-4000004-4004000000000000000000000000000000000000000
χ3944-44-44-4-44i−4i4i−4i00000000000000000000000000000000000000000000002-22i−2i
χ4044-44-44-4-44i−4i4i−4i0000000000000000000000000000000000000000000000-22−2i2i
χ4144-44-44-4-4−4i4i−4i4i00000000000000000000000000000000000000000000002-2−2i2i
χ4244-44-44-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000-222i−2i
χ4344-4-44-44-44i−4i−4i4i000000000000000000000000000000000002-200000002i−2i0000
χ4444-4-44-44-44i−4i−4i4i00000000000000000000000000000000000-220000000−2i2i0000
χ4544-4-44-44-4−4i4i4i−4i000000000000000000000000000000000002-20000000−2i2i0000
χ4644-4-44-44-4−4i4i4i−4i00000000000000000000000000000000000-2200000002i−2i0000
χ474-4444-4-4-4000000004i−4i00000000002-22-22i−2i2i−2i00000000000000000000000000
χ484-4444-4-4-4000000004i−4i0000000000-22-22−2i2i−2i2i00000000000000000000000000
χ494-4444-4-4-400000000−4i4i00000000002-22-2−2i2i−2i2i00000000000000000000000000
χ504-4444-4-4-400000000−4i4i0000000000-22-222i−2i2i−2i00000000000000000000000000
χ514-44-4-444-4000000040000000-400002i2−2i2−2i22i2000000000000000000000000000000
χ524-44-4-444-4000000040000000-40000−2i22i22i2−2i2000000000000000000000000000000
χ534-44-4-444-40000000-4000000040000000022−22−222200000000000000000000000000
χ544-44-4-444-40000000-40000000400000000−222222−2200000000000000000000000000
χ554-4-44-4-444000004-40000000000000000000002-22-22-22-2000000000000000000
χ564-4-44-4-444000004-4000000000000000000000-22-22-22-22000000000000000000
χ574-4-44-4-44400000-440000000000000000000002-22-2-22-22000000000000000000
χ584-4-44-4-44400000-44000000000000000000000-22-222-22-2000000000000000000
χ594-4-4-444-440000000000004-40000000000000022−22−22220000000000000000000000
χ604-4-4-444-440000000000004-400000000000000−222222−220000000000000000000000
χ614-4-4-444-44000000000000-4400000000000000000022−22−2222000000000000000000
χ624-4-4-444-44000000000000-44000000000000000000−222222−22000000000000000000

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