Finite Group Databasebeta

← Group #170329

Character table — Group #170329

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444422444444888888888888888822444444888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-111111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11111-1-1
χ911111111-1-1-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1-111-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-111-1-1-1-111-11
χ1111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-111-1-111-11
χ1211111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-11111-1-11-1
χ1311111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-11-1-11-111-1-1-11
χ1411111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-11-1-11-1-1-1111-1
χ1511111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1-11-11-1-1111-1
χ1611111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-111-1-1-1-111111111-1-1-1-11-11-1-11-1111-1-1-11
χ1722222222222222-2-2-2-2-22-2-2-220000222200000000000000000-200000-2000000
χ1822222222222222-2-2-2-2-22-2-2-220000-2-2-2-2000000000000000002000002000000
χ19222222222222-2-2222-2-2-2-2-22-200000000000000000000000000220-2-20000000
χ20222222222222-2-2222-2-2-2-2-22-200000000000000000000000000-2-20220000000
χ21222222222222-2-2-2-2-222-222-2-2222200000000000000000000-2000-2000000000
χ22222222222222-2-2-2-2-222-222-2-2-2-2-2-20000000000000000000020002000000000
χ2322222222-2-2-2-2222-2-222-2-2-22-2000000000000000000000000002-20-220000000
χ2422222222-2-2-2-2222-2-222-2-2-22-200000000000000000000000000-2202-20000000
χ2522222222-2-2-2-222-222-2-2-222-2-222-2-2000000000000000000002000-2000000000
χ2622222222-2-2-2-222-222-2-2-222-2-2-2-22200000000000000000000-20002000000000
χ2722222222-2-2-2-2-2-2-222222-2-2-22000022-2-200000000000000000-2000002000000
χ2822222222-2-2-2-2-2-2-222222-2-2-220000-2-22200000000000000000200000-2000000
χ29222-22-2-2-22i2i−2i−2i000002i−2i02-2002-22i−2i000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000
χ30222-22-2-2-22i2i−2i−2i000002i−2i02-2002-22i−2i0000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000000000
χ31222-22-2-2-22i2i−2i−2i000002i−2i02-200-22−2i2i000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000000000
χ32222-22-2-2-22i2i−2i−2i000002i−2i02-200-22−2i2i0000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000
χ33222-22-2-2-2−2i−2i2i2i00000−2i2i02-2002-2−2i2i000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000
χ34222-22-2-2-2−2i−2i2i2i00000−2i2i02-2002-2−2i2i0000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000000000
χ35222-22-2-2-2−2i−2i2i2i00000−2i2i02-200-222i−2i000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000000000
χ36222-22-2-2-2−2i−2i2i2i00000−2i2i02-200-222i−2i0000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000
χ3722-2-2-22-222-22-22-2000002000-200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000000000002−22−200
χ3822-2-2-22-222-22-22-2000002000-200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000−22−2200
χ3922-2-2-22-222-22-22-2000002000-20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000−22−2200
χ4022-2-2-22-222-22-22-2000002000-20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000000000002−22−200
χ4122-2-2-22-22-22-22-22000002000-200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200000000000000002−2−2200
χ4222-2-2-22-22-22-22-22000002000-200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000−222−200
χ4322-2-2-22-22-22-22-22000002000-20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000−222−200
χ4422-2-2-22-22-22-22-22000002000-20000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200000000000000002−2−2200
χ45444-44-4-4-44i4i−4i−4i00000−4i4i0-440000000000000000000000000000000000000000
χ46444-44-4-4-4−4i−4i4i4i000004i−4i0-440000000000000000000000000000000000000000
χ4744-44-4-44-44i−4i−4i4i000000000000000000002i−2i−2i2i-222-20000000000000000000000
χ4844-44-4-44-44i−4i−4i4i00000000000000000000−2i2i2i−2i2-2-220000000000000000000000
χ4944-44-4-44-4−4i4i4i−4i000000000000000000002i−2i−2i2i2-2-220000000000000000000000
χ5044-44-4-44-4−4i4i4i−4i00000000000000000000−2i2i2i−2i-222-20000000000000000000000
χ5144-4-4-44-444-44-4-4400000-4000400000000000000000000000000000000000000
χ5244-4-4-44-44-44-444-400000-4000400000000000000000000000000000000000000
χ534-4-4444-4-400000040000000-40000000000000000000002i2−2i22i2−2i200000000000000
χ544-4-4444-4-400000040000000-4000000000000000000000−2i22i2−2i22i200000000000000
χ554-4-4444-4-4000000-4000000040000000000000000022−2222−22000000000000000000
χ564-4-4444-4-4000000-40000000400000000000000000−2222−2222000000000000000000
χ574-4-4-44-44400000004-4000000000000000000000002-2-222-2-2200000000000000
χ584-4-4-44-44400000004-400000000000000000000000-222-2-222-200000000000000
χ594-4-4-44-4440000000-44000000000000000000000002-2-22-222-200000000000000
χ604-4-4-44-4440000000-4400000000000000000000000-222-22-2-2200000000000000
χ618-888-8-8-88000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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