Finite Group Databasebeta

← Group #170102

Character table — Group #170102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1
χ911111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-111-1-11-1
χ1011111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11-1-1-111-11
χ1111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-11-1-111-11
χ1211111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1111-1-11-1
χ1311111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1-11
χ1411111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-1111-1
χ1511111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-11-1-1111-1
χ1611111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1111-1-1-11
χ172222222222222-2-2-222-2-2-2-22-2002222000000000000000000000000-2-2000000
χ182222222222222-2-2-222-2-2-2-22-200-2-2-2-200000000000000000000000022000000
χ19222222222222-2222-2-2-2-2-2-2-22220000220000000000000000-2-2000000000000
χ20222222222222-2222-2-2-2-2-2-2-22-2-20000-2-2000000000000000022000000000000
χ21222222222222-2-2-2-2-2-22222-2-2000000000000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-22222-2-200000000000000000000000000-22-2200000000
χ2322222222-2-2-2-22-222-2-222-2-22-20022-2-2000000000000000000000000-22000000
χ2422222222-2-2-2-22-222-2-222-2-22-200-2-2220000000000000000000000002-2000000
χ2522222222-2-2-2-2-22-2-22222-2-2-22220000-2-200000000000000002-2000000000000
χ2622222222-2-2-2-2-22-2-22222-2-2-22-2-20000220000000000000000-22000000000000
χ2722222222-2-2-2-2-2-22222-2-222-2-2000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-22222-2-222-2-200000000000000000000000000-222-200000000
χ29222-2-2-22-222-2-2-20002-2000020002i−2i2i−2i0022−2−222−2−20000000000000000i2−i2i2−i200
χ30222-2-2-22-222-2-2-20002-2000020002i−2i2i−2i00−2−222−2−2220000000000000000−i2i2−i2i200
χ31222-2-2-22-222-2-2-20002-200002000−2i2i−2i2i0022−2−222−2−20000000000000000−i2i2−i2i200
χ32222-2-2-22-222-2-2-20002-200002000−2i2i−2i2i00−2−222−2−2220000000000000000i2−i2i2−i200
χ33222-2-2-22-2-2-222-2000-22000020002i−2i−2i2i0022−2−2−2−2220000000000000000i2−i2−i2i200
χ34222-2-2-22-2-2-222-2000-22000020002i−2i−2i2i00−2−22222−2−20000000000000000−i2i2i2−i200
χ35222-2-2-22-2-2-222-2000-2200002000−2i2i2i−2i0022−2−2−2−2220000000000000000−i2i2i2−i200
χ36222-2-2-22-2-2-222-2000-2200002000−2i2i2i−2i00−2−22222−2−20000000000000000i2−i2−i2i200
χ3722-222-2-2-22-22-20-22-2000000022i−2i00002i−2ii2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000
χ3822-222-2-2-22-22-20-22-2000000022i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000
χ3922-222-2-2-22-22-20-22-200000002−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2−2−222−2−22200000000000000
χ4022-222-2-2-22-22-20-22-200000002−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i222−2−222−2−200000000000000
χ4122-222-2-2-2-22-220-2-22000000022i−2i0000−2i2ii2−i2i2−i2−i2i2−i2i222−2−2−2−22200000000000000
χ4222-222-2-2-2-22-220-2-22000000022i−2i0000−2i2i−i2i2−i2i2i2−i2i2−i2−2−22222−2−200000000000000
χ4322-222-2-2-2-22-220-2-2200000002−2i2i00002i−2ii2−i2i2−i2−i2i2−i2i2−2−22222−2−200000000000000
χ4422-222-2-2-2-22-220-2-2200000002−2i2i00002i−2i−i2i2−i2i2i2−i2i2−i222−2−2−2−22200000000000000
χ45444-4-4-44-444-4-44000-440000-4000000000000000000000000000000000000000
χ46444-4-4-44-4-4-44440004-40000-4000000000000000000000000000000000000000
χ4744-444-4-4-44-44-404-440000000-400000000000000000000000000000000000000
χ4844-444-4-4-4-44-44044-40000000-400000000000000000000000000000000000000
χ4944-4-4-44-444-4-44000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ5044-4-4-44-444-4-4400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ5144-4-4-44-44-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ5244-4-4-44-44-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ534-444-4-4-4400000000004-4000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ544-444-4-4-4400000000004-400000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ554-444-4-4-440000000000-44000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ564-444-4-4-440000000000-4400000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ574-4-44-444-40000000000004-40000000000000000002i2−2i2−2i22i2000000000000000000
χ584-4-44-444-40000000000004-4000000000000000000−2i22i22i2−2i2000000000000000000
χ594-4-44-444-4000000000000-4400000000000000000000002i2−2i2−2i22i200000000000000
χ604-4-44-444-4000000000000-440000000000000000000000−2i22i22i2−2i200000000000000
χ618-88-888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-88-888000000000000000000000000000000000000000000000000000000

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