Finite Group Databasebeta

← Group #170113

Character table — Group #170113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1
χ911111111-1-1-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-11
χ1111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-11-11-1-111-11
χ1211111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-11-1111-1-11-1
χ1311111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-11-111-111-1-1-11
χ1411111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-11-111-1-1-1111-1
χ1511111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-11-1-1111-1
χ1611111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1111-1-1-11
χ1722222222222222-2-2-2-2-22-2-2-22000022220000000000000000000000-2-2000000
χ1822222222222222-2-2-2-2-22-2-2-220000-2-2-2-2000000000000000000000022000000
χ19222222222222-2-2222-2-2-2-2-22-222220000000000000000000000-2-20000000000
χ20222222222222-2-2222-2-2-2-2-22-2-2-2-2-20000000000000000000000220000000000
χ21222222222222-2-2-2-2-222-222-2-20000000000000000000000002200-2-200000000
χ22222222222222-2-2-2-2-222-222-2-2000000000000000000000000-2-2002200000000
χ2322222222-2-2-2-2222-2-222-2-2-22-222-2-20000000000000000000000-220000000000
χ2422222222-2-2-2-2222-2-222-2-2-22-2-2-22200000000000000000000002-20000000000
χ2522222222-2-2-2-222-222-2-2-222-2-20000000000000000000000002-200-2200000000
χ2622222222-2-2-2-222-222-2-2-222-2-2000000000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-222222-2-2-22000022-2-20000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-222222-2-2-220000-2-22200000000000000000000002-2000000
χ2922-2-2-22-2222-2-22-2000002000-200002i−2i2i−2i22−2−222−2−20000000000000000i2−i2i2−i200
χ3022-2-2-22-2222-2-22-2000002000-200002i−2i2i−2i−2−222−2−2220000000000000000−i2i2−i2i200
χ3122-2-2-22-2222-2-22-2000002000-20000−2i2i−2i2i22−2−222−2−20000000000000000−i2i2−i2i200
χ3222-2-2-22-2222-2-22-2000002000-20000−2i2i−2i2i−2−222−2−2220000000000000000i2−i2i2−i200
χ3322-2-2-22-22-2-222-22000002000-200002i−2i−2i2i22−2−2−2−2220000000000000000i2−i2−i2i200
χ3422-2-2-22-22-2-222-22000002000-200002i−2i−2i2i−2−22222−2−20000000000000000−i2i2i2−i200
χ3522-2-2-22-22-2-222-22000002000-20000−2i2i2i−2i22−2−2−2−2220000000000000000−i2i2i2−i200
χ3622-2-2-22-22-2-222-22000002000-20000−2i2i2i−2i−2−22222−2−20000000000000000i2−i2−i2i200
χ372-222-22-2-22-22-200-22-200000202i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000
χ382-222-22-2-22-22-200-22-200000202i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000
χ392-222-22-2-22-22-200-22-20000020−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−2−222−2−22200000000000000
χ402-222-22-2-22-22-200-22-20000020−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i222−2−222−2−200000000000000
χ412-222-22-2-2-22-2200-2-2200000202i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i222−2−2−2−22200000000000000
χ422-222-22-2-2-22-2200-2-2200000202i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−2−22222−2−200000000000000
χ432-222-22-2-2-22-2200-2-220000020−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−2−22222−2−200000000000000
χ442-222-22-2-2-22-2200-2-220000020−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i222−2−2−2−22200000000000000
χ45444-44-4-4-40000000000004-400000000000000000022−2222−22000000000000000000
χ46444-44-4-4-40000000000004-4000000000000000000−2222−2222000000000000000000
χ47444-44-4-4-4000000000000-44000000000000000000000022−2222−2200000000000000
χ48444-44-4-4-4000000000000-440000000000000000000000−2222−222200000000000000
χ4944-4-4-44-4444-4-4-4400000-4000400000000000000000000000000000000000000
χ5044-4-4-44-44-4-4444-400000-4000400000000000000000000000000000000000000
χ514-444-44-4-44-44-4004-4400000-4000000000000000000000000000000000000000
χ524-444-44-4-4-44-440044-400000-4000000000000000000000000000000000000000
χ534-44-4-4-4440000000004-40000000000000000000002-2-222-2-2200000000000000
χ544-44-4-4-4440000000004-4000000000000000000000-222-2-222-200000000000000
χ554-44-4-4-444000000000-440000000000000000000002-2-22-222-200000000000000
χ564-44-4-4-444000000000-44000000000000000000000-222-22-2-2200000000000000
χ574-4-4-4444-44-4-44000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ584-4-4-4444-44-4-4400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ594-4-4-4444-4-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ604-4-4-4444-4-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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