Finite Group Databasebeta

← Group #168641

Character table — Group #168641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222222244444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-11-1-11-1-1111111-1-1-111-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-11-1-1111111-1-1-111-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-11-1-11-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1211111111-1-1-1-11-1-11-1-1111111-1-1-1-1-111-1-111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-11-1-11-1-11111-1-111-111-1-1-1-1111111-1-1-1-11-1-11-11-1-111-1-1111-1
χ1411111111-1-1-1-11-1-11-1-11111-1-111-111-1-1-1-111-1-1-1-111111-1-11-1111-1-111-1-1-11
χ1511111111-1-1-1-11-1-11-1-11111-1-111-1-1-11111-1-11111-1-1-1-1-11-111-1-1-11111-1-1-11
χ1611111111-1-1-1-11-1-11-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-11-111-111-1-1-1-1111-1
χ17222222222222222-2-2-2-2-22-22222-2000000000000000000-2-2000000000000
χ18222222222222222-2-2-2-2-22-2-2-2-2-2-200000000000000000022000000000000
χ19222222222222-2-2-2222-2-2-220000-200002222000000000000-2-20000000000
χ20222222222222-2-2-2222-2-2-220000-20000-2-2-2-2000000000000220000000000
χ21222222222222-2-2-2-2-2-222-2-2000022222000000000000-2-200000000000000
χ22222222222222-2-2-2-2-2-222-2-200002-2-2-2-20000000000002200000000000000
χ2322222222-2-2-2-22-2-2-222-2-22-222-2-22000000000000000000-22000000000000
χ2422222222-2-2-2-22-2-2-222-2-22-2-2-22220000000000000000002-2000000000000
χ2522222222-2-2-2-2-2222-2-2-2-2-2200002000022-2-2000000000000-220000000000
χ2622222222-2-2-2-2-2222-2-2-2-2-22000020000-2-2220000000000002-20000000000
χ2722222222-2-2-2-2-222-22222-2-20000-222-2-2000000000000-2200000000000000
χ2822222222-2-2-2-2-222-22222-2-20000-2-2-2220000000000002-200000000000000
χ292222-2-2-2-222-2-222-200000-202-22-200000000022−2−222−2−20000002−22−2000000
χ302222-2-2-2-222-2-222-200000-202-22-2000000000−2−222−2−222000000−22−22000000
χ312222-2-2-2-222-2-222-200000-20-22-2200000000022−2−222−2−2000000−22−22000000
χ322222-2-2-2-222-2-222-200000-20-22-22000000000−2−222−2−2220000002−22−2000000
χ332222-2-2-2-2-2-2222-2200000-202-2-2200000000022−2−2−2−2220000002−2−22000000
χ342222-2-2-2-2-2-2222-2200000-202-2-22000000000−2−22222−2−2000000−222−2000000
χ352222-2-2-2-2-2-2222-2200000-20-222-200000000022−2−2−2−222000000−222−2000000
χ362222-2-2-2-2-2-2222-2200000-20-222-2000000000−2−22222−2−20000002−2−22000000
χ372-2-222-2-222-22-200022-2000-20000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000002−22−200
χ382-2-222-2-222-22-200022-2000-20000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000−22−2200
χ392-2-222-2-222-22-200022-2000-2000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000−22−2200
χ402-2-222-2-222-22-200022-2000-2000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000002−22−200
χ412-2-222-2-22-22-220002-22000-20000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200000000002−2−2200
χ422-2-222-2-22-22-220002-22000-20000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000−222−200
χ432-2-222-2-22-22-220002-22000-2000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000−222−200
χ442-2-222-2-22-22-220002-22000-2000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200000000002−2−2200
χ454444-4-4-4-444-4-4-4-4400000400000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-44-400000400000000000000000000000000000000000000
χ4744-4-444-4-400000000004-40000000004-40000000000000000000000000000
χ4844-4-444-4-400000000004-4000000000-440000000000000000000000000000
χ4944-4-444-4-40000000000-4400000004-4000000000000000000000000000000
χ5044-4-444-4-40000000000-440000000-44000000000000000000000000000000
χ514-4-444-4-444-44-4000-4-4400040000000000000000000000000000000000000
χ524-4-444-4-44-44-44000-44-400040000000000000000000000000000000000000
χ534-4-44-444-44-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ544-4-44-444-44-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ554-4-44-444-4-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ564-4-44-444-4-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5788-8-8-8-888000000000000000000000000000000000000000000000000000
χ588-88-88-88-8000000000000000000000000000000000000000000000000000
χ598-88-8-88-88000000000000000000000000000000000000000000000000000

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