Finite Group Databasebeta

← Group #167102

Character table — Group #167102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422222244488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-11-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-11111-1-1-1-11111-1-1-1-11-11-11-111-1-11-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111-11-11-1-1-1111-1-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-111-1-1-111-11-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-111-111-1-1-1111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1111-1-1-11-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11-1-111-1111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-11-1-1111-111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-11-1-11-1111-1-11-1-1-111
χ1722222222222222222-2-2-2-22-2-2000022-222000000000000000000-2-2000000000000
χ1822222222222222222-2-2-2-22-2-20000-2-2-2-2-200000000000000000022000000000000
χ19222222222222-2-2-2-2-22-2-2-2-22-222-2-20020000000000000000000000-220000000000
χ20222222222222-2-2-2-2-22-2-2-2-22-2-2-22200200000000000000000000002-20000000000
χ21222222222222-2-2-2-2-2-2222-2-22000000-20000000000000000002-200000000-220000
χ22222222222222-2-2-2-2-2-2222-2-22000000-2000000000000000000-22000000002-20000
χ2322222222-2-2-2-22222-2222-2-22-2222200-20000000000000000000000-2-20000000000
χ2422222222-2-2-2-22222-2222-2-22-2-2-2-2-200-20000000000000000000000220000000000
χ2522222222-2-2-2-22222-2-2-2-22-2-2200000020000000000000000002200000000-2-20000
χ2622222222-2-2-2-22222-2-2-2-22-2-220000002000000000000000000-2-200000000220000
χ2722222222-2-2-2-2-2-2-2-22-222-22-2-20000222-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-22-2-20000-2-22220000000000000000002-2000000000000
χ2922-2-22-2-2222-2-222-2-220000-20000002-202-200000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2
χ3022-2-22-2-2222-2-222-2-220000-20000002-202-200000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2
χ3122-2-22-2-2222-2-222-2-220000-2000000-220-2200000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2
χ3222-2-22-2-2222-2-222-2-220000-2000000-220-2200000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2
χ3322-2-22-2-22-2-222-2-22220000-20000002-20-2200000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2
χ3422-2-22-2-22-2-222-2-22220000-20000002-20-2200000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2
χ3522-2-22-2-22-2-222-2-22220000-2000000-2202-200000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2
χ3622-2-22-2-22-2-222-2-22220000-2000000-2202-200000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2
χ372-222-2-2-2200002-22-2022-200-202-22-200000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-222-2-2-2200002-22-2022-200-202-22-200000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-222-2-2-2200002-22-2022-200-20-22-2200000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-222-2-2-2200002-22-2022-200-20-22-2200000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-222-2-2-220000-22-2202-2200-202-2-2200000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-222-2-2-220000-22-2202-2200-202-2-2200000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-222-2-2-220000-22-2202-2200-20-222-200000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-222-2-2-220000-22-2202-2200-20-222-200000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ45444-4-44-4-44i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i000000
χ46444-4-44-4-44i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i000000
χ47444-4-44-4-4−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i000000
χ48444-4-44-4-4−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i000000
χ4944-44-4-44-44i−4i−4i4i0000000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ5044-44-4-44-44i−4i−4i4i000000000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ5144-44-4-44-4−4i4i4i−4i0000000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ5244-44-4-44-4−4i4i4i−4i000000000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ5344-4-44-4-4444-4-4-4-444-4000040000000000000000000000000000000000000000000
χ5444-4-44-4-44-4-44444-4-4-4000040000000000000000000000000000000000000000000
χ554-444-4-4-4400004-44-40-4-44004000000000000000000000000000000000000000000
χ564-444-4-4-440000-44-440-44-4004000000000000000000000000000000000000000000
χ574-4-4444-4-4000000000000400-400000000000002i2−2i2−2i22i2000000000000000000000000
χ584-4-4444-4-4000000000000400-40000000000000−2i22i22i2−2i2000000000000000000000000
χ594-4-4444-4-4000000000000-400400000000022−22−22220000000000000000000000000000
χ604-4-4444-4-4000000000000-4004000000000−222222−220000000000000000000000000000
χ614-4-4-4-444400004-4-4400000000000000000000000002-2-222-2-220000000000000000
χ624-4-4-4-444400004-4-440000000000000000000000000-222-2-222-20000000000000000
χ634-4-4-4-44440000-444-400000000000000000000000002-2-22-222-20000000000000000
χ644-4-4-4-44440000-444-40000000000000000000000000-222-22-2-220000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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