Finite Group Databasebeta

← Group #167408

Character table — Group #167408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1111-11-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-11-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-11-11111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-11-111-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-11-1-111-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111
χ1722222222222222222-2-2-2-2-22-2-2222200000000000000000000-20-20000000000000
χ1822222222222222222-2-2-2-2-22-2-2-2-2-2-2000000000000000000002020000000000000
χ19222222222222-2-2-2-2-2222-2-2-22-200000000000000000000000002000-22-200000000
χ20222222222222-2-2-2-2-2222-2-2-22-20000000000000000000000000-20002-2200000000
χ21222222222222-2-2-2-2-2-2-2-222-2-22000022-2-20000000000000000000-2200000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-220000-2-22200000000000000000002-200000000000
χ2322222222-2-2-2-22222-22-2-2-2-2-22200000000000000000000000002000-2-2200000000
χ2422222222-2-2-2-22222-22-2-2-2-2-2220000000000000000000000000-200022-200000000
χ2522222222-2-2-2-22222-2-22222-2-2-2000022220000000000000000000-2-200000000000
χ2622222222-2-2-2-22222-2-22222-2-2-20000-2-2-2-200000000000000000002200000000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-2222-2-20000000000000000000020-20000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-22-2-22200000000000000000000-2020000000000000
χ2922-222-2-2-200002i2i−2i−2i002i−2i2-200000002i−2i2-2i2i2−i2−i222−2−222−2−2i2i2−i2−i20000000000000000
χ3022-222-2-2-200002i2i−2i−2i002i−2i2-200000002i−2i2-2−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000000000
χ3122-222-2-2-200002i2i−2i−2i002i−2i2-20000000−2i2i-22i2i2−i2−i222−2−2−2−222−i2−i2i2i20000000000000000
χ3222-222-2-2-200002i2i−2i−2i002i−2i2-20000000−2i2i-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i20000000000000000
χ3322-222-2-2-20000−2i−2i2i2i00−2i2i2-200000002i−2i-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i20000000000000000
χ3422-222-2-2-20000−2i−2i2i2i00−2i2i2-200000002i−2i-22−i2−i2i2i222−2−2−2−222i2i2−i2−i20000000000000000
χ3522-222-2-2-20000−2i−2i2i2i00−2i2i2-20000000−2i2i2-2i2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000000000
χ3622-222-2-2-20000−2i−2i2i2i00−2i2i2-20000000−2i2i2-2−i2−i2i2i222−2−222−2−2−i2−i2i2i20000000000000000
χ372-2-22-222-222-2-22-22-2200000-2002i−2i2i−2i0000000000002−22−22−22−2000000000000i2−i2i2−i2
χ382-2-22-222-222-2-22-22-2200000-2002i−2i2i−2i000000000000−22−22−22−22000000000000−i2i2−i2i2
χ392-2-22-222-222-2-22-22-2200000-200−2i2i−2i2i0000000000002−22−22−22−2000000000000−i2i2−i2i2
χ402-2-22-222-222-2-22-22-2200000-200−2i2i−2i2i000000000000−22−22−22−22000000000000i2−i2i2−i2
χ412-2-22-222-2-2-222-22-22200000-2002i−2i−2i2i0000000000002−22−2−22−22000000000000i2−i2−i2i2
χ422-2-22-222-2-2-222-22-22200000-2002i−2i−2i2i000000000000−22−222−22−2000000000000−i2i2i2−i2
χ432-2-22-222-2-2-222-22-22200000-200−2i2i2i−2i0000000000002−22−2−22−22000000000000−i2i2i2−i2
χ442-2-22-222-2-2-222-22-22200000-200−2i2i2i−2i000000000000−22−222−22−2000000000000i2−i2−i2i2
χ4544-444-4-4-400004i4i−4i−4i00−4i4i-440000000000000000000000000000000000000000000
χ4644-444-4-4-40000−4i−4i4i4i004i−4i-440000000000000000000000000000000000000000000
χ4744-4-4-44-444-44-40000000000000000000000000000000000000000000002i−2i2i−2i0000
χ4844-4-4-44-444-44-4000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ4944-4-4-44-44-44-440000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5044-4-4-44-44-44-44000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ514-444-4-4-4400004i−4i−4i4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ524-444-4-4-4400004i−4i−4i4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ534-444-4-4-440000−4i4i4i−4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ544-444-4-4-440000−4i4i4i−4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ554-44-444-4-44-4-440000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ564-44-444-4-44-4-44000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ574-44-444-4-4-444-40000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ584-44-444-4-4-444-4000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ594-4-44-444-444-4-4-44-44-4000004000000000000000000000000000000000000000000
χ604-4-44-444-4-4-4444-44-4-4000004000000000000000000000000000000000000000000
χ614-4-4-44-444000000000400000-400000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4-44-444000000000400000-40000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4-44-444000000000-400000400000000022−22−22220000000000000000000000000000
χ644-4-4-44-444000000000-4000004000000000−222222−220000000000000000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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