Finite Group Databasebeta

← Group #167571

Character table — Group #167571

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444424444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-1-1-11-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-11-1111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11-1-11-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1111-1-1-11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-11-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-11-111-1-1-1-1-1-111
χ172222222222222222-2-2-2-222-2-2-200220022000000000000000000-200-20000000000
χ182222222222222222-2-2-2-222-2-2-200-2-200-2-200000000000000000020020000000000
χ19222222222222-2-2-2-222-2-2-2-222-20000000000000000000000000002002-20-2000000
χ20222222222222-2-2-2-222-2-2-2-222-2000000000000000000000000000-200-2202000000
χ21222222222222-2-2-2-2-2-222-2-2-2-222200-2-200000000000000000000002000-20000000
χ22222222222222-2-2-2-2-2-222-2-2-2-22-2-200220000000000000000000000-200020000000
χ2322222222-2-2-2-222222222-2-2-2-2-22200220000000000000000000000-2000-20000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-200-2-20000000000000000000000200020000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2222000000000000000000000000000200-220-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2222000000000000000000000000000-2002-202000000
χ2722222222-2-2-2-2-2-2-2-222-2-222-2-22002200-2-2000000000000000000200-20000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222-2-2200-2-20022000000000000000000-20020000000000
χ2922-22-2-22-22i2i−2i−2i2i2i−2i−2i00002-2000002i−2i002-200000000i2i2−i2−i222−2−20000000000002−2i2−i2
χ3022-22-2-22-22i2i−2i−2i2i2i−2i−2i00002-2000002i−2i002-200000000−i2−i2i2i2−2−222000000000000−22−i2i2
χ3122-22-2-22-22i2i−2i−2i2i2i−2i−2i00002-200000−2i2i00-2200000000i2i2−i2−i222−2−2000000000000−22−i2i2
χ3222-22-2-22-22i2i−2i−2i2i2i−2i−2i00002-200000−2i2i00-2200000000−i2−i2i2i2−2−2220000000000002−2i2−i2
χ3322-22-2-22-2−2i−2i2i2i−2i−2i2i2i00002-2000002i−2i00-2200000000i2i2−i2−i2−2−2220000000000002−2−i2i2
χ3422-22-2-22-2−2i−2i2i2i−2i−2i2i2i00002-2000002i−2i00-2200000000−i2−i2i2i222−2−2000000000000−22i2−i2
χ3522-22-2-22-2−2i−2i2i2i−2i−2i2i2i00002-200000−2i2i002-200000000i2i2−i2−i2−2−222000000000000−22i2−i2
χ3622-22-2-22-2−2i−2i2i2i−2i−2i2i2i00002-200000−2i2i002-200000000−i2−i2i2i222−2−20000000000002−2−i2i2
χ372-2-2222-2-200002i−2i2i−2i2i−2i2-2000002-2002i−2i0022−2−2i2i2−i2−i22−22−2i2−i2i2−i20000000000000000
χ382-2-2222-2-200002i−2i2i−2i2i−2i2-2000002-2002i−2i00−2−222−i2−i2i2i2−22−22−i2i2−i2i20000000000000000
χ392-2-2222-2-200002i−2i2i−2i2i−2i2-200000-2200−2i2i0022−2−2i2i2−i2−i2−22−22−i2i2−i2i20000000000000000
χ402-2-2222-2-200002i−2i2i−2i2i−2i2-200000-2200−2i2i00−2−222−i2−i2i2i22−22−2i2−i2i2−i20000000000000000
χ412-2-2222-2-20000−2i2i−2i2i−2i2i2-2000002-200−2i2i0022−2−2−i2−i2i2i22−22−2−i2i2−i2i20000000000000000
χ422-2-2222-2-20000−2i2i−2i2i−2i2i2-2000002-200−2i2i00−2−222i2i2−i2−i2−22−22i2−i2i2−i20000000000000000
χ432-2-2222-2-20000−2i2i−2i2i−2i2i2-200000-22002i−2i0022−2−2−i2−i2i2i2−22−22i2−i2i2−i20000000000000000
χ442-2-2222-2-20000−2i2i−2i2i−2i2i2-200000-22002i−2i00−2−222i2i2−i2−i22−22−2−i2i2−i2i20000000000000000
χ4544-44-4-44-44i4i−4i−4i−4i−4i4i4i0000-440000000000000000000000000000000000000000000
χ4644-44-4-44-4−4i−4i4i4i4i4i−4i−4i0000-440000000000000000000000000000000000000000000
χ4744-4-44-4-44000000000000004-400000000000002i2−2i22i2−2i2000000000000000000000000
χ4844-4-44-4-44000000000000004-40000000000000−2i22i2−2i22i2000000000000000000000000
χ4944-4-44-4-4400000000000000-440000000002i2−2i22i2−2i20000000000000000000000000000
χ5044-4-44-4-4400000000000000-44000000000−2i22i2−2i22i20000000000000000000000000000
χ514-444-4-4-4400004-4-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ524-444-4-4-4400004-4-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-444-4-4-440000-444-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ544-444-4-4-440000-444-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ554-44-44-44-44i−4i4i−4i0000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ564-44-44-44-44i−4i4i−4i000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ574-44-44-44-4−4i4i−4i4i0000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ584-44-44-44-4−4i4i−4i4i000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ594-4-4444-4-400004i−4i4i−4i−4i4i-44000000000000000000000000000000000000000000000
χ604-4-4444-4-40000−4i4i−4i4i4i−4i-44000000000000000000000000000000000000000000000
χ614-4-4-4-44444-4-4400000000000000000000000000000000000002-2000000002-20000
χ624-4-4-4-44444-4-440000000000000000000000000000000000000-2200000000-220000
χ634-4-4-4-4444-444-400000000000000000000000000000000000002-200000000-220000
χ644-4-4-4-4444-444-40000000000000000000000000000000000000-22000000002-20000
χ65888-8-88-8-8000000000000000000000000000000000000000000000000000000000

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