Finite Group Databasebeta

← Group #167604

Character table — Group #167604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444424444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-11111111111111111-1-11-1-1-1-1-11-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-11111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1-1-11111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-11-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-111-11-1-1-1-111
χ172222222222222222-2-2-2-2-2-222-2002200220000000000000000-200-2000000000000
χ182222222222222222-2-2-2-2-2-222-200-2-200-2-200000000000000002002000000000000
χ19222222222222-2-2-2-222-2-222-2-2-222002200000000000000000000-200000-20000000
χ20222222222222-2-2-2-222-2-222-2-2-2-2-200-2-20000000000000000000020000020000000
χ21222222222222-2-2-2-2-2-222-2-2-2-220000000000000000000000000200-22000-2000000
χ22222222222222-2-2-2-2-2-222-2-2-2-220000000000000000000000000-2002-20002000000
χ2322222222-2-2-2-222222222-2-2-2-2-200000000000000000000000002002-2000-2000000
χ2422222222-2-2-2-222222222-2-2-2-2-20000000000000000000000000-200-220002000000
χ2522222222-2-2-2-22222-2-2-2-222-2-222200-2-200000000000000000000200000-20000000
χ2622222222-2-2-2-22222-2-2-2-222-2-22-2-2002200000000000000000000-20000020000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2222002200-2-20000000000000000200-2000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222200-2-200220000000000000000-2002000000000000
χ292-222-2-2-222i2i−2i−2i2i2i−2i−2i0000002-20002-2002i−2i00000000i2i2−i2−i222−2−2000000000000i2−i22−2
χ302-222-2-2-222i2i−2i−2i2i2i−2i−2i0000002-20002-2002i−2i00000000−i2−i2i2i2−2−222000000000000−i2i2−22
χ312-222-2-2-222i2i−2i−2i2i2i−2i−2i0000002-2000-2200−2i2i00000000i2i2−i2−i222−2−2000000000000−i2i2−22
χ322-222-2-2-222i2i−2i−2i2i2i−2i−2i0000002-2000-2200−2i2i00000000−i2−i2i2i2−2−222000000000000i2−i22−2
χ332-222-2-2-22−2i−2i2i2i−2i−2i2i2i0000002-20002-200−2i2i00000000i2i2−i2−i2−2−222000000000000i2−i2−22
χ342-222-2-2-22−2i−2i2i2i−2i−2i2i2i0000002-20002-200−2i2i00000000−i2−i2i2i222−2−2000000000000−i2i22−2
χ352-222-2-2-22−2i−2i2i2i−2i−2i2i2i0000002-2000-22002i−2i00000000i2i2−i2−i2−2−222000000000000−i2i22−2
χ362-222-2-2-22−2i−2i2i2i−2i−2i2i2i0000002-2000-22002i−2i00000000−i2−i2i2i222−2−2000000000000i2−i2−22
χ372-22-22-22-22i−2i2i−2i00002i−2i002-20002-2002i−2i00i2i2−i2−i222−2−2i2−i2i2−i22−22−20000000000000000
χ382-22-22-22-22i−2i2i−2i00002i−2i002-20002-2002i−2i00−i2−i2i2i2−2−222−i2i2−i2i2−22−220000000000000000
χ392-22-22-22-22i−2i2i−2i00002i−2i002-2000-2200−2i2i00i2i2−i2−i222−2−2−i2i2−i2i2−22−220000000000000000
χ402-22-22-22-22i−2i2i−2i00002i−2i002-2000-2200−2i2i00−i2−i2i2i2−2−222i2−i2i2−i22−22−20000000000000000
χ412-22-22-22-2−2i2i−2i2i0000−2i2i002-20002-200−2i2i00i2i2−i2−i2−2−222i2−i2i2−i2−22−220000000000000000
χ422-22-22-22-2−2i2i−2i2i0000−2i2i002-20002-200−2i2i00−i2−i2i2i222−2−2−i2i2−i2i22−22−20000000000000000
χ432-22-22-22-2−2i2i−2i2i0000−2i2i002-2000-22002i−2i00i2i2−i2−i2−2−222−i2i2−i2i22−22−20000000000000000
χ442-22-22-22-2−2i2i−2i2i0000−2i2i002-2000-22002i−2i00−i2−i2i2i222−2−2i2−i2i2−i2−22−220000000000000000
χ45444-4-44-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ46444-4-44-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ47444-4-44-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ48444-4-44-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
χ4944-4-44-4-4400004i−4i4i−4i000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ5044-4-44-4-4400004i−4i4i−4i00000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ5144-4-44-4-440000−4i4i−4i4i000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ5244-4-44-4-440000−4i4i−4i4i00000000000000000-22-222i−2i2i−2i000000000000000000000000
χ534-444-4-4-444i4i−4i−4i−4i−4i4i4i000000-4400000000000000000000000000000000000000000
χ544-444-4-4-44−4i−4i4i4i4i4i−4i−4i000000-4400000000000000000000000000000000000000000
χ554-44-44-44-44i−4i4i−4i0000−4i4i00-440000000000000000000000000000000000000000000
χ564-44-44-44-4−4i4i−4i4i00004i−4i00-440000000000000000000000000000000000000000000
χ574-4-4444-4-400000000004-4000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-4-4444-4-400000000004-400000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-4-4444-4-40000000000-4400000000000002i2−2i2−2i22i20000000000000000000000000000
χ604-4-4444-4-40000000000-440000000000000−2i22i22i2−2i20000000000000000000000000000
χ614-4-4-4-444400004-4-440000000000000000000000000000000000000002-2002-20000
χ624-4-4-4-444400004-4-44000000000000000000000000000000000000000-2200-220000
χ634-4-4-4-44440000-444-40000000000000000000000000000000000000002-200-220000
χ644-4-4-4-44440000-444-4000000000000000000000000000000000000000-22002-20000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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