Finite Group Databasebeta

← Group #167229

Character table — Group #167229

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422224444488888888888888882444444444448888
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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111-1-111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111-1-1111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-11-1-111-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-1-111
χ1722222222222222222-2-2-2-22-2-20000-222220000000000000000-2-200000000000000
χ1822222222222222222-2-2-2-22-2-20000-2-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-2-22-2-2-2-22-2000020000000000000000000000002-22-200000000
χ20222222222222-2-2-2-2-22-2-2-2-22-200002000000000000000000000000-22-2200000000
χ21222222222222-2-2-2-2-2-2222-2-222222-20000000000000000000000-2-2000000000000
χ22222222222222-2-2-2-2-2-2222-2-22-2-2-2-2-2000000000000000000000022000000000000
χ2322222222-2-2-2-22222-22-222-22-20000-20000000000000000000000002-2-2200000000
χ2422222222-2-2-2-22222-22-222-22-20000-2000000000000000000000000-222-200000000
χ2522222222-2-2-2-22222-2-22-2-2-2-2222-2-220000000000000000000000-22000000000000
χ2622222222-2-2-2-22222-2-22-2-2-2-22-2-222200000000000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-2-20000222-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2-200002-2-22200000000000000002-200000000000000
χ2922-2-222-2-222-2-222-2-2-20000200000002i−2i2i−2i0000000022−2−222−2−2000000000000i2−i2i2−i2
χ3022-2-222-2-222-2-222-2-2-20000200000002i−2i2i−2i00000000−2−222−2−222000000000000−i2i2−i2i2
χ3122-2-222-2-222-2-222-2-2-2000020000000−2i2i−2i2i0000000022−2−222−2−2000000000000−i2i2−i2i2
χ3222-2-222-2-222-2-222-2-2-2000020000000−2i2i−2i2i00000000−2−222−2−222000000000000i2−i2i2−i2
χ3322-2-222-2-2-2-222-2-222-20000200000002i−2i−2i2i0000000022−2−2−2−222000000000000i2−i2−i2i2
χ3422-2-222-2-2-2-222-2-222-20000200000002i−2i−2i2i00000000−2−22222−2−2000000000000−i2i2i2−i2
χ3522-2-222-2-2-2-222-2-222-2000020000000−2i2i2i−2i0000000022−2−2−2−222000000000000−i2i2i2−i2
χ3622-2-222-2-2-2-222-2-222-2000020000000−2i2i2i−2i00000000−2−22222−2−2000000000000i2−i2−i2i2
χ372-2-2-22-2222-22-2000000-22-20022-22-20000022−2−222−2−22−22−22−22−20000000000000000
χ382-2-2-22-2222-22-2000000-22-20022-22-200000−2−222−2−222−22−22−22−220000000000000000
χ392-2-2-22-2222-22-2000000-22-2002-22-220000022−2−222−2−2−22−22−22−220000000000000000
χ402-2-2-22-2222-22-2000000-22-2002-22-2200000−2−222−2−2222−22−22−22−20000000000000000
χ412-2-2-22-222-22-22000000-2-220022-2-220000022−2−2−2−2222−22−2−22−220000000000000000
χ422-2-2-22-222-22-22000000-2-220022-2-2200000−2−22222−2−2−22−222−22−20000000000000000
χ432-2-2-22-222-22-22000000-2-22002-222-20000022−2−2−2−222−22−222−22−20000000000000000
χ442-2-2-22-222-22-22000000-2-22002-222-200000−2−22222−2−22−22−2−22−220000000000000000
χ45444-4-4-44-400004i−4i4i−4i000000000000000000000000000000000000000002-22i−2i0000
χ46444-4-4-44-400004i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i0000
χ47444-4-4-44-40000−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i0000
χ48444-4-4-44-40000−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i0000
χ4944-44-4-4-4400004i−4i−4i4i000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ5044-44-4-4-4400004i−4i−4i4i00000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ5144-44-4-4-440000−4i4i4i−4i000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ5244-44-4-4-440000−4i4i4i−4i00000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ5344-4-444-4-444-4-4-4-44440000-40000000000000000000000000000000000000000000
χ5444-4-444-4-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ554-4444-4-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ564-4444-4-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ574-4444-4-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ584-4444-4-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
χ594-44-4-44-4400000000040000-400000000002i2−2i2−2i22i20000000000000000000000000000
χ604-44-4-44-4400000000040000-40000000000−2i22i22i2−2i20000000000000000000000000000
χ614-44-4-44-44000000000-4000040000000000000022−22−2222000000000000000000000000
χ624-44-4-44-44000000000-40000400000000000000−222222−22000000000000000000000000
χ634-4-4-44-4444-44-40000004-4400-400000000000000000000000000000000000000000
χ644-4-4-44-444-44-4400000044-400-400000000000000000000000000000000000000000
χ658-8-88-888-8000000000000000000000000000000000000000000000000000000000

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