Finite Group Databasebeta

← Group #167639

Character table — Group #167639

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-11111111111111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11-111-1-1-1-11-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-11-1-11-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11-1-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111-1-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-1-1-1-1-111111-11111-1-1-11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-111-11-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-111-11-1-1-1-1-111
χ172222222222222222-2-2-2-2-222-20022-200220000000000000000-20000000-20000000
χ182222222222222222-2-2-2-2-222-200-2-2-200-2-200000000000000002000000020000000
χ19222222222222-2-2-2-2222-2-2-2-220000-2000000000000000000000200-20-2002000000
χ20222222222222-2-2-2-2222-2-2-2-220000-2000000000000000000000-20020200-2000000
χ21222222222222-2-2-2-2-2-2-222-2-2-222002-2-20000000000000000000000020-200000000
χ22222222222222-2-2-2-2-2-2-222-2-2-2-2-20022200000000000000000000000-20200000000
χ2322222222-2-2-2-2222222-222-2-2-22200-22200000000000000000000000-20-200000000
χ2422222222-2-2-2-2222222-222-2-2-2-2-200-2-2-20000000000000000000000020200000000
χ2522222222-2-2-2-22222-2-22-2-2-2-220000200000000000000000000020020-200-2000000
χ2622222222-2-2-2-22222-2-22-2-2-2-2200002000000000000000000000-200-202002000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-222-20022200-2-20000000000000000-2000000020000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-222-200-2-220022000000000000000020000000-20000000
χ2922-2-2-222-22i2i−2i−2i2i2i−2i−2i000002-20002i−2i0002-20000000022−2−2i2i2−i2−i2000000000000i2−i22−2
χ3022-2-2-222-22i2i−2i−2i2i2i−2i−2i000002-20002i−2i0002-200000000−2−222−i2−i2i2i2000000000000−i2i2−22
χ3122-2-2-222-22i2i−2i−2i2i2i−2i−2i000002-2000−2i2i000-220000000022−2−2i2i2−i2−i2000000000000−i2i2−22
χ3222-2-2-222-22i2i−2i−2i2i2i−2i−2i000002-2000−2i2i000-2200000000−2−222−i2−i2i2i2000000000000i2−i22−2
χ3322-2-2-222-2−2i−2i2i2i−2i−2i2i2i000002-20002i−2i000-220000000022−2−2−i2−i2i2i2000000000000i2−i2−22
χ3422-2-2-222-2−2i−2i2i2i−2i−2i2i2i000002-20002i−2i000-2200000000−2−222i2i2−i2−i2000000000000−i2i22−2
χ3522-2-2-222-2−2i−2i2i2i−2i−2i2i2i000002-2000−2i2i0002-20000000022−2−2−i2−i2i2i2000000000000−i2i22−2
χ3622-2-2-222-2−2i−2i2i2i−2i−2i2i2i000002-2000−2i2i0002-200000000−2−222i2i2−i2−i2000000000000i2−i2−22
χ372-222-22-2-200002i−2i2i−2i2i−2i02-20002-20002i−2i0022−2−2i2i2−i2−i22−22−2i2−i2i2−i20000000000000000
χ382-222-22-2-200002i−2i2i−2i2i−2i02-20002-20002i−2i00−2−222−i2−i2i2i2−22−22−i2i2−i2i20000000000000000
χ392-222-22-2-200002i−2i2i−2i2i−2i02-2000-22000−2i2i0022−2−2i2i2−i2−i2−22−22−i2i2−i2i20000000000000000
χ402-222-22-2-200002i−2i2i−2i2i−2i02-2000-22000−2i2i00−2−222−i2−i2i2i22−22−2i2−i2i2−i20000000000000000
χ412-222-22-2-20000−2i2i−2i2i−2i2i02-20002-2000−2i2i0022−2−2−i2−i2i2i22−22−2−i2i2−i2i20000000000000000
χ422-222-22-2-20000−2i2i−2i2i−2i2i02-20002-2000−2i2i00−2−222i2i2−i2−i2−22−22i2−i2i2−i20000000000000000
χ432-222-22-2-20000−2i2i−2i2i−2i2i02-2000-220002i−2i0022−2−2−i2−i2i2i2−22−22i2−i2i2−i20000000000000000
χ442-222-22-2-20000−2i2i−2i2i−2i2i02-2000-220002i−2i00−2−222i2i2−i2−i22−22−2−i2i2−i2i20000000000000000
χ45444-44-4-4-4000000000040000-400000000022−2222−220000000000000000000000000000
χ46444-44-4-4-4000000000040000-4000000000−2222−22220000000000000000000000000000
χ47444-44-4-4-40000000000-40000400000000000002i2−2i22i2−2i2000000000000000000000000
χ48444-44-4-4-40000000000-4000040000000000000−2i22i2−2i22i2000000000000000000000000
χ4944-4-4-444-44i4i−4i−4i−4i−4i4i4i00000-44000000000000000000000000000000000000000000
χ5044-4-4-444-4−4i−4i4i4i4i4i−4i−4i00000-44000000000000000000000000000000000000000000
χ514-444-44-4-400004i−4i4i−4i−4i4i0-4400000000000000000000000000000000000000000000
χ524-444-44-4-40000−4i4i−4i4i4i−4i0-4400000000000000000000000000000000000000000000
χ534-44-4-4-4444-44-40000000000000000000002-2-222-2-22000000000000000000000000
χ544-44-4-4-4444-44-4000000000000000000000-222-2-222-2000000000000000000000000
χ554-44-4-4-444-44-440000000000000000000002-2-22-222-2000000000000000000000000
χ564-44-4-4-444-44-44000000000000000000000-222-22-2-22000000000000000000000000
χ574-4-444-44-44i−4i−4i4i0000000000000000000000000000000000000002-20000002i−2i0000
χ584-4-444-44-44i−4i−4i4i000000000000000000000000000000000000000-22000000−2i2i0000
χ594-4-444-44-4−4i4i4i−4i0000000000000000000000000000000000000002-2000000−2i2i0000
χ604-4-444-44-4−4i4i4i−4i000000000000000000000000000000000000000-220000002i−2i0000
χ614-4-4-444-4400004-4-4400000000000000000000000002-2-222-2-220000000000000000
χ624-4-4-444-4400004-4-440000000000000000000000000-222-2-222-20000000000000000
χ634-4-4-444-440000-444-400000000000000000000000002-2-22-222-20000000000000000
χ644-4-4-444-440000-444-40000000000000000000000000-222-22-2-220000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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