Finite Group Databasebeta

← Group #167743

Character table — Group #167743

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
χ311111111111111111111111111-1-1111-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11-11-111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-1-11-11-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-11-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-11-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1111-11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-11111111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111-11-1-1-1-1-1-1-111
χ172222222222222222-2-2-222-2-2-20022-200220000000000000000000000-20-20000000
χ182222222222222222-2-2-222-2-2-200-2-2-200-2-200000000000000000000002020000000
χ19222222222222-2-2-2-222-2-2-222-20000-2000000000000000000000200-200-202000000
χ20222222222222-2-2-2-222-2-2-222-20000-2000000000000000000000-20020020-2000000
χ21222222222222-2-2-2-2-2-22-2-2-2-2222002-2-200000000000000000020000-20000000000
χ22222222222222-2-2-2-2-2-22-2-2-2-22-2-200222000000000000000000-2000020000000000
χ2322222222-2-2-2-22222222-2-2-2-222200-222000000000000000000-20000-20000000000
χ2422222222-2-2-2-22222222-2-2-2-22-2-200-2-2-20000000000000000002000020000000000
χ2522222222-2-2-2-22222-2-2-2-2-222-200002000000000000000000000200-20020-2000000
χ2622222222-2-2-2-22222-2-2-2-2-222-200002000000000000000000000-200200-202000000
χ2722222222-2-2-2-2-2-2-2-222-222-2-2-20022200-2-2000000000000000000000020-20000000
χ2822222222-2-2-2-2-2-2-2-222-222-2-2-200-2-2200220000000000000000000000-2020000000
χ29222-2-2-22-22i2i−2i−2i2i2i−2i−2i0002-2000002i−2i0002-20000000022−2−2i2i2−i2−i2000000000000i2−i22−2
χ30222-2-2-22-22i2i−2i−2i2i2i−2i−2i0002-2000002i−2i0002-200000000−2−222−i2−i2i2i2000000000000−i2i2−22
χ31222-2-2-22-22i2i−2i−2i2i2i−2i−2i0002-200000−2i2i000-220000000022−2−2i2i2−i2−i2000000000000−i2i2−22
χ32222-2-2-22-22i2i−2i−2i2i2i−2i−2i0002-200000−2i2i000-2200000000−2−222−i2−i2i2i2000000000000i2−i22−2
χ33222-2-2-22-2−2i−2i2i2i−2i−2i2i2i0002-2000002i−2i000-220000000022−2−2−i2−i2i2i2000000000000i2−i2−22
χ34222-2-2-22-2−2i−2i2i2i−2i−2i2i2i0002-2000002i−2i000-2200000000−2−222i2i2−i2−i2000000000000−i2i22−2
χ35222-2-2-22-2−2i−2i2i2i−2i−2i2i2i0002-200000−2i2i0002-20000000022−2−2−i2−i2i2i2000000000000−i2i22−2
χ36222-2-2-22-2−2i−2i2i2i−2i−2i2i2i0002-200000−2i2i0002-200000000−2−222i2i2−i2−i2000000000000i2−i2−22
χ372-22-22-2-2200002-22-22-220000-22i−2i0002i−2i00i2i2−i2−i2i2i2−i2−i22−22−22−22−20000000000000000
χ382-22-22-2-2200002-22-22-220000-22i−2i0002i−2i00−i2−i2i2i2−i2−i2i2i2−22−22−22−220000000000000000
χ392-22-22-2-2200002-22-22-220000-2−2i2i000−2i2i00i2i2−i2−i2i2i2−i2−i2−22−22−22−220000000000000000
χ402-22-22-2-2200002-22-22-220000-2−2i2i000−2i2i00−i2−i2i2i2−i2−i2i2i22−22−22−22−20000000000000000
χ412-22-22-2-220000-22-22-2220000-22i−2i000−2i2i00i2i2−i2−i2−i2−i2i2i22−22−2−22−220000000000000000
χ422-22-22-2-220000-22-22-2220000-22i−2i000−2i2i00−i2−i2i2i2i2i2−i2−i2−22−222−22−20000000000000000
χ432-22-22-2-220000-22-22-2220000-2−2i2i0002i−2i00i2i2−i2−i2−i2−i2i2i2−22−222−22−20000000000000000
χ442-22-22-2-220000-22-22-2220000-2−2i2i0002i−2i00−i2−i2i2i2i2i2−i2−i22−22−2−22−220000000000000000
χ45444-4-4-44-44i4i−4i−4i−4i−4i4i4i000-4400000000000000000000000000000000000000000000
χ46444-4-4-44-4−4i−4i4i4i4i4i−4i−4i000-4400000000000000000000000000000000000000000000
χ4744-44-4-4-444-44-40000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4844-44-4-4-444-44-4000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4944-44-4-4-44-44-440000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5044-44-4-4-44-44-44000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5144-4-444-4-44i−4i−4i4i0000000000000000000000000000000000000002-20000002i−2i0000
χ5244-4-444-4-44i−4i−4i4i000000000000000000000000000000000000000-22000000−2i2i0000
χ5344-4-444-4-4−4i4i4i−4i0000000000000000000000000000000000000002-2000000−2i2i0000
χ5444-4-444-4-4−4i4i4i−4i000000000000000000000000000000000000000-220000002i−2i0000
χ554-444-44-4-400004i−4i−4i4i00000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ564-444-44-4-400004i−4i−4i4i0000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ574-444-44-4-40000−4i4i4i−4i00000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ584-444-44-4-40000−4i4i4i−4i0000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ594-44-44-4-4400004-44-4-44-40000400000000000000000000000000000000000000000
χ604-44-44-4-440000-44-444-4-40000400000000000000000000000000000000000000000
χ614-4-4-4-444400000000000004-40000000000000022−22−2222000000000000000000000000
χ624-4-4-4-444400000000000004-400000000000000−222222−22000000000000000000000000
χ634-4-4-4-44440000000000000-44000000000022−22−22220000000000000000000000000000
χ644-4-4-4-44440000000000000-440000000000−222222−220000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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