Finite Group Databasebeta

← Group #170212

Character table — Group #170212

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444422444444444444444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-1-111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111-1-111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1-11-1-1-1-111
χ911111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-11-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-11-1-1-1-111-11
χ1111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11
χ1211111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1
χ1311111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-111111-11-11-1-11-1-1111-1
χ1411111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-11-1-1111-1-1-11
χ1511111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-11-111-1-1-11
χ1611111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-11-1-1-1111-1
χ17222222222222222-2-2-2-2-2-2-2-22000000000000000000000000020-2-2002000000
χ18222222222222222-2-2-2-2-2-2-2-220000000000000000000000000-202200-2000000
χ19222222222222-2-2-222-2-2-2-222-2002200220000000000000000-200000-20000000
χ20222222222222-2-2-222-2-2-2-222-200-2-200-2-2000000000000000020000020000000
χ21222222222222-2-2-2-2-22222-2-2-222002200000000000000000000-200-200000000
χ22222222222222-2-2-2-2-22222-2-2-2-2-200-2-200000000000000000000200200000000
χ2322222222-2-2-2-222-222-2-222-2-2-22200-2-200000000000000000000200-200000000
χ2422222222-2-2-2-222-222-2-222-2-2-2-2-2002200000000000000000000-200200000000
χ2522222222-2-2-2-222-2-2-222-2-222-2002200-2-20000000000000000-20000020000000
χ2622222222-2-2-2-222-2-2-222-2-222-200-2-200220000000000000000200000-20000000
χ2722222222-2-2-2-2-2-222222-2-2-2-22000000000000000000000000020-2200-2000000
χ2822222222-2-2-2-2-2-222222-2-2-2-220000000000000000000000000-202-2002000000
χ29222-2-2-2-222i2i−2i−2i0002i−2i00002-20002i−2i002-200000000i2i2−i2−i222−2−2000000002−2i2−i200
χ30222-2-2-2-222i2i−2i−2i0002i−2i00002-20002i−2i002-200000000−i2−i2i2i2−2−22200000000−22−i2i200
χ31222-2-2-2-222i2i−2i−2i0002i−2i00002-2000−2i2i00-2200000000i2i2−i2−i222−2−200000000−22−i2i200
χ32222-2-2-2-222i2i−2i−2i0002i−2i00002-2000−2i2i00-2200000000−i2−i2i2i2−2−222000000002−2i2−i200
χ33222-2-2-2-22−2i−2i2i2i000−2i2i00002-20002i−2i00-2200000000i2i2−i2−i2−2−222000000002−2−i2i200
χ34222-2-2-2-22−2i−2i2i2i000−2i2i00002-20002i−2i00-2200000000−i2−i2i2i222−2−200000000−22i2−i200
χ35222-2-2-2-22−2i−2i2i2i000−2i2i00002-2000−2i2i002-200000000i2i2−i2−i2−2−22200000000−22i2−i200
χ36222-2-2-2-22−2i−2i2i2i000−2i2i00002-2000−2i2i002-200000000−i2−i2i2i222−2−2000000002−2−i2i200
χ372-222-22-2-22i−2i2i−2i000002i−2i2-20002-2002i−2i0022−2−2i2i2−i2−i22−22−2i2−i2i2−i200000000000000
χ382-222-22-2-22i−2i2i−2i000002i−2i2-20002-2002i−2i00−2−222−i2−i2i2i2−22−22−i2i2−i2i200000000000000
χ392-222-22-2-22i−2i2i−2i000002i−2i2-2000-2200−2i2i0022−2−2i2i2−i2−i2−22−22−i2i2−i2i200000000000000
χ402-222-22-2-22i−2i2i−2i000002i−2i2-2000-2200−2i2i00−2−222−i2−i2i2i22−22−2i2−i2i2−i200000000000000
χ412-222-22-2-2−2i2i−2i2i00000−2i2i2-20002-200−2i2i0022−2−2−i2−i2i2i22−22−2−i2i2−i2i200000000000000
χ422-222-22-2-2−2i2i−2i2i00000−2i2i2-20002-200−2i2i00−2−222i2i2−i2−i2−22−22i2−i2i2−i200000000000000
χ432-222-22-2-2−2i2i−2i2i00000−2i2i2-2000-22002i−2i0022−2−2−i2−i2i2i2−22−22i2−i2i2−i200000000000000
χ442-222-22-2-2−2i2i−2i2i00000−2i2i2-2000-22002i−2i00−2−222i2i2−i2−i22−22−2−i2i2−i2i200000000000000
χ45444-4-4-4-444i4i−4i−4i000−4i4i0000-44000000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i0004i−4i0000-44000000000000000000000000000000000000000
χ4744-4-444-4-4000000400000000-40000000022−2222−2200000000000000000000000000
χ4844-4-444-4-4000000400000000-400000000−2222−222200000000000000000000000000
χ4944-4-444-4-4000000-40000000040000000000002i2−2i22i2−2i20000000000000000000000
χ5044-4-444-4-4000000-4000000004000000000000−2i22i2−2i22i20000000000000000000000
χ514-444-44-4-44i−4i4i−4i00000−4i4i-4400000000000000000000000000000000000000000
χ524-444-44-4-4−4i4i−4i4i000004i−4i-4400000000000000000000000000000000000000000
χ534-44-44-44-44-4-4400000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ544-44-44-44-44-4-440000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ554-44-44-44-4-444-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ564-44-44-44-4-444-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ574-4-4-4-444400004-40000000000000000002-2-222-2-220000000000000000000000
χ584-4-4-4-444400004-4000000000000000000-222-2-222-20000000000000000000000
χ594-4-4-4-44440000-440000000000000000002-2-22-222-20000000000000000000000
χ604-4-4-4-44440000-44000000000000000000-222-22-2-220000000000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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