Finite Group Databasebeta

← Group #170139

Character table — Group #170139

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444422444444444444444444888888888888888824444444888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-11-11-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-11-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1111111-1-1
χ911111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-1-11
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1-1111-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1111-1-1-1-1-1111-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1111-1-1-111-1-1-11
χ1722222222222222-2-22-2-2-2-2-2-22002200220000000000000000000-20-200000000
χ1822222222222222-2-22-2-2-2-2-2-2200-2-200-2-2000000000000000000020200000000
χ19222222222222-2-222-2-2-2-2-222-22200220000000000000000000-2-200000000000
χ20222222222222-2-222-2-2-2-2-222-2-2-200-2-200000000000000000002200000000000
χ21222222222222-2-2-2-2-22222-2-2-20000000000000000000000002000-202-2000000
χ22222222222222-2-2-2-2-22222-2-2-2000000000000000000000000-200020-22000000
χ2322222222-2-2-2-22222-2-2-222-2-2-20000000000000000000000002000-20-22000000
χ2422222222-2-2-2-22222-2-2-222-2-2-2000000000000000000000000-2000202-2000000
χ2522222222-2-2-2-222-2-2-222-2-222-22200-2-20000000000000000000-2200000000000
χ2622222222-2-2-2-222-2-2-222-2-222-2-2-2002200000000000000000002-200000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-22002200-2-2000000000000000000020-200000000
χ2822222222-2-2-2-2-2-222222-2-2-2-2200-2-200220000000000000000000-20200000000
χ29222-2-22-2-22i2i−2i−2i002i−2i000002-202i−2i002-20022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000000000
χ30222-2-22-2-22i2i−2i−2i002i−2i000002-202i−2i002-200−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000000000
χ31222-2-22-2-22i2i−2i−2i002i−2i000002-20−2i2i00-220022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000
χ32222-2-22-2-22i2i−2i−2i002i−2i000002-20−2i2i00-2200−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000
χ33222-2-22-2-2−2i−2i2i2i00−2i2i000002-202i−2i00-220022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000
χ34222-2-22-2-2−2i−2i2i2i00−2i2i000002-202i−2i00-2200−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000
χ35222-2-22-2-2−2i−2i2i2i00−2i2i000002-20−2i2i002-20022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000000000
χ36222-2-22-2-2−2i−2i2i2i00−2i2i000002-20−2i2i002-200−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000000000
χ372-22-2-2-2222-22-22-2002000000-2002i−2i002i−2i2−22−22−22−20000000000000000i2−i2i2−i200
χ382-22-2-2-2222-22-22-2002000000-2002i−2i002i−2i−22−22−22−220000000000000000−i2i2−i2i200
χ392-22-2-2-2222-22-22-2002000000-200−2i2i00−2i2i2−22−22−22−20000000000000000−i2i2−i2i200
χ402-22-2-2-2222-22-22-2002000000-200−2i2i00−2i2i−22−22−22−220000000000000000i2−i2i2−i200
χ412-22-2-2-222-22-22-22002000000-2002i−2i00−2i2i2−22−2−22−220000000000000000i2−i2−i2i200
χ422-22-2-2-222-22-22-22002000000-2002i−2i00−2i2i−22−222−22−20000000000000000−i2i2i2−i200
χ432-22-2-2-222-22-22-22002000000-200−2i2i002i−2i2−22−2−22−220000000000000000−i2i2i2−i200
χ442-22-2-2-222-22-22-22002000000-200−2i2i002i−2i−22−222−22−20000000000000000i2−i2−i2i200
χ45444-4-44-4-44i4i−4i−4i00−4i4i00000-44000000000000000000000000000000000000000
χ46444-4-44-4-4−4i−4i4i4i004i−4i00000-44000000000000000000000000000000000000000
χ4744-44-4-44-40000000004i−4i0000000000000000000002-22-22i−2i2i−2i00000000000000
χ4844-44-4-44-40000000004i−4i000000000000000000000-22-22−2i2i−2i2i00000000000000
χ4944-44-4-44-4000000000−4i4i0000000000000000000002-22-2−2i2i−2i2i00000000000000
χ5044-44-4-44-4000000000−4i4i000000000000000000000-22-222i−2i2i−2i00000000000000
χ5144-4-44-4-44000000000004-4000000000000000000000002i2−2i2−2i22i200000000000000
χ5244-4-44-4-44000000000004-400000000000000000000000−2i22i22i2−2i200000000000000
χ5344-4-44-4-4400000000000-4400000000000000000002i2−2i2−2i22i2000000000000000000
χ5444-4-44-4-4400000000000-440000000000000000000−2i22i22i2−2i2000000000000000000
χ554-4444-4-4-44i−4i−4i4i000000000000000000002-2-222i−2i−2i2i0000000000000000000000
χ564-4444-4-4-44i−4i−4i4i00000000000000000000-222-2−2i2i2i−2i0000000000000000000000
χ574-4444-4-4-4−4i4i4i−4i000000000000000000002-2-22−2i2i2i−2i0000000000000000000000
χ584-4444-4-4-4−4i4i4i−4i00000000000000000000-222-22i−2i−2i2i0000000000000000000000
χ594-44-4-4-4444-44-4-4400-4000000400000000000000000000000000000000000000
χ604-44-4-4-444-44-444-400-4000000400000000000000000000000000000000000000
χ618-8-88-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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