Finite Group Databasebeta

← Group #169721

Character table — Group #169721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444422444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111111111-1-11-1-1-11-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11-1-1-1-111
χ911111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-1-11-11-1-111-11
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1-11-1111-1-11-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1111-1
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-111111-1-1-11
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-11-111-1-1-11
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-11-1-1-1111-1
χ1722222222222222-2-2-2-2-2-222-2-2002200220000000000000000-200-20000000000
χ1822222222222222-2-2-2-2-2-222-2-200-2-200-2-2000000000000000020020000000000
χ19222222222222-2-222-2-2-22-2-2-220000000000000000000000000200-220-2000000
χ20222222222222-2-222-2-2-22-2-2-220000000000000000000000000-2002-202000000
χ21222222222222-2-2-2-2222-2-2-22-222002200000000000000000000-2000-20000000
χ22222222222222-2-2-2-2222-2-2-22-2-2-200-2-200000000000000000000200020000000
χ2322222222-2-2-2-222222-2-2-2-2-22-22200-2-200000000000000000000-200020000000
χ2422222222-2-2-2-222222-2-2-2-2-22-2-2-20022000000000000000000002000-20000000
χ2522222222-2-2-2-222-2-2-2222-2-2-220000000000000000000000000200-2-202000000
χ2622222222-2-2-2-222-2-2-2222-2-2-220000000000000000000000000-200220-2000000
χ2722222222-2-2-2-2-2-222-222-222-2-2002200-2-20000000000000000200-20000000000
χ2822222222-2-2-2-2-2-222-222-222-2-200-2-200220000000000000000-20020000000000
χ292-2222-2-2-22i2i−2i−2i2i−2i0000002-200002-2002i−2i0000000022−2−2i2i2−i2−i2000000002−2i2−i200
χ302-2222-2-2-22i2i−2i−2i2i−2i0000002-200002-2002i−2i00000000−2−222−i2−i2i2i200000000−22−i2i200
χ312-2222-2-2-22i2i−2i−2i2i−2i0000002-20000-2200−2i2i0000000022−2−2i2i2−i2−i200000000−22−i2i200
χ322-2222-2-2-22i2i−2i−2i2i−2i0000002-20000-2200−2i2i00000000−2−222−i2−i2i2i2000000002−2i2−i200
χ332-2222-2-2-2−2i−2i2i2i−2i2i0000002-200002-200−2i2i0000000022−2−2−i2−i2i2i2000000002−2−i2i200
χ342-2222-2-2-2−2i−2i2i2i−2i2i0000002-200002-200−2i2i00000000−2−222i2i2−i2−i200000000−22i2−i200
χ352-2222-2-2-2−2i−2i2i2i−2i2i0000002-20000-22002i−2i0000000022−2−2−i2−i2i2i200000000−22i2−i200
χ362-2222-2-2-2−2i−2i2i2i−2i2i0000002-20000-22002i−2i00000000−2−222i2i2−i2−i2000000002−2−i2i200
χ372-2-22-222-22-22-2000022-2000-202-2002-200i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-2-22-222-22-22-2000022-2000-202-2002-200−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ392-2-22-222-22-22-2000022-2000-20-2200-2200i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-2-22-222-22-22-2000022-2000-20-2200-2200−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ412-2-22-222-2-22-2200002-22000-202-200-2200i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ422-2-22-222-2-22-2200002-22000-202-200-2200−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-2-22-222-2-22-2200002-22000-20-22002-200i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ442-2-22-222-2-22-2200002-22000-20-22002-200−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ4544-44-4-4-444i−4i−4i4i00000000000000000000000000002i−2i−2i2i-222-200000000000000
χ4644-44-4-4-444i−4i−4i4i0000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ4744-44-4-4-44−4i4i4i−4i00000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ4844-44-4-4-44−4i4i4i−4i0000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ4944-4-44-44-40000004i−4i00000000000000002i−2i2i−2i2-22-20000000000000000000000
χ5044-4-44-44-40000004i−4i0000000000000000−2i2i−2i2i-22-220000000000000000000000
χ5144-4-44-44-4000000−4i4i00000000000000002i−2i2i−2i-22-220000000000000000000000
χ5244-4-44-44-4000000−4i4i0000000000000000−2i2i−2i2i2-22-20000000000000000000000
χ534-4444-4-4-44i4i−4i−4i−4i4i000000-440000000000000000000000000000000000000000
χ544-4444-4-4-4−4i−4i4i4i4i−4i000000-440000000000000000000000000000000000000000
χ554-44-4-4-444000000000004000-40000000000002i2−2i2−2i22i20000000000000000000000
χ564-44-4-4-444000000000004000-4000000000000−2i22i22i2−2i20000000000000000000000
χ574-44-4-4-44400000000000-400040000000022−22−222200000000000000000000000000
χ584-44-4-4-44400000000000-4000400000000−222222−2200000000000000000000000000
χ594-4-44-444-44-44-40000-4-440004000000000000000000000000000000000000000
χ604-4-44-444-4-44-440000-44-40004000000000000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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