Finite Group Databasebeta

← Group #170249

Character table — Group #170249

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
χ311111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1111-11111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1111-1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111-11-1-1111-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-11
χ1722222222222222-2-2-2-22-2-2-2-220022002200000000000000000-20-20000000000
χ1822222222222222-2-2-2-22-2-2-2-2200-2-200-2-2000000000000000002020000000000
χ19222222222222-2-222-2-2-2-2-222-200000000000000000000000000202-2-20000000
χ20222222222222-2-222-2-2-2-2-222-200000000000000000000000000-20-2220000000
χ21222222222222-2-2-2-222-222-2-2-2220022000000000000000000-2000000-2000000
χ22222222222222-2-2-2-222-222-2-2-2-2-200-2-200000000000000000020000002000000
χ2322222222-2-2-2-22222-2-2-222-2-2-22200-2-2000000000000000000-20000002000000
χ2422222222-2-2-2-22222-2-2-222-2-2-2-2-200220000000000000000002000000-2000000
χ2522222222-2-2-2-222-2-222-2-2-222-20000000000000000000000000020-22-20000000
χ2622222222-2-2-2-222-2-222-2-2-222-200000000000000000000000000-202-220000000
χ2722222222-2-2-2-2-2-222222-2-2-2-22002200-2-200000000000000000-2020000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-2200-2-200220000000000000000020-20000000000
χ292-222-22-2-22i2i−2i−2i00002i−2i02-20002i−2i002-200i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000
χ302-222-22-2-22i2i−2i−2i00002i−2i02-20002i−2i002-200−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000
χ312-222-22-2-22i2i−2i−2i00002i−2i02-2000−2i2i00-2200i2i2−i2−i222−2−2−2−222−i2−i2i2i200000000000000
χ322-222-22-2-22i2i−2i−2i00002i−2i02-2000−2i2i00-2200−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000000000
χ332-222-22-2-2−2i−2i2i2i0000−2i2i02-20002i−2i00-2200i2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000000000
χ342-222-22-2-2−2i−2i2i2i0000−2i2i02-20002i−2i00-2200−i2−i2i2i222−2−2−2−222i2i2−i2−i200000000000000
χ352-222-22-2-2−2i−2i2i2i0000−2i2i02-2000−2i2i002-200i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000
χ362-222-22-2-2−2i−2i2i2i0000−2i2i02-2000−2i2i002-200−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000
χ372-2-2-222-222-22-22-2000020000-2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200000000000000002−22−200
χ382-2-2-222-222-22-22-2000020000-2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000−22−2200
χ392-2-2-222-222-22-22-2000020000-200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000−22−2200
χ402-2-2-222-222-22-22-2000020000-200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200000000000000002−22−200
χ412-2-2-222-22-22-22-22000020000-2002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i200000000000000002−2−2200
χ422-2-2-222-22-22-22-22000020000-2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000−222−200
χ432-2-2-222-22-22-22-22000020000-200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000−222−200
χ442-2-2-222-22-22-22-22000020000-200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i200000000000000002−2−2200
χ45444-4-4-4-440000004i−4i0000000000000000000000002i−2i2i−2i2-22-200000000000000
χ46444-4-4-4-440000004i−4i000000000000000000000000−2i2i−2i2i-22-2200000000000000
χ47444-4-4-4-44000000−4i4i0000000000000000000000002i−2i2i−2i-22-2200000000000000
χ48444-4-4-4-44000000−4i4i000000000000000000000000−2i2i−2i2i2-22-200000000000000
χ4944-4-4-444-44i−4i−4i4i000000000000000000002-2-22−2i2i2i−2i0000000000000000000000
χ5044-4-4-444-44i−4i−4i4i00000000000000000000-222-22i−2i−2i2i0000000000000000000000
χ5144-4-4-444-4−4i4i4i−4i000000000000000000002-2-222i−2i−2i2i0000000000000000000000
χ5244-4-4-444-4−4i4i4i−4i00000000000000000000-222-2−2i2i2i−2i0000000000000000000000
χ534-444-44-4-44i4i−4i−4i0000−4i4i0-4400000000000000000000000000000000000000000
χ544-444-44-4-4−4i−4i4i4i00004i−4i0-4400000000000000000000000000000000000000000
χ554-44-44-44-400000000000004-40000000000000000000002i2−2i2−2i22i200000000000000
χ564-44-44-44-400000000000004-4000000000000000000000−2i22i22i2−2i200000000000000
χ574-44-44-44-40000000000000-44000000000000000002i2−2i2−2i22i2000000000000000000
χ584-44-44-44-40000000000000-4400000000000000000−2i22i22i2−2i2000000000000000000
χ594-4-4-444-444-44-4-440000-40000400000000000000000000000000000000000000
χ604-4-4-444-44-44-444-40000-40000400000000000000000000000000000000000000
χ6188-888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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