Finite Group Databasebeta

← Group #170206

Character table — Group #170206

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444422444444444422444444888888888888888824444444888844
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
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-11-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-11-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-11-1-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-11-1-11-1-111-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-11-1-1111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-11-1-11111-1-1-11
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1111-111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-1111-1
χ1722222222222222-2-2-2-22-2-2-2-2200000000000000000000000022000-20-2000000
χ1822222222222222-2-2-2-22-2-2-2-22000000000000000000000000-2-2000202000000
χ19222222222222-2-222-2-2-2-2-222-2002200220000000000000000000-2-2000000000
χ20222222222222-2-222-2-2-2-2-222-200-2-200-2-2000000000000000000022000000000
χ21222222222222-2-2-2-222-222-2-2-222002200000000000000000000-2000-20000000
χ22222222222222-2-2-2-222-222-2-2-2-2-200-2-200000000000000000000200020000000
χ2322222222-2-2-2-22222-2-2-222-2-2-22200-2-200000000000000000000-200020000000
χ2422222222-2-2-2-22222-2-2-222-2-2-2-2-20022000000000000000000002000-20000000
χ2522222222-2-2-2-222-2-222-2-2-222-2002200-2-20000000000000000000-22000000000
χ2622222222-2-2-2-222-2-222-2-2-222-200-2-2002200000000000000000002-2000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-220000000000000000000000002-2000-202000000
χ2822222222-2-2-2-2-2-222222-2-2-2-22000000000000000000000000-2200020-2000000
χ292-222-22-2-22i2i−2i−2i00002i−2i02-20002-2002i−2i00i2i2−i2−i222−2−2i2i2−i2−i222−2−200000000000000
χ302-222-22-2-22i2i−2i−2i00002i−2i02-20002-2002i−2i00−i2−i2i2i2−2−222−i2−i2i2i2−2−22200000000000000
χ312-222-22-2-22i2i−2i−2i00002i−2i02-2000-2200−2i2i00i2i2−i2−i222−2−2−i2−i2i2i2−2−22200000000000000
χ322-222-22-2-22i2i−2i−2i00002i−2i02-2000-2200−2i2i00−i2−i2i2i2−2−222i2i2−i2−i222−2−200000000000000
χ332-222-22-2-2−2i−2i2i2i0000−2i2i02-20002-200−2i2i00i2i2−i2−i2−2−222i2i2−i2−i2−2−22200000000000000
χ342-222-22-2-2−2i−2i2i2i0000−2i2i02-20002-200−2i2i00−i2−i2i2i222−2−2−i2−i2i2i222−2−200000000000000
χ352-222-22-2-2−2i−2i2i2i0000−2i2i02-2000-22002i−2i00i2i2−i2−i2−2−222−i2−i2i2i222−2−200000000000000
χ362-222-22-2-2−2i−2i2i2i0000−2i2i02-2000-22002i−2i00−i2−i2i2i222−2−2i2i2−i2−i2−2−22200000000000000
χ372-22-22-22-22i−2i2i−2i002i−2i000002-20002-2002i−2i000000002−22−2i2−i2i2−i2000000002−2i2−i200
χ382-22-22-22-22i−2i2i−2i002i−2i000002-20002-2002i−2i00000000−22−22−i2i2−i2i200000000−22−i2i200
χ392-22-22-22-22i−2i2i−2i002i−2i000002-2000-2200−2i2i000000002−22−2i2−i2i2−i200000000−22−i2i200
χ402-22-22-22-22i−2i2i−2i002i−2i000002-2000-2200−2i2i00000000−22−22−i2i2−i2i2000000002−2i2−i200
χ412-22-22-22-2−2i2i−2i2i00−2i2i000002-20002-200−2i2i000000002−22−2−i2i2−i2i2000000002−2−i2i200
χ422-22-22-22-2−2i2i−2i2i00−2i2i000002-20002-200−2i2i00000000−22−22i2−i2i2−i200000000−22i2−i200
χ432-22-22-22-2−2i2i−2i2i00−2i2i000002-2000-22002i−2i000000002−22−2−i2i2−i2i200000000−22i2−i200
χ442-22-22-22-2−2i2i−2i2i00−2i2i000002-2000-22002i−2i00000000−22−22i2−i2i2−i2000000002−2−i2i200
χ45444-4-4-4-444-4-4400000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ46444-4-4-4-444-4-440000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ47444-4-4-4-44-444-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ48444-4-4-4-44-444-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ4944-4-4-444-400004-40000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ5044-4-4-444-400004-4000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ5144-4-4-444-40000-440000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ5244-4-4-444-40000-44000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ534-444-44-4-44i4i−4i−4i0000−4i4i0-4400000000000000000000000000000000000000000
χ544-444-44-4-4−4i−4i4i4i00004i−4i0-4400000000000000000000000000000000000000000
χ554-44-44-44-44i−4i4i−4i00−4i4i00000-44000000000000000000000000000000000000000
χ564-44-44-44-4−4i4i−4i4i004i−4i00000-44000000000000000000000000000000000000000
χ574-4-4-444-44000000000040000-40000000000002i2−2i2−2i22i20000000000000000000000
χ584-4-4-444-44000000000040000-4000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-4-444-440000000000-4000040000000022−22−222200000000000000000000000000
χ604-4-4-444-440000000000-40000400000000−222222−2200000000000000000000000000
χ6188-888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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