Finite Group Databasebeta

← Group #263223

Character table — Group #263223

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444222244888888882244444444888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-11-11-11-1
χ1011111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-11-11-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-1-11-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-111-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-1-111-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1-111-1-111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-111-1-11-111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-111-11-1-11
χ1722222222-2-2-2-2222222-2-20000000022-2-2-2-222-2-2000000000000000000000000
χ1822222222-2-2-2-2222222-2-200000000-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-222-2-2-2-2-2-200000000-2-2222222-2-2000000000000000000000000
χ21222222-2-22222-2-222-2-2-2-22222-2-2-2-2002-2000000000022-2-20000000000000000
χ22222222-2-22222-2-222-2-2-2-2-2-2-2-22222002-20000000000-2-2220000000000000000
χ23222222-2-22222-2-2-2-222-2-22222-2-2-2-200-220000000000-2-2220000000000000000
χ24222222-2-22222-2-2-2-222-2-2-2-2-2-2222200-22000000000022-2-20000000000000000
χ25222222-2-2-2-2-2-2-2-222-2-2220000000000-220000002i2i−2i−2i00002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-2-222-2-2220000000000-22000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2-2-2-2222200000000002-20000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2-2-2-2222200000000002-2000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292222-2-22-2-2-2222-200002-222-2-222-2-2000000000000000000000002020-20-20000
χ302222-2-22-2-2-2222-200002-222-2-222-2-200000000000000000000000-20-202020000
χ312222-2-22-2-2-2222-200002-2-2-222-2-2220000000000000000000000020-20-2020000
χ322222-2-22-2-2-2222-200002-2-2-222-2-22200000000000000000000000-202020-20000
χ332222-2-2-22-2-222-220000-2222-2-2-2-22200000000000000000000002020-20-200000
χ342222-2-2-22-2-222-220000-2222-2-2-2-2220000000000000000000000-20-2020200000
χ352222-2-2-22-2-222-220000-22-2-22222-2-2000000000000000000000020-20-20200000
χ362222-2-2-22-2-222-220000-22-2-22222-2-20000000000000000000000-202020-200000
χ3722-2-22-2220000-2-22-22-2002−22−22−22−22-200002-2002−22−22−22−22−22−2000000000000
χ3822-2-22-2220000-2-22-22-2002−22−22−22−2-220000-2200−22−222−22−2−22−22000000000000
χ3922-2-22-2220000-2-22-22-200−22−22−22−222-200002-200−22−22−22−22−22−22000000000000
χ4022-2-22-2220000-2-22-22-200−22−22−22−22-220000-22002−22−2−22−222−22−2000000000000
χ4122-2-22-2220000-2-2-22-22002−22−22−22−22-20000-2200−22−22−22−222−22−2000000000000
χ4222-2-22-2220000-2-2-22-22002−22−22−22−2-2200002-2002−22−2−22−22−22−22000000000000
χ4322-2-22-2220000-2-2-22-2200−22−22−22−222-20000-22002−22−22−22−2−22−22000000000000
χ4422-2-22-2220000-2-2-22-2200−22−22−22−22-2200002-200−22−222−22−22−22−2000000000000
χ4522-2-22-2-2-20000222-2-22002−22−2−22−2200002i−2i002i−2ii2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ4622-2-22-2-2-20000222-2-22002−22−2−22−220000−2i2i00−2i2i−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ4722-2-22-2-2-20000222-2-2200−22−222−22−200002i−2i002i−2i−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ4822-2-22-2-2-20000222-2-2200−22−222−22−20000−2i2i00−2i2ii2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ4922-2-22-2-2-2000022-222-2002−22−2−22−2200002i−2i00−2i2i−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ5022-2-22-2-2-2000022-222-2002−22−2−22−220000−2i2i002i−2ii2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ5122-2-22-2-2-2000022-222-200−22−222−22−200002i−2i00−2i2ii2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ5222-2-22-2-2-2000022-222-200−22−222−22−20000−2i2i002i−2i−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ534444-4-44-444-4-44-40000-44000000000000000000000000000000000000000000
χ544444-4-4-4444-4-4-4400004-4000000000000000000000000000000000000000000
χ5544-4-4-444-40000-4400000022−22−222222−22−22220000000000000000000000000000000000
χ5644-4-4-444-40000-44000000−222222−22−222222−220000000000000000000000000000000000
χ5744-4-4-44-4400004-400000022−22−2222−222222−220000000000000000000000000000000000
χ5844-4-4-44-4400004-4000000−222222−2222−22−22220000000000000000000000000000000000
χ598-88-800008i−8i0000000000000000000000000000000000000000000000000000
χ608-88-80000−8i8i0000000000000000000000000000000000000000000000000000
χ618-8-880000008-800000000000000000000000000000000000000000000000000
χ628-8-88000000-8800000000000000000000000000000000000000000000000000

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