Finite Group Databasebeta

← Group #267539

Character table — Group #267539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444448888888888888888888881616161616161616161616161616161632
order12222244444444444444422444888888888888888822244444888888884
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ5111111111111111111-1-1111-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1
χ6111111111111111111-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11
χ7111111111111111111-1-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ8111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1
χ911111111111111-1-1-1-1111-1-111111-1-111-1-111-1-11111-1-111-1-1111-111-1-1-1-1-1
χ1011111111111111-1-1-1-1111-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11-111-1-1111
χ1111111111111111-1-1-1-1111-1-1111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111111
χ1211111111111111-1-1-1-1111-1-1111-1-111-1-111-1-1111111-1-1-1-11111-11-1-111-1-1-1
χ1311111111111111-1-1-1-1-1-11-1-1-1-1-111-1-111-1-111-1-1111111-1-111-1-11-1-1-111-1-11
χ1411111111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1111-1-1-11111-1
χ1511111111111111-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111-1111-1-111-1
χ1611111111111111-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1111-1-1-1-11
χ1722222222-222-2-2-2222200-2-2-2000222200000000000000000000-2-20000000
χ1822222222-222-2-2-2222200-2-2-2000-2-2-2-200000000000000000000220000000
χ1922222222-222-2-2-2-2-2-2-200-22200022-2-200000000000000000000-220000000
χ2022222222-222-2-2-2-2-2-2-200-222000-2-222000000000000000000002-20000000
χ21222222-2-22-2-22-2-222-2-22222-2-2-2200000000000000002-2000000000000000
χ22222222-2-22-2-22-2-222-2-2-2-222-222-20000000000000000-22000000000000000
χ23222222-2-22-2-22-2-2-2-222222-22-2-220000000000000000-22000000000000000
χ24222222-2-22-2-22-2-2-2-222-2-22-2222-200000000000000002-2000000000000000
χ25222222-2-2-2-2-2-22222-2-200-2-22000000000000000000000000000002i−2i2i−2i000
χ26222222-2-2-2-2-2-22222-2-200-2-2200000000000000000000000000000−2i2i−2i2i000
χ27222222-2-2-2-2-2-222-2-22200-22-2000000000000000000000000000002i−2i−2i2i000
χ28222222-2-2-2-2-2-222-2-22200-22-200000000000000000000000000000−2i2i2i−2i000
χ292222-2-22-222-222-2000022-2002-2-20000002200-2-2000000002-200000000000
χ302222-2-22-222-222-2000022-2002-2-2000000-2-2002200000000-2200000000000
χ312222-2-22-222-222-20000-2-2-200-2220000002200-2-200000000-2200000000000
χ322222-2-22-222-222-20000-2-2-200-222000000-2-20022000000002-200000000000
χ332222-2-2-222-222-22000022-200-22-200002200-2-200000000-220000000000000
χ342222-2-2-222-222-22000022-200-22-20000-2-20022000000002-20000000000000
χ352222-2-2-222-222-220000-2-2-2002-2200002200-2-2000000002-20000000000000
χ362222-2-2-222-222-220000-2-2-2002-220000-2-2002200000000-220000000000000
χ3722-2-2-222-20-220002i−2i2i−2i000000002-22i−2ii2−i22−2i2−i22−2i2i2−i2−i2000000000000002−20
χ3822-2-2-222-20-220002i−2i2i−2i000000002-22i−2i−i2i2−22−i2i2−22−i2−i2i2i200000000000000−220
χ3922-2-2-222-20-220002i−2i2i−2i00000000-22−2i2ii2−i22−2i2−i22−2−i2−i2i2i200000000000000−220
χ4022-2-2-222-20-220002i−2i2i−2i00000000-22−2i2i−i2i2−22−i2i2−22i2i2−i2−i2000000000000002−20
χ4122-2-2-222-20-22000−2i2i−2i2i000000002-2−2i2ii2−i2−22i2−i2−22i2i2−i2−i200000000000000−220
χ4222-2-2-222-20-22000−2i2i−2i2i000000002-2−2i2i−i2i22−2−i2i22−2−i2−i2i2i2000000000000002−20
χ4322-2-2-222-20-22000−2i2i−2i2i00000000-222i−2ii2−i2−22i2−i2−22−i2−i2i2i2000000000000002−20
χ4422-2-2-222-20-22000−2i2i−2i2i00000000-222i−2i−i2i22−2−i2i22−2i2i2−i2−i200000000000000−220
χ454444-4-44-4-44-4-4-44000000400000000000000000000000000000000000000
χ464444-4-4-44-4-44-44-4000000400000000000000000000000000000000000000
χ4744-4-44-4440-4-400000000000000000000022−2200−2222000000000000000000000
χ4844-4-44-4440-4-4000000000000000000000−22220022−22000000000000000000000
χ4944-4-44-4-4-404400000000000000000002i2−2i200−2i22i200000000000000000000000
χ5044-4-44-4-4-40440000000000000000000−2i22i2002i2−2i200000000000000000000000
χ5144-4-4-44-4404-40004i−4i−4i4i00000000000000000000000000000000000000000
χ5244-4-4-44-4404-4000−4i4i4i−4i00000000000000000000000000000000000000000
χ534-4-440000-40040000004-40000000000000000002-22-20000002-2000000000
χ544-4-440000-40040000004-4000000000000000000-22-22000000-22000000000
χ554-4-440000-4004000000-440000000000000000002-22-2000000-22000000000
χ564-4-440000-4004000000-44000000000000000000-22-220000002-2000000000
χ578-88-800000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ588-88-80000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ598-8-880000800-800000000000000000000000000000000000000000000000

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