Finite Group Databasebeta

← Group #240110

Character table — Group #240110

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444888888888888888822244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-11111-1-1
χ911111111-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-111-11-1-11-111-1-11111-1-1-1-1
χ1011111111-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11-111-1-1-11-1-111-1-1-1-11111
χ1111111111-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-11-1-1111-1-1-111-1-111-1-111
χ1211111111-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11-111-1111-1-111-1-111-1-1
χ1311111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-11-1-1111-111-1-1-1-1-1-11111
χ1411111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11-111-11-1-1111111-1-1-1-1
χ1511111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1111111-11-1-11-1-1-11111-1-111-1-1
χ1611111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-111111-111-1-1-1111-1-1-1-111-1-111
χ1722222222222222-2-2-2-2-2-2-22-2-22-20000000000000000000000002i−2i2i−2i00000000
χ1822222222222222-2-2-2-2-2-2-22-2-22-2000000000000000000000000−2i2i−2i2i00000000
χ1922222222-2-2-2-222-2-2-2-222-2-222-2-20000000000000000000000002i−2i−2i2i00000000
χ2022222222-2-2-2-222-2-2-2-222-2-222-2-2000000000000000000000000−2i2i2i−2i00000000
χ21222222-2-222-2-2-2-22222-2-2-2222-2-20000000000000000200-2-2200000000000000
χ22222222-2-222-2-2-2-22222-2-2-2222-2-20000000000000000-20022-200000000000000
χ23222222-2-222-2-2-2-2-2-2-2-22222-2-2-220000000000000000000000000000002i−2i2i−2i00
χ24222222-2-222-2-2-2-2-2-2-2-22222-2-2-22000000000000000000000000000000−2i2i−2i2i00
χ25222222-2-2-2-222-2-2222222-2-2-2-22-20000000000000000200-22-200000000000000
χ26222222-2-2-2-222-2-2222222-2-2-2-22-20000000000000000-2002-2200000000000000
χ27222222-2-2-2-222-2-2-2-2-2-2-2-22-222220000000000000000000000000000002i−2i−2i2i00
χ28222222-2-2-2-222-2-2-2-2-2-2-2-22-22222000000000000000000000000000000−2i2i2i−2i00
χ292222-2-22222-2-2-2-222-2-22-22-22-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ302222-2-22222-2-2-2-222-2-22-22-22-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ312222-2-22222-2-2-2-2-2-222-22-2-2-222200000000000000000000000000002-200002-2
χ322222-2-22222-2-2-2-2-2-222-22-2-2-22220000000000000000000000000000-220000-22
χ332222-2-222-2-222-2-222-2-2-2222-22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ342222-2-222-2-222-2-222-2-2-2222-22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ352222-2-222-2-222-2-2-2-2222-2-222-2-2200000000000000000000000000002-20000-22
χ362222-2-222-2-222-2-2-2-2222-2-222-2-220000000000000000000000000000-2200002-2
χ372222-2-2-2-222222222-2-2-22-2-22-2-220000000022-2-222-2-200000000000000000000
χ382222-2-2-2-222222222-2-2-22-2-22-2-2200000000-2-222-2-22200000000000000000000
χ392222-2-2-2-2222222-2-2222-22-2-22-2-2000000000000000002-2000-22000000000000
χ402222-2-2-2-2222222-2-2222-22-2-22-2-200000000000000000-220002-2000000000000
χ412222-2-2-2-2-2-2-2-22222-2-22-2-22-22220000000022-2-2-2-22200000000000000000000
χ422222-2-2-2-2-2-2-2-22222-2-22-2-22-222200000000-2-22222-2-200000000000000000000
χ432222-2-2-2-2-2-2-2-222-2-222-22222-22-20000000000000000022000-2-2000000000000
χ442222-2-2-2-2-2-2-2-222-2-222-22222-22-200000000000000000-2-200022000000000000
χ4544-4-400004i−4i4i−4i4-4000000000000000000000022−22002i2−2i200000000000000000000
χ4644-4-400004i−4i4i−4i4-40000000000000000000000−222200−2i22i200000000000000000000
χ4744-4-400004i−4i−4i4i-44000000000000000000002i2−2i20022−220000000000000000000000
χ4844-4-400004i−4i−4i4i-4400000000000000000000−2i22i200−22220000000000000000000000
χ4944-4-40000−4i4i4i−4i-44000000000000000000002i2−2i200−22220000000000000000000000
χ5044-4-40000−4i4i4i−4i-4400000000000000000000−2i22i20022−220000000000000000000000
χ5144-4-40000−4i4i−4i4i4-4000000000000000000000022−2200−2i22i200000000000000000000
χ5244-4-40000−4i4i−4i4i4-40000000000000000000000−2222002i2−2i200000000000000000000
χ534-4-444-4000000004-44-40000000000002i2−2i22i2−2i20000000000000000000000000000
χ544-4-444-4000000004-44-4000000000000−2i22i2−2i22i20000000000000000000000000000
χ554-4-444-400000000-44-440000000022−2222−2200000000000000000000000000000000
χ564-4-444-400000000-44-4400000000−2222−222200000000000000000000000000000000
χ574-4-44-44000000004-4-4400000000000022−22−22220000000000000000000000000000
χ584-4-44-44000000004-4-44000000000000−222222−220000000000000000000000000000
χ594-4-44-4400000000-444-4000000002i2−2i2−2i22i200000000000000000000000000000000
χ604-4-44-4400000000-444-400000000−2i22i22i2−2i200000000000000000000000000000000
χ618-88-8008i−8i000000000000000000000000000000000000000000000000000000
χ628-88-800−8i8i000000000000000000000000000000000000000000000000000000

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