Finite Group Databasebeta

← Group #238921

Character table — Group #238921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444444444448888888822244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-111111-1-1-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-11-1-111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-1111-1-111-1-111-1-1
χ1011111111-1-11-1-111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-111-11-1-1-111-1-11111-1-1
χ1111111111-1-11-1-111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1-1-111-1-111
χ1211111111-1-11-1-111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-1-11111-1-1-1-111
χ1311111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111
χ1411111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-111-1-111
χ1511111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11-1-111-1-11111-1-1
χ1611111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-111-1-111-1-111-1-1
χ172222222222-2222-2-2-22-2-2-2-22-2-22000000000000000000000000000000002-22-2
χ182222222222-2222-2-2-22-2-2-2-22-2-2200000000000000000000000000000000-22-22
χ1922222222-2-2-2-2-22-2-2-2222-2-2-222-2000000000000000000000000000000002-2-22
χ2022222222-2-2-2-2-22-2-2-2222-2-2-222-200000000000000000000000000000000-222-2
χ21222222-2-2222-2-2-2222-2-2-2-2-2222-222-2-222-2-20000000000000000000000000000
χ22222222-2-2222-2-2-2222-2-2-2-2-2222-2-2-222-2-2220000000000000000000000000000
χ23222222-2-222-2-2-2-2-2-2-2-222222-2-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ24222222-2-222-2-2-2-2-2-2-2-222222-2-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ25222222-2-2-2-2222-2222-222-2-2-2-2-2222-2-2-2-2220000000000000000000000000000
χ26222222-2-2-2-2222-2222-222-2-2-2-2-22-2-22222-2-20000000000000000000000000000
χ27222222-2-2-2-2-222-2-2-2-2-2-2-222-2222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ28222222-2-2-2-2-222-2-2-2-2-2-2-222-222200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292222-2-22222222-2-2-22-22-22-2-22-2-20000000000000000000000002i−2i2i−2i00000000
χ302222-2-22222222-2-2-22-22-22-2-22-2-2000000000000000000000000−2i2i−2i2i00000000
χ312222-2-22222-222-222-2-2-22-22-2-22-200000000000000000000000000002i−2i2i−2i0000
χ322222-2-22222-222-222-2-2-22-22-2-22-20000000000000000000000000000−2i2i−2i2i0000
χ332222-2-222-2-22-2-2-2-2-22-2-222-22-2220000000000000000000000002i−2i−2i2i00000000
χ342222-2-222-2-22-2-2-2-2-22-2-222-22-222000000000000000000000000−2i2i2i−2i00000000
χ352222-2-222-2-2-2-2-2-222-2-22-2-2222-2200000000000000000000000000002i−2i−2i2i0000
χ362222-2-222-2-2-2-2-2-222-2-22-2-2222-220000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2222-2-22-2-222-22-22-22-22000000000000000022000-2-20000000000000
χ382222-2-2-2-2222-2-22-2-222-22-22-22-220000000000000000-2-2000220000000000000
χ392222-2-2-2-222-2-2-2222-222-22-2-2-22200000000000000000022-200-2000000000000
χ402222-2-2-2-222-2-2-2222-222-22-2-2-222000000000000000000-2-22002000000000000
χ412222-2-2-2-2-2-22222-2-2222-2-222-22-200000000000000002-2000-220000000000000
χ422222-2-2-2-2-2-22222-2-2222-2-222-22-20000000000000000-220002-20000000000000
χ432222-2-2-2-2-2-2-222222-22-222-222-2-20000000000000000002-2200-2000000000000
χ442222-2-2-2-2-2-2-222222-22-222-222-2-2000000000000000000-22-2002000000000000
χ4544-4-4004i−4i4-404i−4i00000000000002-22i−2i2-22i−2i0000000000000000000000000000
χ4644-4-4004i−4i4-404i−4i0000000000000-22−2i2i-22−2i2i0000000000000000000000000000
χ4744-4-4004i−4i-440−4i4i00000000000002-22i−2i-22−2i2i0000000000000000000000000000
χ4844-4-4004i−4i-440−4i4i0000000000000-22−2i2i2-22i−2i0000000000000000000000000000
χ4944-4-400−4i4i4-40−4i4i00000000000002-2−2i2i2-2−2i2i0000000000000000000000000000
χ5044-4-400−4i4i4-40−4i4i0000000000000-222i−2i-222i−2i0000000000000000000000000000
χ5144-4-400−4i4i-4404i−4i00000000000002-2−2i2i-222i−2i0000000000000000000000000000
χ5244-4-400−4i4i-4404i−4i0000000000000-222i−2i2-2−2i2i0000000000000000000000000000
χ534-4-444-4000040004-4-40000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-4-444-4000040004-4-4000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-4-444-40000-4000-44400000000000000000000022−22−222200000000000000000000
χ564-4-444-40000-4000-444000000000000000000000−222222−2200000000000000000000
χ574-4-44-4400004000-44-4000000000000000002i2−2i22i2−2i2000000000000000000000000
χ584-4-44-4400004000-44-400000000000000000−2i22i2−2i22i2000000000000000000000000
χ594-4-44-440000-40004-440000000000000000022−22−2222000000000000000000000000
χ604-4-44-440000-40004-4400000000000000000−222222−22000000000000000000000000
χ618-88-80000000008000-800000000000000000000000000000000000000000000
χ628-88-8000000000-8000800000000000000000000000000000000000000000000

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