Finite Group Databasebeta

← Group #118539

Character table — Group #118539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444888888888888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111-1-11-1-111-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111-1-11-1-111-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−i
χ1111111-1-11-1-111-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i-1-1-1-1111111-1-1-1-111ii−i−i−i−iii−i−iii
χ1211111-1-11-1-111-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i-1-1-1-11111-1-11111-1-1−i−iiiii−i−i−i−iii
χ1311111-1-11-1-111-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ1411111-1-11-1-111-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii
χ1511111-1-11-1-111-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii-1-1-1-1111111-1-1-1-111−i−iiiii−i−iii−i−i
χ1611111-1-11-1-111-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii-1-1-1-11111-1-11111-1-1ii−i−i−i−iiiii−i−i
χ172222222222-2-222-2-2-2-2222-2-2-2-2-200000000000000000000000000002i−2i2i−2i0000
χ182222222222-2-222-2-2-2-2222-2-2-2-2-20000000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-222-2-222-2-22-2-22-22-2-20000000000000000000000002i−2i2i−2i00000000
χ2022222222-2-222-2-222-2-22-2-22-22-2-2000000000000000000000000−2i2i−2i2i00000000
χ2122222222-2-2-2-2-2-2-2-2222-2-2-22-2220000000022-2-222-2-200000000000000000000
χ2222222222-2-2-2-2-2-2-2-2222-2-2-22-22200000000-2-222-2-22200000000000000000000
χ2322222-2-22222222-2-222-2-2-22-2-22-20000000000000000000000002-2-2200000000
χ2422222-2-22222222-2-222-2-2-22-2-22-2000000000000000000000000-222-200000000
χ2522222-2-2222-2-22222-2-2-2-2-2-222-220000000022-2-2-2-22200000000000000000000
χ2622222-2-2222-2-22222-2-2-2-2-2-222-2200000000-2-22222-2-200000000000000000000
χ2722222-2-22-2-2-2-2-2-22222-222-2-222-200000000000000000000000000002-2-220000
χ2822222-2-22-2-2-2-2-2-22222-222-2-222-20000000000000000000000000000-222-20000
χ292222-222-22222-2-22222-22-2-2-2-2-22000000000000000000000000000000002-22-2
χ302222-222-22222-2-22222-22-2-2-2-2-2200000000000000000000000000000000-22-22
χ312222-222-222-2-2-2-2-2-2-2-2-22-22222-200000000000000002-22-20000000000000000
χ322222-222-222-2-2-2-2-2-2-2-2-22-22222-20000000000000000-22-220000000000000000
χ332222-222-2-2-2222222-2-2-2-22-22-22-2000000000000000000002i−2i2i−2i000000000000
χ342222-222-2-2-2222222-2-2-2-22-22-22-200000000000000000000−2i2i−2i2i000000000000
χ352222-222-2-2-2-2-222-2-222-2-222-22-2222-2-222-2-20000000000000000000000000000
χ362222-222-2-2-2-2-222-2-222-2-222-22-22-2-222-2-2220000000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2222-22-222-2-2000000000000000000002i−2i−2i2i000000000000
χ382222-2-2-2-22222-2-2-2-2222-22-222-2-200000000000000000000−2i2i2i−2i000000000000
χ392222-2-2-2-222-2-2-2-222-2-22-222-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-2-222-2-2-2-222-2-22-222-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-2-2-2-22222-2-2-2-222-2-2-2222000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-22222-2-2-2-222-2-2-222200000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-2-2-222222222-222-2-2-200000000000000002-2-220000000000000000
χ442222-2-2-2-2-2-2-2-222222222-222-2-2-20000000000000000-222-20000000000000000
χ4544-4-4400-44-4004-4000000000000000000000022−2222−220000000000000000000000
χ4644-4-4400-44-4004-40000000000000000000000−2222−22220000000000000000000000
χ4744-4-4400-4-4400-44000000000000000000000022−22−22220000000000000000000000
χ4844-4-4400-4-4400-440000000000000000000000−222222−220000000000000000000000
χ4944-4-4-40044-400-44000000000000000000002i2−2i200002i2−2i200000000000000000000
χ5044-4-4-40044-400-4400000000000000000000−2i22i20000−2i22i200000000000000000000
χ5144-4-4-4004-44004-4000000000000000000002i2−2i20000−2i22i200000000000000000000
χ5244-4-4-4004-44004-400000000000000000000−2i22i200002i2−2i200000000000000000000
χ534-44-404-40004i−4i004i−4i00000000002-22i−2i2-22i−2i0000000000000000000000000000
χ544-44-404-40004i−4i004i−4i0000000000-22−2i2i-22−2i2i0000000000000000000000000000
χ554-44-404-4000−4i4i00−4i4i00000000002-2−2i2i2-2−2i2i0000000000000000000000000000
χ564-44-404-4000−4i4i00−4i4i0000000000-222i−2i-222i−2i0000000000000000000000000000
χ574-44-40-440004i−4i00−4i4i00000000002i−2i-22−2i2i2-20000000000000000000000000000
χ584-44-40-440004i−4i00−4i4i0000000000−2i2i2-22i−2i-220000000000000000000000000000
χ594-44-40-44000−4i4i004i−4i00000000002i−2i2-2−2i2i-220000000000000000000000000000
χ604-44-40-44000−4i4i004i−4i0000000000−2i2i-222i−2i2-20000000000000000000000000000
χ618-8-880000000000008i−8i00000000000000000000000000000000000000000000
χ628-8-88000000000000−8i8i00000000000000000000000000000000000000000000

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