Finite Group Databasebeta

← Group #116608

Character table — Group #116608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444888888888888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111-1-11-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-11-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-11-1-111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ12111111-1-11-1-111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ13111111-1-11-1-111-1-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ14111111-1-11-1-111-1-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ15111111-1-11-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-11-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2222-2-2-2-2-2-20000000022-2-222-2-200000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-200000000-2-222-2-22200000000000000000000
χ1922222222-2-2-2-2-22222-22-222-2-2-2-200000000000000002-22-20000000000000000
χ2022222222-2-2-2-2-22222-22-222-2-2-2-20000000000000000-22-220000000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-22-2-2-222222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-22-2-2-22222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ23222222-2-22-2-22222222-2-2-2-2-2-2220000000022-2-2-2-22200000000000000000000
χ24222222-2-22-2-22222222-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000
χ25222222-2-2-222-2-22222-2-22-2-222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ26222222-2-2-222-2-22222-2-22-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ27222222-2-2-222-2-2-2-2-2-2-2-2222-2-22200000000000000002-2-220000000000000000
χ28222222-2-2-222-2-2-2-2-2-2-2-2222-2-2220000000000000000-222-20000000000000000
χ292222-2-222222-2-222-2-22-2-22-22-22-20000000000000000000000002-22-200000000
χ302222-2-222222-2-222-2-22-2-22-22-22-2000000000000000000000000-22-2200000000
χ312222-2-222222-2-2-2-2222-2-2-22-22-22000000000000000000002-22-2000000000000
χ322222-2-222222-2-2-2-2222-2-2-22-22-2200000000000000000000-22-22000000000000
χ332222-2-222-2-2-22222-2-2-2-222-2-22-2200000000000000000000000000002-22-20000
χ342222-2-222-2-2-22222-2-2-2-222-2-22-220000000000000000000000000000-22-220000
χ352222-2-222-2-2-222-2-222-2-22-222-22-2000000000000000000000000000000002-22-2
χ362222-2-222-2-2-222-2-222-2-22-222-22-200000000000000000000000000000000-22-22
χ372222-2-2-2-22-2-2-2-222-2-2222-22-222-2000000000000000000002i−2i−2i2i000000000000
χ382222-2-2-2-22-2-2-2-222-2-2222-22-222-200000000000000000000−2i2i2i−2i000000000000
χ392222-2-2-2-22-2-2-2-2-2-2222222-22-2-220000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-22-2-2-2-2-2-2222222-22-2-22000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-2222222-2-2-22-2-222-2-22000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2222222-2-2-22-2-222-2-2200000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-22222-2-222-22-22-2-222-200000000000000000000000000002i−2i−2i2i0000
χ442222-2-2-2-2-22222-2-222-22-22-2-222-20000000000000000000000000000−2i2i2i−2i0000
χ4544-4-4004-444-4000000-4000000002-22-22-22-20000000000000000000000000000
χ4644-4-4004-444-4000000-400000000-22-22-22-220000000000000000000000000000
χ4744-4-4004-4-4-440000004000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ4844-4-4004-4-4-44000000400000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ4944-4-400-444-44000000-4000000002-22-2-22-220000000000000000000000000000
χ5044-4-400-444-44000000-400000000-22-222-22-20000000000000000000000000000
χ5144-4-400-44-44-40000004000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5244-4-400-44-44-4000000400000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ534-44-44-400000004i−4i4i−4i00000000000000000002i2−2i222−220000000000000000000000
χ544-44-44-400000004i−4i4i−4i0000000000000000000−2i22i2−22220000000000000000000000
χ554-44-44-40000000−4i4i−4i4i00000000000000000002i2−2i2−22220000000000000000000000
χ564-44-44-40000000−4i4i−4i4i0000000000000000000−2i22i222−220000000000000000000000
χ574-44-4-4400000004i−4i−4i4i0000000000000000022−2200002i2−2i200000000000000000000
χ584-44-4-4400000004i−4i−4i4i00000000000000000−22220000−2i22i200000000000000000000
χ594-44-4-440000000−4i4i4i−4i0000000000000000022−220000−2i22i200000000000000000000
χ604-44-4-440000000−4i4i4i−4i00000000000000000−222200002i2−2i200000000000000000000
χ618-8-8800000008i−8i0000000000000000000000000000000000000000000000000
χ628-8-880000000−8i8i0000000000000000000000000000000000000000000000000

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