Finite Group Databasebeta

← Group #115995

Character table — Group #115995

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222222222222222222222444444444444444424444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ9111111111-1-111-1-1-11-1111-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1i−i11-1-1ii−i−ii−iii−i−i
χ10111111111-1-111-1-1-11-1111-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111i−i-1-111−i−iiii−i−i−iii
χ11111111111-1-111-1-1-11-1111-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1−ii11-1-1−i−iii−ii−i−iii
χ12111111111-1-111-1-1-11-1111-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111−ii-1-111ii−i−i−iiii−i−i
χ13111111111-1-111-1-1-11-1111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1−ii-1-111−i−iii−iiii−i−i
χ14111111111-1-111-1-1-11-1111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111−ii11-1-1ii−i−i−ii−i−iii
χ15111111111-1-111-1-1-11-1111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1i−i-1-111ii−i−ii−i−i−iii
χ16111111111-1-111-1-1-11-1111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111i−i11-1-1−i−iiii−iii−i−i
χ1722222222-222-2-2-2-2-2-2-22-2-2222-2-200000000000000002-22-20000000000000000
χ1822222222-222-2-2-2-2-2-2-22-2-2222-2-20000000000000000-22-220000000000000000
χ1922222222-2-2-2-2-2222-222-2-2-2-2-22200000000000000002-2-220000000000000000
χ2022222222-2-2-2-2-2222-222-2-2-2-2-2220000000000000000-222-20000000000000000
χ21222222-2-2222222-2-222-2-2-22-2-22-222-2-222-2-20000000000000000000000000000
χ22222222-2-2222222-2-222-2-2-22-2-22-2-2-222-2-2220000000000000000000000000000
χ23222222-2-22-2-222-2222-2-2-2-2-222-2222-2-2-2-2220000000000000000000000000000
χ24222222-2-22-2-222-2222-2-2-2-2-222-22-2-22222-2-20000000000000000000000000000
χ25222222-2-2-222-2-2-222-2-2-2222-2-2-2200000000000000000000002i−2i2i−2i0000000000
χ26222222-2-2-222-2-2-222-2-2-2222-2-2-220000000000000000000000−2i2i−2i2i0000000000
χ27222222-2-2-2-2-2-2-22-2-2-22-222-2222-200000000000000000000002i−2i−2i2i0000000000
χ28222222-2-2-2-2-2-2-22-2-2-22-222-2222-20000000000000000000000−2i2i2i−2i0000000000
χ292222-2-222222-2-222222-22-2-22-2-2-2000000000000000000002200000000-2-20000
χ302222-2-222222-2-222222-22-2-22-2-2-200000000000000000000-2-200000000220000
χ312222-2-2222-2-2-2-2-2-2-22-2-22-22-2222000000000000000000002i−2i00000000−2i2i0000
χ322222-2-2222-2-2-2-2-2-2-22-2-22-22-222200000000000000000000−2i2i000000002i−2i0000
χ332222-2-222-22222-2-2-2-2-2-2-22-22-222000000000000000000000000002i−2i2i−2i000000
χ342222-2-222-22222-2-2-2-2-2-2-22-22-22200000000000000000000000000−2i2i−2i2i000000
χ352222-2-222-2-2-222222-22-2-222-22-2-2000000000000000000000000002-2-22000000
χ362222-2-222-2-2-222222-22-2-222-22-2-200000000000000000000000000-222-2000000
χ372222-2-2-2-2222-2-22-2-2222-22-2-22-220000000022-2-222-2-200000000000000000000
χ382222-2-2-2-2222-2-22-2-2222-22-2-22-2200000000-2-222-2-22200000000000000000000
χ392222-2-2-2-22-2-2-2-2-2222-22-2222-22-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ402222-2-2-2-22-2-2-2-2-2222-22-2222-22-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ412222-2-2-2-2-22222-222-2-222-2-2-222-2000000000000000000000000000000002i−2i2i−2i
χ422222-2-2-2-2-22222-222-2-222-2-2-222-200000000000000000000000000000000−2i2i−2i2i
χ432222-2-2-2-2-2-2-2222-2-2-2222-222-2-22000000000000000000000000000000002-2-22
χ442222-2-2-2-2-2-2-2222-2-2-2222-222-2-2200000000000000000000000000000000-222-2
χ4544-4-4004-40000044-40-400000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4644-4-4004-40000044-40-40000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4744-4-4004-400000-4-440400000000000000002-22-2-22-2200000000000000000000
χ4844-4-4004-400000-4-44040000000000000000-22-222-22-200000000000000000000
χ4944-4-400-44000004-440-400000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ5044-4-400-44000004-440-40000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ5144-4-400-4400000-44-40400000000000000002-2-22-222-200000000000000000000
χ5244-4-400-4400000-44-4040000000000000000-222-22-2-2200000000000000000000
χ534-44-44-4004004-4000-40000000000000004i−4i0000000000000000000000000000
χ544-44-44-4004004-4000-4000000000000000−4i4i0000000000000000000000000000
χ554-44-44-400-400-44000400000000000004-4000000000000000000000000000000
χ564-44-44-400-400-4400040000000000000-44000000000000000000000000000000
χ574-44-4-4400400-44000-4000000000004i−4i00000000000000000000000000000000
χ584-44-4-4400400-44000-400000000000−4i4i00000000000000000000000000000000
χ594-44-4-4400-4004-400040000000004-40000000000000000000000000000000000
χ604-44-4-4400-4004-40004000000000-440000000000000000000000000000000000
χ618-8-88000008-8000000000000000000000000000000000000000000000000000
χ628-8-8800000-88000000000000000000000000000000000000000000000000000

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