Finite Group Databasebeta

← Group #112739

Character table — Group #112739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444444444448888888822224444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ91111-1-111-1-1-111-1-1-1-1-11-1111-1-11iiii−i−i−i−i1111-1-1-1-11-11-11-11-1ii−i−iii−i−iii−i−i
χ101111-1-111-1-1-111-1-1-1-1-11-1111-1-11iiii−i−i−i−i1111-1-1-1-1-11-11-11-11−i−iiiii−i−i−i−iii
χ111111-1-111-1-1-111-1-1-1-1-11-1111-1-11iiii−i−i−i−i-1-1-1-111111-1-111-1-11ii−i−i−i−iii−i−iii
χ121111-1-111-1-1-111-1-1-1-1-11-1111-1-11iiii−i−i−i−i-1-1-1-11111-111-1-111-1−i−iii−i−iiiii−i−i
χ131111-1-111-1-1-111-1-1-1-1-11-1111-1-11−i−i−i−iiiii1111-1-1-1-11-11-11-11-1−i−iii−i−iii−i−iii
χ141111-1-111-1-1-111-1-1-1-1-11-1111-1-11−i−i−i−iiiii1111-1-1-1-1-11-11-11-11ii−i−i−i−iiiii−i−i
χ151111-1-111-1-1-111-1-1-1-1-11-1111-1-11−i−i−i−iiiii-1-1-1-111111-1-111-1-11−i−iiiii−i−iii−i−i
χ161111-1-111-1-1-111-1-1-1-1-11-1111-1-11−i−i−i−iiiii-1-1-1-11111-111-1-111-1ii−i−iii−i−i−i−iii
χ1722222222222-2-222-2-22-2-22-2-2-2-220000000022-2-222-2-200000000000000000000
χ1822222222222-2-222-2-22-2-22-2-2-2-2200000000-2-222-2-22200000000000000000000
χ19222222222-2-222-2-2222-2-2-22-22-2-20000000000000000000000002-22-200000000
χ20222222222-2-222-2-2222-2-2-22-22-2-2000000000000000000000000-22-2200000000
χ21222222222-2-2-2-2-2-2-2-2222-2-22-22-2000000000000000000000000000000002-22-2
χ22222222222-2-2-2-2-2-2-2-2222-2-22-22-200000000000000000000000000000000-22-22
χ23222222-2-2-22222-2-222-2-2-22-22-22-222-2-222-2-20000000000000000000000000000
χ24222222-2-2-22222-2-222-2-2-22-22-22-2-2-222-2-2220000000000000000000000000000
χ25222222-2-2-222-2-2-2-2-2-2-22222-22-2-200000000000000000000000000002i−2i2i−2i0000
χ26222222-2-2-222-2-2-2-2-2-2-22222-22-2-20000000000000000000000000000−2i2i−2i2i0000
χ27222222-2-2-2-2-2222222-222-2-2-2-2-2200000000000000002-200-2200000000000000
χ28222222-2-2-2-2-2222222-222-2-2-2-2-220000000000000000-22002-200000000000000
χ29222222-2-2-2-2-2-2-222-2-2-2-2-2-2222220000000000000000002-200-22000000000000
χ30222222-2-2-2-2-2-2-222-2-2-2-2-2-222222000000000000000000-22002-2000000000000
χ312222-2-222-2222222-2-2-2-22-22-2-22-20000000000000000000000002i−2i−2i2i00000000
χ322222-2-222-2222222-2-2-2-22-22-2-22-2000000000000000000000000−2i2i2i−2i00000000
χ332222-2-222-222-2-22222-22-2-2-222-2-2000000000000000000000000000000002i−2i−2i2i
χ342222-2-222-222-2-22222-22-2-2-222-2-200000000000000000000000000000000−2i2i2i−2i
χ352222-2-222-2-2-2-2-2-2-222-2-222-2-22220000000022-2-2-2-22200000000000000000000
χ362222-2-222-2-2-2-2-2-2-222-2-222-2-222200000000-2-22222-2-200000000000000000000
χ372222-2-2-2-222222-2-2-2-222-2-2-2-222200000000000000002200-2-200000000000000
χ382222-2-2-2-222222-2-2-2-222-2-2-2-22220000000000000000-2-2002200000000000000
χ392222-2-2-2-2222-2-2-2-2222-22-222-2-220000000000000000002200-2-2000000000000
χ402222-2-2-2-2222-2-2-2-2222-22-222-2-22000000000000000000-2-20022000000000000
χ412222-2-2-2-22-2-22222-2-22-222-222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422222-2-2-2-22-2-22222-2-22-222-222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432222-2-2-2-22-2-2-2-2222222-222-2-22-200000000000000000000000000002-2-220000
χ442222-2-2-2-22-2-2-2-2222222-222-2-22-20000000000000000000000000000-222-20000
χ4544-4-4004i−4i04-4004i−4i000000000002-22i−2i2-22i−2i0000000000000000000000000000
χ4644-4-4004i−4i04-4004i−4i00000000000-22−2i2i-22−2i2i0000000000000000000000000000
χ4744-4-4004i−4i0-4400−4i4i000000000002i−2i-22−2i2i2-20000000000000000000000000000
χ4844-4-4004i−4i0-4400−4i4i00000000000−2i2i2-22i−2i-220000000000000000000000000000
χ4944-4-400−4i4i04-400−4i4i000000000002-2−2i2i2-2−2i2i0000000000000000000000000000
χ5044-4-400−4i4i04-400−4i4i00000000000-222i−2i-222i−2i0000000000000000000000000000
χ5144-4-400−4i4i0-44004i−4i000000000002i−2i2-2−2i2i-220000000000000000000000000000
χ5244-4-400−4i4i0-44004i−4i00000000000−2i2i-222i−2i2-20000000000000000000000000000
χ534-4-444-4000004-4004-4000000000000000002-22-22-22-200000000000000000000
χ544-4-444-4000004-4004-400000000000000000-22-22-22-2200000000000000000000
χ554-4-444-400000-4400-44000000000000000002-2-222-2-2200000000000000000000
χ564-4-444-400000-4400-4400000000000000000-222-2-222-200000000000000000000
χ574-4-44-44000004-400-44000000000000000002-22-2-22-2200000000000000000000
χ584-4-44-44000004-400-4400000000000000000-22-222-22-200000000000000000000
χ594-4-44-4400000-44004-4000000000000000002-2-22-222-200000000000000000000
χ604-4-44-4400000-44004-400000000000000000-222-22-2-2200000000000000000000
χ618-88-80000800000000-800000000000000000000000000000000000000000000
χ628-88-80000-800000000800000000000000000000000000000000000000000000

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