Finite Group Databasebeta

← Group #141409

Character table — Group #141409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122244444444448888888824888888888888888888881616161616161616161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ91111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i
χ101111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−ii−ii
χ111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii
χ121111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−i
χ131111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ1922222222-2-2-2-22200000000-2-20000000022-2-2000022-2-222−2−222−2−222−2−222−2−200000000
χ2022222222-2-2-2-22200000000-2-20000000022-2-2000022-2-2−2−222−2−222−2−222−2−22200000000
χ2122222222-2-2-2-22200000000-2-200000000-2-2220000-2-22222−2−222−2−2−2−222−2−22200000000
χ2222222222-2-2-2-22200000000-2-200000000-2-2220000-2-222−2−222−2−22222−2−222−2−200000000
χ23222222-2-222-2-2-2-200000000-22000022-2-2000022-2-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ24222222-2-222-2-2-2-200000000-22000022-2-2000022-2-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ25222222-2-222-2-2-2-200000000-220000-2-2220000-2-2220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ26222222-2-222-2-2-2-200000000-220000-2-2220000-2-2220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ27222222-2-2-2-222-2-22222-2-2-2-22-222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ28222222-2-2-2-222-2-22222-2-2-2-22-222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ29222222-2-2-2-222-2-2-2-2-2-222222-2-2-22200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ30222222-2-2-2-222-2-2-2-2-2-222222-2-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ312222-2-2222222-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-2222222-2-222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-222-2-2-2-2-2-200000000220000000022-2-20000-2-222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ342222-2-222-2-2-2-2-2-200000000220000000022-2-20000-2-222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ352222-2-222-2-2-2-2-2-2000000002200000000-2-222000022-2-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ362222-2-222-2-2-2-2-2-2000000002200000000-2-222000022-2-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ372222-2-2-2-222-2-222000000002-2000022-2-20000-2-22200002−22−2−22−222−22−2−22−2200000000
χ382222-2-2-2-222-2-222000000002-2000022-2-20000-2-2220000−22−222−22−2−22−222−22−200000000
χ392222-2-2-2-222-2-222000000002-20000-2-222000022-2-200002−22−2−22−22−22−222−22−200000000
χ402222-2-2-2-222-2-222000000002-20000-2-222000022-2-20000−22−222−22−22−22−2−22−2200000000
χ412222-2-2-2-2-2-222222222-2-2-2-2-22-2-22200000000000000002-2-22-222-20000000000000000
χ422222-2-2-2-2-2-222222222-2-2-2-2-22-2-2220000000000000000-222-22-2-220000000000000000
χ432222-2-2-2-2-2-22222-2-2-2-22222-2222-2-20000000000000000000000002-2-22-222-200000000
χ442222-2-2-2-2-2-22222-2-2-2-22222-2222-2-2000000000000000000000000-222-22-2-2200000000
χ4544-4-400004-400002i22i2−2i2−2i22i22i2−2i2−2i2000000000022−2222−224i−4i000000000000000000000000000000
χ4644-4-400004-400002i22i2−2i2−2i22i22i2−2i2−2i20000000000−2222−2222−4i4i000000000000000000000000000000
χ4744-4-400004-40000−2i2−2i22i22i2−2i2−2i22i22i2000000000022−2222−22−4i4i000000000000000000000000000000
χ4844-4-400004-40000−2i2−2i22i22i2−2i2−2i22i22i20000000000−2222−22224i−4i000000000000000000000000000000
χ4944-4-40000-4400002i22i2−2i2−2i2−2i2−2i22i22i2000000000022−22−2222004i−4i0000000000000000000000000000
χ5044-4-40000-4400002i22i2−2i2−2i2−2i2−2i22i22i20000000000−222222−2200−4i4i0000000000000000000000000000
χ5144-4-40000-440000−2i2−2i22i22i22i22i2−2i2−2i2000000000022−22−222200−4i4i0000000000000000000000000000
χ5244-4-40000-440000−2i2−2i22i22i22i22i2−2i2−2i20000000000−222222−22004i−4i0000000000000000000000000000
χ534-44-44i−4i4-400004i−4i2i2−2i22i2−2i22i2−2i22i2−2i20022−2222−220000000000000000000000000000000000000000
χ544-44-44i−4i4-400004i−4i−2i22i2−2i22i2−2i22i2−2i22i200−2222−22220000000000000000000000000000000000000000
χ554-44-44i−4i-440000−4i4i2i2−2i22i2−2i2−2i22i2−2i22i20022−22−22220000000000000000000000000000000000000000
χ564-44-44i−4i-440000−4i4i−2i22i2−2i22i22i2−2i22i2−2i200−222222−220000000000000000000000000000000000000000
χ574-44-4−4i4i4-40000−4i4i2i2−2i22i2−2i22i2−2i22i2−2i200−2222−22220000000000000000000000000000000000000000
χ584-44-4−4i4i4-40000−4i4i−2i22i2−2i22i2−2i22i2−2i22i20022−2222−220000000000000000000000000000000000000000
χ594-44-4−4i4i-4400004i−4i2i2−2i22i2−2i2−2i22i2−2i22i200−222222−220000000000000000000000000000000000000000
χ604-44-4−4i4i-4400004i−4i−2i22i2−2i22i22i2−2i22i2−2i20022−22−22220000000000000000000000000000000000000000
χ614-4-440000004-40000004-4-4400000022−2222−220000000022−2222−22000000000000000000000000
χ624-4-440000004-40000004-4-44000000−2222−222200000000−2222−2222000000000000000000000000
χ634-4-440000004-4000000-444-400000022−2222−2200000000−2222−2222000000000000000000000000
χ644-4-440000004-4000000-444-4000000−2222−22220000000022−2222−22000000000000000000000000
χ654-4-44000000-44004-4-44000000000022−22−22220000000022−22−2222000000000000000000000000
χ664-4-44000000-44004-4-440000000000−222222−2200000000−222222−22000000000000000000000000
χ674-4-44000000-4400-444-4000000000022−22−222200000000−222222−22000000000000000000000000
χ684-4-44000000-4400-444-40000000000−222222−220000000022−22−2222000000000000000000000000

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