Finite Group Databasebeta

← Group #112813

Character table — Group #112813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222224444444444444444448888888888888888222244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1111111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1111111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1111111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-11111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-11111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-111111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-111111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-222-2-2-2-2-2-22-22-2-2-200000000000000000000000000002i−2i2i−2i00000000
χ18222222222222-2-222-2-2-2-2-2-22-22-2-2-20000000000000000000000000000−2i2i−2i2i00000000
χ192222222222-2-222-2-2-2-2-2-222-2-2-222-20000000000000000000000000000000000002i−2i2i−2i
χ202222222222-2-222-2-2-2-2-2-222-2-2-222-2000000000000000000000000000000000000−2i2i−2i2i
χ212222222222-2-2-2-2-2-22222-2-2-22-2-2-2200000000000000002-22-200000000000000000000
χ222222222222-2-2-2-2-2-22222-2-2-22-2-2-220000000000000000-22-2200000000000000000000
χ23222222-2-2-2-222-2-2-2-22222222-2-2-22-200000000000000000000000000002-2-2200000000
χ24222222-2-2-2-222-2-2-2-22222222-2-2-22-20000000000000000000000000000-222-200000000
χ25222222-2-2-2-2-2-222222222-2-2-2-222-2-20000000000000000000000000000000000002-2-22
χ26222222-2-2-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000000000000000-222-2
χ27222222-2-2-2-2-2-2-2-222-2-2-2-222-222-22200000000000000002-2-2200000000000000000000
χ28222222-2-2-2-2-2-2-2-222-2-2-2-222-222-2220000000000000000-222-200000000000000000000
χ292222-2-222-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-222-2-222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-222-2-222-2-222-2-22222-22-22-2-20000000000000000000000002-22-2000000000000
χ322222-2-222-2-222-2-222-2-22222-22-22-2-2000000000000000000000000-22-22000000000000
χ332222-2-222-2-2-2-222-2-2-2-222-2-2222-22-2000000000000000000000000000000002i−2i2i−2i0000
χ342222-2-222-2-2-2-222-2-2-2-222-2-2222-22-200000000000000000000000000000000−2i2i−2i2i0000
χ352222-2-222-2-2-2-2-2-2-2-222-2-2222-222-22000000000000000000002-22-20000000000000000
χ362222-2-222-2-2-2-2-2-2-2-222-2-2222-222-2200000000000000000000-22-220000000000000000
χ372222-2-2-2-2222222-2-2-2-22222-2-22-2-222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ382222-2-2-2-2222222-2-2-2-22222-2-22-2-22-2-2-2-222222222-2-2-2-2000000000000000000000000
χ392222-2-2-2-22222-2-2-2-222-2-2-2-2-22222-20000000000000000000000002i−2i−2i2i000000000000
χ402222-2-2-2-22222-2-2-2-222-2-2-2-2-22222-2000000000000000000000000−2i2i2i−2i000000000000
χ412222-2-2-2-222-2-2222222-2-22222-2-2-2-2000000000000000000000000000000002-2-220000
χ422222-2-2-2-222-2-2222222-2-22222-2-2-2-200000000000000000000000000000000-222-20000
χ432222-2-2-2-222-2-2-2-222-2-222-2-22-2-2222000000000000000000002-2-220000000000000000
χ442222-2-2-2-222-2-2-2-222-2-222-2-22-2-222200000000000000000000-222-20000000000000000
χ4544-4-4004-4004-4004-400000000000000002i22i2−2i2−2i200002i22i2−2i2−2i2000000000000000000000000
χ4644-4-4004-4004-4004-40000000000000000−2i2−2i22i22i20000−2i2−2i22i22i2000000000000000000000000
χ4744-4-4004-400-4400-440000000000002i22i2−2i2−2i200002i22i2−2i2−2i20000000000000000000000000000
χ4844-4-4004-400-4400-44000000000000−2i2−2i22i22i20000−2i2−2i22i22i20000000000000000000000000000
χ4944-4-400-44004-400-4400000000000000002i22i2−2i2−2i20000−2i2−2i22i22i2000000000000000000000000
χ5044-4-400-44004-400-440000000000000000−2i2−2i22i22i200002i22i2−2i2−2i2000000000000000000000000
χ5144-4-400-4400-44004-40000000000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000
χ5244-4-400-4400-44004-4000000000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000
χ534-44-44-400000000004-44-4000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-44-400000000004-44-400000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-44-40000000000-44-44000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ564-44-44-40000000000-44-4400000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ574-44-4-4400000000004-4-44000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ584-44-4-4400000000004-4-4400000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ594-44-4-440000000000-444-4000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ604-44-4-440000000000-444-400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ614-4-4400004-4004-40000004-4000000000022−22−222222−22−22220000000000000000000000000000
χ624-4-4400004-4004-40000004-40000000000−222222−22−222222−220000000000000000000000000000
χ634-4-4400004-400-44000000-4400000022−22−22220000000022−22−2222000000000000000000000000
χ644-4-4400004-400-44000000-44000000−222222−2200000000−222222−22000000000000000000000000
χ654-4-440000-44004-4000000-44000000000022−22−2222−222222−220000000000000000000000000000
χ664-4-440000-44004-4000000-440000000000−222222−2222−22−22220000000000000000000000000000
χ674-4-440000-4400-440000004-400000022−22−222200000000−222222−22000000000000000000000000
χ684-4-440000-4400-440000004-4000000−222222−220000000022−22−2222000000000000000000000000

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