Finite Group Databasebeta

← Group #347944

Character table — Group #347944

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222222244444444444444444444444444444444444444444444444444444444416161616323232323232
order12222244444488882222222244444444444444444448888888888888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-111-1-11-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ61111111111111111-1-1-1-111-1-11-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ71111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ81111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ9111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1
χ10111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11
χ11111111111111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11
χ12111111111111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1
χ13111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-1-1-111-1-11
χ14111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1111-1-111-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-11-111-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-11-1-11
χ172222222222-2-2000022222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ182222222222-2-200002222-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ192222222222-2-20000-2-2-2-222-2-2-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ202222222222-2-20000-2-2-2-2-2-222-2222222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000
χ21222222-2-2-2-222222222-2-20000222-2-20000-2-200000000-2-2-2-200000000222222-2-2-2-2000000000000000000
χ22222222-2-2-2-2222222-2-22200002-2-2220000-2-200000000-2-2-2-20000000022-2-2-2-22222000000000000000000
χ23222222-2-2-2-222-2-2-2-222-2-20000222-2-20000-2-200000000222200000000-2-2-2-2-2-22222000000000000000000
χ24222222-2-2-2-222-2-2-2-2-2-22200002-2-2220000-2-200000000222200000000-2-22222-2-2-2-2000000000000000000
χ25222222-2-2-2-2-2-2000022-2-20000-2-2-2220000220000000000002i2i−2i−2i2i2i−2i−2i00000000002i2i−2i−2i2i2i−2i−2i0000000000
χ26222222-2-2-2-2-2-2000022-2-20000-2-2-222000022000000000000−2i−2i2i2i−2i−2i2i2i0000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ27222222-2-2-2-2-2-20000-2-2220000-222-2-20000220000000000002i2i−2i−2i−2i−2i2i2i00000000002i2i−2i−2i−2i−2i2i2i0000000000
χ28222222-2-2-2-2-2-20000-2-2220000-222-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i0000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ292222-2-222-2-222222200000022-2000000222-20000-2-2-2-222-2-20000-2-2-2-2-2-200000000000022220000000000
χ302222-2-222-2-2222222000000-2-2-2000000-2-22-20000222222-2-200002222-2-2000000000000-2-2-2-20000000000
χ312222-2-222-2-222-2-2-2-200000022-2000000222-20000-2-2-2-2-2-2220000222222000000000000-2-2-2-20000000000
χ322222-2-222-2-222-2-2-2-2000000-2-2-2000000-2-22-200002222-2-2220000-2-2-2-22200000000000022220000000000
χ332222-2-222-2-2-2-20000000000222000000-2-2-220000-2-22200002i2i−2i−2i0000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000
χ342222-2-222-2-2-2-20000000000222000000-2-2-220000-2-2220000−2i−2i2i2i000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000
χ352222-2-222-2-2-2-20000000000-2-2200000022-22000022-2-200002i2i−2i−2i000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000
χ362222-2-222-2-2-2-20000000000-2-2200000022-22000022-2-20000−2i−2i2i2i0000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000
χ372222-2-2-2-22222222200002200-200002200-22-2-2-2-20000-2-222-2-2-2-20000-2-200000000222200000000000000
χ382222-2-2-2-2222222220000-2-200-20000-2-200-2222220000-2-22222220000-2-200000000-2-2-2-200000000000000
χ392222-2-2-2-22222-2-2-2-200002200-200002200-22-2-2-2-2000022-2-2222200002200000000-2-2-2-200000000000000
χ402222-2-2-2-22222-2-2-2-20000-2-200-20000-2-200-222222000022-2-2-2-2-2-200002200000000222200000000000000
χ412222-2-2-2-222-2-200000000220020000-2-2002-2-2-2220000000000002i2i−2i−2i002i2i−2i−2i−2i−2i2i2i0000−2i−2i2i2i0000000000
χ422222-2-2-2-222-2-200000000220020000-2-2002-2-2-222000000000000−2i−2i2i2i00−2i−2i2i2i2i2i−2i−2i00002i2i−2i−2i0000000000
χ432222-2-2-2-222-2-200000000-2-2002000022002-222-2-20000000000002i2i−2i−2i00−2i−2i2i2i2i2i−2i−2i0000−2i−2i2i2i0000000000
χ442222-2-2-2-222-2-200000000-2-2002000022002-222-2-2000000000000−2i−2i2i2i002i2i−2i−2i−2i−2i2i2i00002i2i−2i−2i0000000000
χ452-22-22-22-22-200i2i2−i2−i20000002-202i−2i2i−2i2i−2i0000002i−2i2-200i2−i2i2−i22−22−2i2−i2i2−i2i2−i22−22−22−22−22−22−2i2−i2i2−i20000000000
χ462-22-22-22-22-200i2i2−i2−i20000002-20−2i2i−2i2i−2i2i000000−2i2i2-200i2−i2i2−i2−22−22i2−i2i2−i2i2−i2−22−22−22−22−22−22i2−i2i2−i20000000000
χ472-22-22-22-22-200i2i2−i2−i2000000-2202i−2i2i−2i−2i2i000000−2i2i-2200i2−i2i2−i2−22−22−i2i2−i2i2i2−i22−22−22−22−2−22−22−i2i2−i2i20000000000
χ482-22-22-22-22-200i2i2−i2−i2000000-220−2i2i−2i2i2i−2i0000002i−2i-2200i2−i2i2−i22−22−2−i2i2−i2i2i2−i2−22−22−22−222−22−2−i2i2−i2i20000000000
χ492-22-22-22-22-200−i2−i2i2i20000002-202i−2i2i−2i2i−2i0000002i−2i2-200−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−22−22−22−22−22−22−i2i2−i2i20000000000
χ502-22-22-22-22-200−i2−i2i2i20000002-20−2i2i−2i2i−2i2i000000−2i2i2-200−i2i2−i2i22−22−2−i2i2−i2i2−i2i22−22−22−22−22−22−2−i2i2−i2i20000000000
χ512-22-22-22-22-200−i2−i2i2i2000000-2202i−2i2i−2i−2i2i000000−2i2i-2200−i2i2−i2i22−22−2i2−i2i2−i2−i2i2−22−22−22−222−22−2i2−i2i2−i20000000000
χ522-22-22-22-22-200−i2−i2i2i2000000-220−2i2i−2i2i2i−2i0000002i−2i-2200−i2i2−i2i2−22−22i2−i2i2−i2−i2i22−22−22−22−2−22−22i2−i2i2−i20000000000
χ532-22-22-2-22-2200i2i2−i2−i200002-20002i−2i−2i2i002i−2i002-200002i−2i−i2i2−i2i2i2−i2−i2i22−2−22i2−i22−22−2−22−22i2−i2−i2i22−2−220000000000
χ542-22-22-2-22-2200i2i2−i2−i200002-2000−2i2i2i−2i00−2i2i002-20000−2i2i−i2i2−i2i2i2−i2−i2i2−222−2i2−i2−22−222−22−2i2−i2−i2i2−222−20000000000
χ552-22-22-2-22-2200i2i2−i2−i20000-220002i−2i−2i2i00−2i2i00-220000−2i2i−i2i2−i2i2−i2i2i2−i2−222−2i2−i22−22−2−22−22−i2i2i2−i2−222−20000000000
χ562-22-22-2-22-2200i2i2−i2−i20000-22000−2i2i2i−2i002i−2i00-2200002i−2i−i2i2−i2i2−i2i2i2−i22−2−22i2−i2−22−222−22−2−i2i2i2−i22−2−220000000000
χ572-22-22-2-22-2200−i2−i2i2i200002-20002i−2i−2i2i002i−2i002-200002i−2ii2−i2i2−i2−i2i2i2−i2−222−2−i2i2−22−222−22−2−i2i2i2−i2−222−20000000000
χ582-22-22-2-22-2200−i2−i2i2i200002-2000−2i2i2i−2i00−2i2i002-20000−2i2ii2−i2i2−i2−i2i2i2−i22−2−22−i2i22−22−2−22−22−i2i2i2−i22−2−220000000000
χ592-22-22-2-22-2200−i2−i2i2i20000-220002i−2i−2i2i00−2i2i00-220000−2i2ii2−i2i2−i2i2−i2−i2i22−2−22−i2i2−22−222−22−2i2−i2−i2i22−2−220000000000
χ602-22-22-2-22-2200−i2−i2i2i20000-22000−2i2i2i−2i002i−2i00-2200002i−2ii2−i2i2−i2i2−i2−i2i2−222−2−i2i22−22−2−22−22i2−i2−i2i2−222−20000000000
χ612-22-2-222-2-2200i2i2−i2−i22-22-22-22-200000000000-2200-2200i2−i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2i2−i20000000000
χ622-22-2-222-2-2200i2i2−i2−i22-22-2-22-22000000000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i20000000000
χ632-22-2-222-2-2200i2i2−i2−i2-22-222-2-2200000000000-22002-200i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i20000000000
χ642-22-2-222-2-2200i2i2−i2−i2-22-22-222-2000000000002-200-2200i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i20000000000
χ652-22-2-222-2-2200−i2−i2i2i22-22-22-22-200000000000-2200-2200−i2i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2−i2i20000000000
χ662-22-2-222-2-2200−i2−i2i2i22-22-2-22-22000000000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i20000000000
χ672-22-2-222-2-2200−i2−i2i2i2-22-222-2-2200000000000-22002-200−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i20000000000
χ682-22-2-222-2-2200−i2−i2i2i2-22-22-222-2000000000002-200-2200−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i20000000000
χ692-22-2-22-222-200i2i2−i2−i22-2-220000000002i−2i2i−2i0000−2i2i00−2i2i−i2i2i2−i2−22−22−222−2−i2i2−i2i2i2−i2i2−i2−i2i22−22−22−2−220000000000
χ702-22-2-22-222-200i2i2−i2−i22-2-22000000000−2i2i−2i2i00002i−2i002i−2i−i2i2i2−i22−22−22−2−22−i2i2−i2i2i2−i2i2−i2−i2i2−22−22−222−20000000000
χ712-22-2-22-222-200i2i2−i2−i2-222-20000000002i−2i−2i2i0000−2i2i002i−2i−i2i2i2−i2−22−222−2−22−i2i2i2−i2−i2i2−i2i2i2−i22−22−2−222−20000000000
χ722-22-2-22-222-200i2i2−i2−i2-222-2000000000−2i2i2i−2i00002i−2i00−2i2i−i2i2i2−i22−22−2−222−2−i2i2i2−i2−i2i2−i2i2i2−i2−22−222−2−220000000000
χ732-22-2-22-222-200−i2−i2i2i22-2-220000000002i−2i2i−2i0000−2i2i00−2i2ii2−i2−i2i22−22−22−2−22i2−i2i2−i2−i2i2−i2i2i2−i2−22−22−222−20000000000
χ742-22-2-22-222-200−i2−i2i2i22-2-22000000000−2i2i−2i2i00002i−2i002i−2ii2−i2−i2i2−22−22−222−2i2−i2i2−i2−i2i2−i2i2i2−i22−22−22−2−220000000000
χ752-22-2-22-222-200−i2−i2i2i2-222-20000000002i−2i−2i2i0000−2i2i002i−2ii2−i2−i2i22−22−2−222−2i2−i2−i2i2i2−i2i2−i2−i2i2−22−222−2−220000000000
χ762-22-2-22-222-200−i2−i2i2i2-222-2000000000−2i2i2i−2i00002i−2i00−2i2ii2−i2−i2i2−22−222−2−22i2−i2−i2i2i2−i2i2−i2−i2i22−22−2−222−20000000000
χ7744-4-4000000-444-44-40000000000000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ7844-4-4000000-444-44-4000000000000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ7944-4-4000000-44-44-440000000000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ8044-4-4000000-44-44-44000000000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ8188-8-80000008-800000000000000000000000000000000000000000000000000000000000000000000000
χ828-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000000000000000000

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