Finite Group Databasebeta

← Group #347949

Character table — Group #347949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222222244444444444444444444444444444444444444444444444444444444416161616323232323232
order12222244444488882222444444444444444444444448888888888888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ81111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
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
χ11111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-11
χ12111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1
χ13111111111111-1-1-1-1-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-11-111-1
χ14111111111111-1-1-1-1-1-1111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111-11-1-11
χ15111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-11-11
χ16111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-11-1
χ1722222222-222-200002222-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222-222-2000022-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000
χ1922222222-222-20000-2-222-222-2-2-2-222-2-2-2-2-2-222-2-222220000000000000000000000000000000000000000
χ2022222222-222-20000-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ21222222-2-22-2-222222000020000000022-2-2-2-2000022-2-22200000000-2-2-2-2000000002222-2-2-2-20000000000
χ22222222-2-22-2-2222220000200000000-2-222-2-20000-2-2222200000000-2-2-2-200000000-2-2-2-222220000000000
χ23222222-2-22-2-22-2-2-2-2000020000000022-2-2-2-2000022-2-2-2-200000000222200000000-2-2-2-222220000000000
χ24222222-2-22-2-22-2-2-2-20000200000000-2-222-2-20000-2-222-2-2000000002222000000002222-2-2-2-20000000000
χ25222222-2-2-2-2-2-200000000-20000000022-2-2220000-2-222002i2i−2i−2i2i2i−2i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000
χ26222222-2-2-2-2-2-200000000-20000000022-2-2220000-2-22200−2i−2i2i2i−2i−2i2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ27222222-2-2-2-2-2-200000000-200000000-2-22222000022-2-2002i2i−2i−2i−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000
χ28222222-2-2-2-2-2-200000000-200000000-2-22222000022-2-200−2i−2i2i2i2i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-2-22-222-2222220022-2002200-2-200002-200-2-20000-2-20000222222-2-20000-2-2-2-2000000000000000000
χ302222-2-22-222-22222200-2-2-200-2-2002200002-200220000-2-20000-2-2-2-222-2-200002222000000000000000000
χ312222-2-22-222-22-2-2-2-20022-2002200-2-200002-200-2-20000220000-2-2-2-2-2-22200002222000000000000000000
χ322222-2-22-222-22-2-2-2-200-2-2-200-2-2002200002-2002200002200002222-2-2220000-2-2-2-2000000000000000000
χ332222-2-22-2-22-2-200000022200-2-200-2-20000-2200220000002i2i−2i−2i00000000−2i−2i2i2i00002i2i−2i−2i2i2i−2i−2i0000000000
χ342222-2-22-2-22-2-200000022200-2-200-2-20000-220022000000−2i−2i2i2i000000002i2i−2i−2i0000−2i−2i2i2i−2i−2i2i2i0000000000
χ352222-2-22-2-22-2-2000000-2-22002200220000-2200-2-20000002i2i−2i−2i00000000−2i−2i2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000
χ362222-2-22-2-22-2-2000000-2-22002200220000-2200-2-2000000−2i−2i2i2i000000002i2i−2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000
χ372222-2-2-222-22222222200-22200-2-2000000-22-2-2000000-2-222220000-2-222-2-2-2-20000000000000000000000
χ382222-2-2-222-2222222-2-200-2-2-20022000000-2222000000-2-2-2-2-2-20000-2-22222220000000000000000000000
χ392222-2-2-222-222-2-2-2-22200-22200-2-2000000-22-2-200000022-2-2-2-2000022-2-222220000000000000000000000
χ402222-2-2-222-222-2-2-2-2-2-200-2-2-20022000000-2222000000222222000022-2-2-2-2-2-20000000000000000000000
χ412222-2-2-22-2-22-2000022002-2-200-2-20000002-2220000000000002i2i−2i−2i00000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000
χ422222-2-2-22-2-22-2000022002-2-200-2-20000002-222000000000000−2i−2i2i2i000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000
χ432222-2-2-22-2-22-20000-2-20022200220000002-2-2-20000000000002i2i−2i−2i00000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000
χ442222-2-2-22-2-22-20000-2-20022200220000002-2-2-2000000000000−2i−2i2i2i000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000
χ452-22-22-2220-2-2022−2−22-22-2000002-22-22-22-200000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−20000000000
χ462-22-22-2220-2-2022−2−22-2-22000002-2-22-22-2200000000002−22−22−2−22−222−22−22−22−2−22−22−22−22−22−220000000000
χ472-22-22-2220-2-2022−2−2-222-200000-222-2-22-2200000000002−2−22−222−22−22−22−2−22−222−22−2−22−22−22−220000000000
χ482-22-22-2220-2-2022−2−2-22-2200000-22-222-22-200000000002−2−22−22−22−222−22−2−22−22−22−222−22−22−22−20000000000
χ492-22-22-2220-2-20−2−2222-22-2000002-22-22-22-20000000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−220000000000
χ502-22-22-2220-2-20−2−2222-2-22000002-2-22-22-220000000000−22−22−222−22−2−22−22−22−222−22−22−22−22−22−20000000000
χ512-22-22-2220-2-20−2−222-222-200000-222-2-22-220000000000−222−22−2−22−22−22−222−22−2−22−222−22−22−22−20000000000
χ522-22-22-2220-2-20−2−222-22-2200000-22-222-22-20000000000−222−22−22−22−2−22−222−22−22−22−2−22−22−22−220000000000
χ532-22-22-2-2-2022022−2−2000002i−2i2i−2i00002-2-22002i−2i2i−2i00002−2i2−i2−i2i2i2−i2−i2i2−22−22i2−i2−i2i2i2−i2−i2i22−22−2−22−220000000000
χ542-22-22-2-2-2022022−2−2000002i−2i−2i2i0000-222-2002i−2i−2i2i00002−2i2−i2−i2i2−i2i2i2−i2−22−22i2−i2−i2i2−i2i2i2−i2−22−222−22−20000000000
χ552-22-22-2-2-2022022−2−200000−2i2i2i−2i0000-222-200−2i2i2i−2i00002−2−i2i2i2−i2i2−i2−i2i2−22−22−i2i2i2−i2i2−i2−i2i2−22−222−22−20000000000
χ562-22-22-2-2-2022022−2−200000−2i2i−2i2i00002-2-2200−2i2i−2i2i00002−2−i2i2i2−i2−i2i2i2−i2−22−22−i2i2i2−i2−i2i2i2−i22−22−2−22−220000000000
χ572-22-22-2-2-20220−2−222000002i−2i2i−2i00002-2-22002i−2i2i−2i0000−22−i2i2i2−i2−i2i2i2−i22−22−2−i2i2i2−i2−i2i2i2−i2−22−222−22−20000000000
χ582-22-22-2-2-20220−2−222000002i−2i−2i2i0000-222-2002i−2i−2i2i0000−22−i2i2i2−i2i2−i2−i2i22−22−2−i2i2i2−i2i2−i2−i2i22−22−2−22−220000000000
χ592-22-22-2-2-20220−2−22200000−2i2i2i−2i0000-222-200−2i2i2i−2i0000−22i2−i2−i2i2−i2i2i2−i22−22−2i2−i2−i2i2−i2i2i2−i22−22−2−22−220000000000
χ602-22-22-2-2-20220−2−22200000−2i2i−2i2i00002-2-2200−2i2i−2i2i0000−22i2−i2−i2i2i2−i2−i2i22−22−2i2−i2−i2i2i2−i2−i2i2−22−222−22−20000000000
χ612-22-2-222-20-22022−2−2002-202i−2i0000-22000000−2i2i002i−2i2i−2i−22i2−i2−i2i22−22−22−2−22−i2i2i2−i2−22−22i2−i2−i2i2i2−i2−i2i20000000000
χ622-22-2-222-20-22022−2−2002-20−2i2i0000-220000002i−2i00−2i2i−2i2i−22−i2i2i2−i22−22−22−2−22i2−i2−i2i2−22−22−i2i2i2−i2−i2i2i2−i20000000000
χ632-22-2-222-20-22022−2−200-2202i−2i00002-2000000−2i2i00−2i2i−2i2i−22i2−i2−i2i2−22−222−2−22−i2i2i2−i22−22−2−i2i2i2−i2−i2i2i2−i20000000000
χ642-22-2-222-20-22022−2−200-220−2i2i00002-20000002i−2i002i−2i2i−2i−22−i2i2i2−i2−22−222−2−22i2−i2−i2i22−22−2i2−i2−i2i2i2−i2−i2i20000000000
χ652-22-2-222-20-220−2−222002-202i−2i0000-22000000−2i2i002i−2i2i−2i2−2−i2i2i2−i2−22−22−222−2i2−i2−i2i22−22−2−i2i2i2−i2−i2i2i2−i20000000000
χ662-22-2-222-20-220−2−222002-20−2i2i0000-220000002i−2i00−2i2i−2i2i2−2i2−i2−i2i2−22−22−222−2−i2i2i2−i22−22−2i2−i2−i2i2i2−i2−i2i20000000000
χ672-22-2-222-20-220−2−22200-2202i−2i00002-2000000−2i2i00−2i2i−2i2i2−2−i2i2i2−i22−22−2−222−2i2−i2−i2i2−22−22i2−i2−i2i2i2−i2−i2i20000000000
χ682-22-2-222-20-220−2−22200-220−2i2i00002-20000002i−2i002i−2i2i−2i2−2i2−i2−i2i22−22−2−222−2−i2i2i2−i2−22−22−i2i2i2−i2−i2i2i2−i20000000000
χ692-22-2-22-2202-2022−2−22-2000002i−2i-220000000000−2i2i2i−2i−2i2i−222−22−2i2−i2−i2i2−222−2−22−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000
χ702-22-2-22-2202-2022−2−22-200000−2i2i-2200000000002i−2i−2i2i2i−2i−222−22−2−i2i2i2−i2−222−2−22−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000
χ712-22-2-22-2202-2022−2−2-22000002i−2i2-20000000000−2i2i−2i2i2i−2i−22−22−22i2−i2−i2i2−222−22−22−2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ722-22-2-22-2202-2022−2−2-2200000−2i2i2-200000000002i−2i2i−2i−2i2i−22−22−22−i2i2i2−i2−222−22−22−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ732-22-2-22-2202-20−2−2222-2000002i−2i-220000000000−2i2i2i−2i−2i2i2−2−22−22−i2i2i2−i22−2−222−22−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000
χ742-22-2-22-2202-20−2−2222-200000−2i2i-2200000000002i−2i−2i2i2i−2i2−2−22−22i2−i2−i2i22−2−222−22−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000
χ752-22-2-22-2202-20−2−222-22000002i−2i2-20000000000−2i2i−2i2i2i−2i2−22−22−2−i2i2i2−i22−2−22−22−22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ762-22-2-22-2202-20−2−222-2200000−2i2i2-200000000002i−2i2i−2i−2i2i2−22−22−2i2−i2−i2i22−2−22−22−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ7744-4-40000400-44-44-40000000000000000000000000000000000000000000000000000000002-22-2000000
χ7844-4-40000400-44-44-4000000000000000000000000000000000000000000000000000000000-22-22000000
χ7944-4-40000400-4-44-440000000000000000000000000000000000000000000000000000000002-2-22000000
χ8044-4-40000400-4-44-44000000000000000000000000000000000000000000000000000000000-222-2000000
χ8188-8-80000-800800000000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880000000042−42−42420000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800000000−424242−420000000000000000000000000000000000000000000000000000000000000000000

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