Finite Group Databasebeta

← Group #351548

Character table — Group #351548

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222224444444444444444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444442244444444444444444444444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-2222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000000000000000
χ2122222222-2-22222-2-222-2-2220000000000000000-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2222222222-2-22222-2-222-2-2220000000000000000-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2322222222-2-22222-2-2-2-222-2-20000000000000000-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-22222-2-2-2-222-2-20000000000000000-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000222200000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000022220000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ29222-22-2-2-2220000-2-22-22-20022-2-222-2-200000000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ30222-22-2-2-2220000-2-22-22-20022-2-222-2-2000000000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ31222-22-2-2-2220000-2-22-22-200-2-222-2-22200000000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−222000000000000
χ32222-22-2-2-2220000-2-22-22-200-2-222-2-222000000000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−2000000000000
χ33222-22-2-2-2220000-2-2-22-220022-2-2-2-22200000000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−222000000000000
χ34222-22-2-2-2220000-2-2-22-220022-2-2-2-222000000000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2000000000000
χ35222-22-2-2-2220000-2-2-22-2200-2-22222-2-200000000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−2000000000000
χ36222-22-2-2-2220000-2-2-22-2200-2-22222-2-2000000000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−222000000000000
χ37222-22-2-2-2-2-20000222-2-2200000000002i2i−2i−2i2i2i−2i−2i000022−2−2−2−22222−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ38222-22-2-2-2-2-20000222-2-2200000000002i2i−2i−2i2i2i−2i−2i0000−2−22222−2−2−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ39222-22-2-2-2-2-20000222-2-220000000000−2i−2i2i2i−2i−2i2i2i000022−2−2−2−22222−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ40222-22-2-2-2-2-20000222-2-220000000000−2i−2i2i2i−2i−2i2i2i0000−2−22222−2−2−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ41222-22-2-2-2-2-2000022-222-200000000002i2i−2i−2i−2i−2i2i2i000022−2−2−2−222−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ42222-22-2-2-2-2-2000022-222-200000000002i2i−2i−2i−2i−2i2i2i0000−2−22222−2−222−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ43222-22-2-2-2-2-2000022-222-20000000000−2i−2i2i2i2i2i−2i−2i000022−2−2−2−222−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ44222-22-2-2-2-2-2000022-222-20000000000−2i−2i2i2i2i2i−2i−2i0000−2−22222−2−222−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ452-222-2-2-222-222-2-22-200000000002i−2i2i−2i00002i−2i2i−2i2-200000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-200000000000000000000
χ462-222-2-2-222-222-2-22-200000000002i−2i2i−2i00002i−2i2i−2i2-20000000000−2i2i−2i2i−2i2i−2i2i-22-22-22-2200000000000000000000
χ472-222-2-2-222-222-2-22-20000000000−2i2i−2i2i0000−2i2i−2i2i2-200000000002i−2i2i−2i2i−2i2i−2i-22-22-22-2200000000000000000000
χ482-222-2-2-222-222-2-22-20000000000−2i2i−2i2i0000−2i2i−2i2i2-20000000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-200000000000000000000
χ492-222-2-2-222-2-2-2222-200000000002i−2i2i−2i0000−2i2i−2i2i-22002-22-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ502-222-2-2-222-2-2-2222-200000000002i−2i2i−2i0000−2i2i−2i2i-2200-22-22-22-220000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ512-222-2-2-222-2-2-2222-20000000000−2i2i−2i2i00002i−2i2i−2i-22002-22-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ522-222-2-2-222-2-2-2222-20000000000−2i2i−2i2i00002i−2i2i−2i-2200-22-22-22-2200000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ532-222-2-2-22-2222-2-2-220000002i−2i2i−2i00002i−2i2i−2i0000-2200000000002i−2i2i−2i−2i2i−2i2i000000002-22-2-22-22000000000000
χ542-222-2-2-22-2222-2-2-220000002i−2i2i−2i00002i−2i2i−2i0000-220000000000−2i2i−2i2i2i−2i2i−2i00000000-22-222-22-2000000000000
χ552-222-2-2-22-2222-2-2-22000000−2i2i−2i2i0000−2i2i−2i2i0000-2200000000002i−2i2i−2i−2i2i−2i2i00000000-22-222-22-2000000000000
χ562-222-2-2-22-2222-2-2-22000000−2i2i−2i2i0000−2i2i−2i2i0000-220000000000−2i2i−2i2i2i−2i2i−2i000000002-22-2-22-22000000000000
χ572-222-2-2-22-22-2-222-220000002i−2i2i−2i0000−2i2i−2i2i00002-2002-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ582-222-2-2-22-22-2-222-220000002i−2i2i−2i0000−2i2i−2i2i00002-200-22-222-22-200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ592-222-2-2-22-22-2-222-22000000−2i2i−2i2i00002i−2i2i−2i00002-2002-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ602-222-2-2-22-22-2-222-22000000−2i2i−2i2i00002i−2i2i−2i00002-200-22-222-22-2000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ612-22-2-222-22-20000-2200002i−2i00002i−2i−2i2i2-2-220000002i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i2−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ622-22-2-222-22-20000-2200002i−2i00002i−2i−2i2i2-2-220000002i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i22−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ632-22-2-222-22-20000-2200002i−2i0000−2i2i2i−2i-222-20000002i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i22−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ642-22-2-222-22-20000-2200002i−2i0000−2i2i2i−2i-222-20000002i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i2−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ652-22-2-222-22-20000-220000−2i2i00002i−2i−2i2i-222-2000000−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i22−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ662-22-2-222-22-20000-220000−2i2i00002i−2i−2i2i-222-2000000−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ672-22-2-222-22-20000-220000−2i2i0000−2i2i2i−2i2-2-22000000−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i2−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ682-22-2-222-22-20000-220000−2i2i0000−2i2i2i−2i2-2-22000000−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i22−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ692-22-2-222-2-2200002-200002i−2i2i−2i−2i2i000000002-2-2200−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ702-22-2-222-2-2200002-200002i−2i2i−2i−2i2i000000002-2-2200−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ712-22-2-222-2-2200002-200002i−2i−2i2i2i−2i00000000-222-200−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i22−2−22−222−2000000000000
χ722-22-2-222-2-2200002-200002i−2i−2i2i2i−2i00000000-222-200−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−222−22−2−22000000000000
χ732-22-2-222-2-2200002-20000−2i2i2i−2i−2i2i00000000-222-2002i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ742-22-2-222-2-2200002-20000−2i2i2i−2i−2i2i00000000-222-2002i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ752-22-2-222-2-2200002-20000−2i2i−2i2i2i−2i000000002-2-22002i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−222−22−2−22000000000000
χ762-22-2-222-2-2200002-20000−2i2i−2i2i2i−2i000000002-2-22002i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i22−2−22−222−2000000000000
χ7744-44-44-4-4004-44-4000000000000000000000000000000000000000000000000000000000000000022−22000000
χ7844-44-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000−2222000000
χ7944-44-44-4-400-44-4400000000000000000000000000000000000000000000000000000000000000000022−220000
χ8044-44-44-4-400-44-44000000000000000000000000000000000000000000000000000000000000000000−22220000
χ814-4-444-44-4004-4-44000000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ824-4-444-44-4004-4-4400000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ834-4-444-44-400-444-40000000000000000000000000000000000000000000000000000000000002i2−2i20000000000
χ844-4-444-44-400-444-4000000000000000000000000000000000000000000000000000000000000−2i22i20000000000
χ8588-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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