Finite Group Databasebeta

← Group #10628815

Character table — Group #10628815

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111111111111444444444444444444444161616161616161616161616161616161616161616161616161616161616161616161616161616161616
order1222336666662444444661212121212121212121212122224444466666688888812121212121212121212242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-111-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-111-11-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111-11-1-11-111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111111-1-11-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111
χ91111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ101111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-111-11-1-1−1−i32−1+i321+i321−i32−1−i32−1+i32-1-111-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ121111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-11-1-111−1−i32−1+i321+i321−i321+i321−i32-1-1-1-111−1−i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ131111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-111-1-11+i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111+i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ141111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11-1-11-1111+i321−i32−1−i32−1+i321+i321−i32-1-111-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ151111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11-1-11111+i321−i321+i321−i32−1−i32−1+i3211-1-1-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ161111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321111111+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ171111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ181111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ191111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-111-11-1-1−1+i32−1−i321−i321+i32−1+i32−1−i32-1-111-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ201111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-11-1-111−1+i32−1−i321−i321+i321−i321+i32-1-1-1-111−1+i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ211111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-111-1-11−i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111−i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ221111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11-1-11-1111−i321+i32−1+i32−1−i321−i321+i32-1-111-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ231111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-1-11111−i321+i321−i321+i32−1+i32−1−i3211-1-1-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ241111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321111111−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222-2-22-2-2222-2-22-2-22-2-22-2-20000000000000000002-20000000000000000002-22-2
χ2622222222222222-2-22-2-2222-2-22-2-22-2-22-2-2000000000000000000-22000000000000000000-22-22
χ272222222222222-22-2-22-222-22-2-22-2-22-2-22-200000000000000002-200000000000000002-22-20000
χ282222222222222-22-2-22-222-22-2-22-2-22-2-22-20000000000000000-220000000000000000-22-220000
χ292222222222222-2-22-2-2222-2-22-2-22-2-22-2-22000000000000002-2000000000000002-22-200000000
χ302222222222222-2-22-2-2222-2-22-2-22-2-22-2-2200000000000000-2200000000000000-22-2200000000
χ31222222222222-2222-2-2-2-2-2222222-2-2-2-2-2-20000002i−2i0000000000000000002i−2i2i−2i000000000000
χ32222222222222-2222-2-2-2-2-2222222-2-2-2-2-2-2000000−2i2i000000000000000000−2i2i−2i2i000000000000
χ33222222222222-22-2-2-222-2-22-2-22-2-2-222-222200-20000220000000000-2-200000000000000000000
χ34222222222222-22-2-2-222-2-22-2-22-2-2-222-222-20020000-2-200000000002200000000000000000000
χ35222222222222-2-22-22-22-2-2-22-2-22-22-222-220200-200000220000000000-2-2000000000000000000
χ36222222222222-2-22-22-22-2-2-22-2-22-22-222-220-200200000-2-2000000000022000000000000000000
χ37222222222222-2-2-2222-2-2-2-2-22-2-2222-222-200200-2000000220000000000-2-20000000000000000
χ38222222222222-2-2-2222-2-2-2-2-22-2-2222-222-200-2002000000-2-20000000000220000000000000000
χ392222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-22-2-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i30000000000000000002-2000000000000000000−1−i31+i3−1+i31−i3
χ402222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322-2-22-2-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3000000000000000000-220000000000000000001+i3−1−i31−i3−1+i3
χ412222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-22-2-22-2−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i300000000000000002-20000000000000000−1−i31+i3−1+i31−i30000
χ422222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-22-2-22-2−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i30000000000000000-2200000000000000001+i3−1−i31−i3−1+i30000
χ432222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-2-22-2-22−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i3000000000000002-200000000000000−1−i31+i3−1+i31−i300000000
χ442222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32-2-22-2-22−1−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i300000000000000-22000000000000001+i3−1−i31−i3−1+i300000000
χ452222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2222-2-2-21+i31−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i30000002i−2i0000000000000000002ζ11−2ζ112ζ7−2ζ7000000000000
χ462222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2222-2-2-21+i31−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31+i31−i31−i31−i3000000−2i2i000000000000000000−2ζ112ζ11−2ζ72ζ7000000000000
χ472222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-22-2-2-2221+i31−i3−1−i31+i31+i3−1+i31−i31−i31+i3−1−i3−1−i31−i3−1+i3−1+i3200-20000−1−i3−1+i300000000001+i31−i300000000000000000000
χ482222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-22-2-2-2221+i31−i3−1−i31+i31+i3−1+i31−i31−i31+i3−1−i3−1−i31−i3−1+i3−1+i3-200200001+i31−i30000000000−1−i3−1+i300000000000000000000
χ492222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-22-22-221+i31−i31+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1−i3−1+i31−i3−1+i30200-200000−1−i3−1+i300000000001+i31−i3000000000000000000
χ502222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-22-22-221+i31−i31+i3−1−i31+i31−i3−1+i31−i3−1−i31+i3−1−i3−1+i31−i3−1+i30-2002000001+i31−i30000000000−1−i3−1+i3000000000000000000
χ512222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-2-2222-21+i31−i31+i31+i3−1−i31−i31−i3−1+i3−1−i3−1−i31+i3−1+i3−1+i31−i300200-2000000−1−i3−1+i300000000001+i31−i30000000000000000
χ522222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-2-2222-21+i31−i31+i31+i3−1−i31−i31−i3−1+i3−1−i3−1−i31+i3−1+i3−1+i31−i300-20020000001+i31−i30000000000−1−i3−1+i30000000000000000
χ532222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322-2-22-2-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i30000000000000000002-2000000000000000000−1+i31−i3−1−i31+i3
χ542222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322-2-22-2-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3−1+i31−i31−i3−1−i31+i31+i3000000000000000000-220000000000000000001−i3−1+i31+i3−1−i3
χ552222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-22-2-22-2−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i300000000000000002-20000000000000000−1+i31−i3−1−i31+i30000
χ562222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-22-2-22-2−1+i3−1−i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i30000000000000000-2200000000000000001−i3−1+i31+i3−1−i30000
χ572222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-2-22-2-22−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i3000000000000002-200000000000000−1+i31−i3−1−i31+i300000000
χ582222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32-2-22-2-22−1+i3−1−i31−i31−i3−1+i31+i31+i3−1−i31−i31−i3−1+i31+i31+i3−1−i300000000000000-22000000000000001−i3−1+i31+i3−1−i300000000
χ592222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2222-2-2-21−i31+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i30000002i−2i0000000000000000002ζ7−2ζ72ζ11−2ζ11000000000000
χ602222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2222-2-2-21−i31+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i31−i31−i31−i31+i31+i31+i3000000−2i2i000000000000000000−2ζ72ζ7−2ζ112ζ11000000000000
χ612222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-22-2-2-2221−i31+i3−1+i31−i31−i3−1−i31+i31+i31−i3−1+i3−1+i31+i3−1−i3−1−i3200-20000−1+i3−1−i300000000001−i31+i300000000000000000000
χ622222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-22-2-2-2221−i31+i3−1+i31−i31−i3−1−i31+i31+i31−i3−1+i3−1+i31+i3−1−i3−1−i3-200200001−i31+i30000000000−1+i3−1−i300000000000000000000
χ632222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-22-22-221−i31+i31−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1+i3−1−i31+i3−1−i30200-200000−1+i3−1−i300000000001−i31+i3000000000000000000
χ642222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-22-22-221−i31+i31−i3−1+i31−i31+i3−1−i31+i3−1+i31−i3−1+i3−1−i31+i3−1−i30-2002000001−i31+i30000000000−1+i3−1−i3000000000000000000
χ652222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-2-2222-21−i31+i31−i31−i3−1+i31+i31+i3−1−i3−1+i3−1+i31−i3−1−i3−1−i31+i300200-2000000−1+i3−1−i300000000001−i31+i30000000000000000
χ662222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-2-2222-21−i31+i31−i31−i3−1+i31+i31+i3−1−i3−1+i3−1+i31−i3−1−i3−1−i31+i300-20020000001−i31+i30000000000−1+i3−1−i30000000000000000
χ6788-8-8888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000
χ6888-8-8−4−4i3−4+4i3−4−4i34+4i34+4i3−4+4i34−4i34−4i3000000000000000000000000000000000000000000000000000000000000000
χ6988-8-8−4+4i3−4−4i3−4+4i34−4i34−4i3−4−4i34+4i34+4i3000000000000000000000000000000000000000000000000000000000000000
χ708-88-888-88-8-88-8000000000000000000000000000000000000000000000000000000000000000
χ718-88-8−4−4i3−4+4i34+4i3−4−4i34+4i34−4i3−4+4i34−4i3000000000000000000000000000000000000000000000000000000000000000
χ728-88-8−4+4i3−4−4i34−4i3−4+4i34−4i34+4i3−4−4i34+4i3000000000000000000000000000000000000000000000000000000000000000
χ738-8-8888-8-88-8-88000000000000000000000000000000000000000000000000000000000000000
χ748-8-88−4−4i3−4+4i34+4i34+4i3−4−4i34−4i34−4i3−4+4i3000000000000000000000000000000000000000000000000000000000000000
χ758-8-88−4+4i3−4−4i34−4i34−4i3−4+4i34+4i34+4i3−4−4i3000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.