Finite Group Databasebeta

← Group #10628821

Character table — Group #10628821

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111111111222222444444444444444444888888888888161616161616161616161616161616161616161616161616161616161616161616161616
order122233666666441212121224444466121212121212121212124444121212121212121222444466668888881212121212121212242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111
χ91111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−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
χ101111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-11-1-1-1−1−i32−1+i321+i321−i3211-1-1-1-1−1−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+i3211−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-11-11-1-11+i321−i32−1−i32−1+i32-1-111-1-11+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+i3211−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1111+i321−i321+i321−i32-1-1-1-1111+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+i3211−1−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+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111-1-1−1−i32−1+i32−1−i32−1+i32-1-1-1-111−1−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+i3211−1−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+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-11-111−1−i32−1+i321+i321−i32-1-111-1-1−1−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+i3211−1−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+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11-11111+i321−i32−1−i32−1+i3211-1-1-1-11+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+i3211−1−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+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1-1-11+i321−i321+i321−i321111111+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−i3211−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+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
χ181111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-11-1-1-1−1+i32−1−i321−i321+i3211-1-1-1-1−1+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−i3211−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-11-11-1-11−i321+i32−1+i32−1−i32-1-111-1-11−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−i3211−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1111−i321+i321−i321+i32-1-1-1-1111−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−i3211−1+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−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111-1-1−1+i32−1−i32−1+i32−1−i32-1-1-1-111−1+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−i3211−1+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−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-11-111−1+i32−1−i321−i321+i32-1-111-1-1−1+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−i3211−1+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−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11-11111−i321+i32−1+i32−1−i3211-1-1-1-11−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−i3211−1+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−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1-1-11−i321+i321−i321+i321111111−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
χ252222222222222222222-22-2-2-222-2-22-22-2-2-2-2-200000000000000000000002-20000000000002-22-200000000
χ262222222222222222222-22-2-2-222-2-22-22-2-2-2-2-20000000000000000000000-22000000000000-22-2200000000
χ27222222222222222222-22-2-2-22-2-222-2-2-2-2-2-222000000000000020-200002200000000-2-20000000000000000
χ28222222222222222222-22-2-2-22-2-222-2-2-2-2-2-2220000000000000-2020000-2-200000000220000000000000000
χ29222222222222222222-2-2-222-2-2-2-2-2-22-2222-2-200000000000000002-2000000000000002-22-2000000000000
χ30222222222222222222-2-2-222-2-2-2-2-2-22-2222-2-20000000000000000-2200000000000000-22-22000000000000
χ31222222222222-2-2-2-2-2-222-2-22-22222-2-2-2-222-2-20000000000000000000000002-2000000000000002-22-20000
χ32222222222222-2-2-2-2-2-222-2-22-22222-2-2-2-222-2-2000000000000000000000000-2200000000000000-22-220000
χ33222222222222-2-2-2-2-2-22-2-22-2222-2-2-22-22-2-222000000000000000000000000002-200000000000000002-22-2
χ34222222222222-2-2-2-2-2-22-2-22-2222-2-2-22-22-2-22200000000000000000000000000-220000000000000000-22-22
χ35222222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-22-222-2-2-2-22-22-2222200000000000020-20002200000000-2-2000000000000000000
χ38222222222222-2-2-2-2-2-2-2-22-222-2-2-2-22-22-22222000000000000-202000-2-20000000022000000000000000000
χ392222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i32-22-2-2-2−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i300000000000000000000002-2000000000000−1−i31+i3−1+i31−i300000000
χ402222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i32-22-2-2-2−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i30000000000000000000000-220000000000001+i3−1−i31−i3−1+i300000000
χ412222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i3-22-2-2-221+i31−i3−1−i3−1+i31+i31+i31−i31−i31+i31−i3−1−i3−1+i3000000000000020-20000−1−i3−1+i3000000001+i31−i30000000000000000
χ422222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i3-22-2-2-221+i31−i3−1−i3−1+i31+i31+i31−i31−i31+i31−i3−1−i3−1+i30000000000000-20200001+i31−i300000000−1−i3−1+i30000000000000000
χ432222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-2-222-21+i31−i31+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i31+i31−i300000000000000002-200000000000000−1−i31+i3−1+i31−i3000000000000
χ442222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i3-2-2-222-21+i31−i31+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i31+i31−i30000000000000000-22000000000000001+i3−1−i31−i3−1+i3000000000000
χ452222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i322-2-22-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i31+i31−i30000000000000000000000002-200000000000000−1−i31+i3−1+i31−i30000
χ462222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i322-2-22-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i31+i31−i3000000000000000000000000-22000000000000001+i3−1−i31−i3−1+i30000
χ472222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i32-2-22-22−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i31+i31−i3−1−i3−1+i3000000000000000000000000002-20000000000000000−1−i31+i3−1+i31−i3
χ482222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i32-2-22-22−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i31+i31−i3−1−i3−1+i300000000000000000000000000-2200000000000000001+i3−1−i31−i3−1+i3
χ492222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i3-2222-2-21+i31−i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i32i2i−2i−2i2ζ112ζ11−2ζ11−2ζ112ζ72ζ7−2ζ7−2ζ7000000000000000000000000000000000000
χ502222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i3-2222-2-21+i31−i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i3−2i−2i2i2i−2ζ11−2ζ112ζ112ζ11−2ζ7−2ζ72ζ72ζ7000000000000000000000000000000000000
χ512222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i3-2-22-2221+i31−i31+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3−1−i3−1+i300000000000020-2000−1−i3−1+i3000000001+i31−i3000000000000000000
χ522222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3-2-21+i31−i31+i31−i3-2-22-2221+i31−i31+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000-2020001+i31−i300000000−1−i3−1+i3000000000000000000
χ532222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1−i3−1+i3−1−i32-22-2-2-2−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i300000000000000000000002-2000000000000−1+i31−i3−1−i31+i300000000
χ542222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1−i3−1+i3−1−i32-22-2-2-2−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i30000000000000000000000-220000000000001−i3−1+i31+i3−1−i300000000
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χ754-44-4−2+2i3−2−2i32−2i32+2i3−2+2i32−2i3−2−2i32+2i34-4−2+2i3−2−2i32−2i32+2i30000000000000000002i−2i2i−2i2ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000000000000000
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χ774-44-4−2+2i3−2−2i32−2i32+2i3−2+2i32−2i3−2−2i32+2i3-442−2i32+2i3−2+2i3−2−2i30000000000000000002-2-22−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000000000000000000000000000
χ784-44-4−2+2i3−2−2i32−2i32+2i3−2+2i32−2i3−2−2i32+2i3-442−2i32+2i3−2+2i3−2−2i3000000000000000000-222-21−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000000000000000000000000000
χ7988-8-88888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8−4−4i3−4+4i3−4−4i3−4+4i34+4i34+4i34−4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-8−4+4i3−4−4i3−4+4i3−4−4i34−4i34−4i34+4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000
χ828-8-8888-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-88−4−4i3−4+4i34+4i34−4i34+4i3−4−4i34−4i3−4+4i3000000000000000000000000000000000000000000000000000000000000000000000000
χ848-8-88−4+4i3−4−4i34−4i34+4i34−4i3−4+4i34+4i3−4−4i3000000000000000000000000000000000000000000000000000000000000000000000000

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