Finite Group Databasebeta

← Group #13164396

Character table — Group #13164396

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11222223333333333666666666666666662424242424242424242424243636363636363636363636361122222333333333366666666666666666242424242424242424242424363636363636363636363636
order1234612122233666666466666612121212121212121212333666121212121212224466661212121222646121222666666664666666121212121212121212126666661212121212122244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ4111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ5111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ6111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ7111-11-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11-11-11-11-1111-11-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-11-11-11-11-11-1
χ8111-11-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11-11-11-11-11111-11-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-11-11-11-11-11
χ9111-11-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32111-11-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ10111-11-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32111-11-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ11111-11-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32111-11-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ12111-11-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32111-11-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ132222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ14222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3222−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32000000000000222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3222−1−i3−1−i3−1+i3−1+i322−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32000000000000
χ15222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3222−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32000000000000222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3222−1+i3−1+i3−1−i3−1−i322−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32000000000000
χ16222-22-2-22222222222-2222222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111000000000000222-22-2-22222222222-2222222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111000000000000
χ17222-22-2-222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-222−1−i3−1−i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i3-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000222-22-2-222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-222−1−i3−1−i3−1+i3−1+i3-2-21+i31+i31+i31+i31−i31−i31−i31−i3-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ18222-22-2-222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-222−1+i3−1+i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i3-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000222-22-2-222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-222−1+i3−1+i3−1−i3−1−i3-2-21−i31−i31−i31−i31+i31+i31+i31+i3-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ192-220-200-2222-2-2-2-22202-22-22-20000000000222-2-2-20000000000000000002-220-200-2222-2-2-2-22202-22-22-20000000000222-2-2-2000000000000000000
χ202-220-200-2222-2-2-2-22202-22-22-20000000000-1-1-11113−33−33−30000000000002-220-200-2222-2-2-2-22202-22-22-20000000000-1-1-11113−33−33−3000000000000
χ212-220-200-2222-2-2-2-22202-22-22-20000000000-1-1-1111−33−33−330000000000002-220-200-2222-2-2-2-22202-22-22-20000000000-1-1-1111−33−33−33000000000000
χ222-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i300000000002−1−i3−1+i3-21+i31−i30000000000000000002-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i300000000002−1−i3−1+i3-21+i31−i3000000000000000000
χ232-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i30000000000-11+i321−i321−1−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110000000000002-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i30000000000-11+i321−i321−1−i32−1+i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ242-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i30000000000-11+i321−i321−1−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ110000000000002-220-200-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i302-2−1−i31+i3−1+i31−i30000000000-11+i321−i321−1−i32−1+i32−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ252-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i300000000002−1+i3−1−i3-21−i31+i30000000000000000002-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i300000000002−1+i3−1−i3-21−i31+i3000000000000000000
χ262-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i30000000000-11−i321+i321−1+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110000000000002-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i30000000000-11−i321+i321−1+i32−1−i323−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ272-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i30000000000-11−i321+i321−1+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ110000000000002-220-200-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i302-2−1+i31−i3−1−i31+i30000000000-11−i321+i321−1+i32−1−i32−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ283333333-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-100000000000011-1-11111-1-1-1-13333333-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-100000000000011-1-11111-1-1-1-1
χ293333333-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-1000000000000-1-111-1-1-1-111113333333-1-133-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-1000000000000-1-111-1-1-1-11111
χ303333333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-1-1-11+i321+i321−i321−i32-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i3200000000000011-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i323333333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-1-1-11+i321+i321−i321−i32-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i3200000000000011-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ313333333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-1-1-11+i321+i321−i321−i32-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32000000000000-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i323333333-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i32-1-1-11+i321+i321−i321−i32-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32000000000000-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ323333333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-1-1-11−i321−i321+i321+i32-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i3200000000000011-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i323333333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-1-1-11−i321−i321+i321+i32-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i3200000000000011-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ333333333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-1-1-11−i321−i321+i321+i32-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32000000000000-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i323333333-1-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i321−i321+i32-1-1-11−i321−i321+i321+i32-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32000000000000-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ34333-33-3-3-1-133-1-133-1-11-1-1-1-1-1-111-3111-31110000000000001-1-111-11-1-11-11333-33-3-3-1-133-1-133-1-11-1-1-1-1-1-111-3111-31110000000000001-1-111-11-1-11-11
χ35333-33-3-3-1-133-1-133-1-11-1-1-1-1-1-111-3111-3111000000000000-111-1-11-111-11-1333-33-3-3-1-133-1-133-1-11-1-1-1-1-1-111-3111-3111000000000000-111-1-11-111-11-1
χ36333-33-3-3-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i321-1-11+i321+i321−i321−i32113+3i32−1−i32−1−i32−1−i323−3i32−1+i32−1+i32−1+i320000000000001-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32333-33-3-3-1-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i321+i321−i321-1-11+i321+i321−i321−i32113+3i32−1−i32−1−i32−1−i323−3i32−1+i32−1+i32−1+i320000000000001-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.