Finite Group Databasebeta

← Group #72259862

Character table — Group #72259862

Order 8064.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size116666677777777771212122424243232363636424242424242424242424242424242727272848484848484848484848484848484144144144168168168168168168168168168168168168168168168192192224224224224224224224224224224
order1224471433446612121212244488361428282246666661212121212121428284446612121212121212121212285656266881212242424242424242421423366121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ3111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-111-1-11111111-1-1-111-1-11111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111-1-111-1-1-1-11-1-1-1-1-111111-1-1-1-1-1-1-111-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ51111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−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+i321111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ61111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-1-1-111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ71111111−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i3211111111111-1-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32111-1-1-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32111-11+i321−i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32
χ81111111−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321-1-1-1-1-111111-1-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1-1-111−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1-11−1−i32−1+i32111+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32
χ91111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+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−i321111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ101111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-1-1-111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ111111111−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i3211111111111-1-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32111-1-1-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32111-11−i321+i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32
χ121111111−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321-1-1-1-1-111111-1-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1-1-111−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1-11−1+i32−1−i32111−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i32
χ1322222222222222222200000-1-1222222222222222222200200222200000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1
χ14222222222-2-222-2-2-2-2200000-1-1222-2-2-2-2-2-2-222-2-22222200-20022-2-200000000000000000000000000-1-1-1-1-1-1111111
χ152222222−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3200000-1-1222222−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3200200−1−i3−1+i3−1−i3−1+i300000000000000000000000000-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i32
χ162222222−1−i3−1+i3-2-2−1−i3−1+i31+i31+i31−i31−i3200000-1-1222-2-2-21+i31+i31−i31−i3−1−i3−1+i31+i31−i3−1−i3−1−i3−1+i3−1+i3200-200−1−i3−1+i31+i31−i300000000000000000000000000-1-11+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32
χ172222222−1+i3−1−i322−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3200000-1-1222222−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3200200−1+i3−1−i3−1+i3−1−i300000000000000000000000000-1-11−i321+i321−i321+i32-1-11−i321−i321+i321+i32
χ182222222−1+i3−1−i3-2-2−1+i3−1−i31−i31−i31+i31+i3200000-1-1222-2-2-21−i31−i31+i31+i3−1+i3−1−i31−i31+i3−1+i3−1+i3−1−i3−1−i3200-200−1+i3−1−i31−i31+i300000000000000000000000000-1-11−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32
χ19333-1-1333333333333-1111-1-1003-1-1-1-13-1-1-1-13333-1-1-1-1-111-111-1-1-1-1111111111-1-1111-1-111-1-1-1-1-1-1-1-1000000000000
χ20333-1-1333333333333-1-1-1-111003-1-1-1-13-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111000000000000
χ21333-1-13333-3-333-3-3-3-3-1111-1-1003-1-111-3111133-3-3-1-1-1-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-11111000000000000
χ22333-1-13333-3-333-3-3-3-3-1-1-1-111003-1-111-3111133-3-3-1-1-1-1-1-1-1111-1-111-1-1-1-11111-111111-1-1-1-11111-1-1-1-1000000000000
χ23333-1-133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1111-1-1003-1-1-1-131+i321+i321−i321−i32−3−3i32−3+3i32−3−3i32−3+3i321+i321+i321−i321−i32-111-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32000000000000
χ24333-1-133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-111003-1-1-1-131+i321+i321−i321−i32−3−3i32−3+3i32−3−3i32−3+3i321+i321+i321−i321−i32-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-111-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32000000000000
χ25333-1-133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-1111-1-1003-1-111-3−1−i32−1−i32−1+i32−1+i32−3−3i32−3+3i323+3i323−3i321+i321+i321−i321−i32-1111-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1-1-11+i321−i3211−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ26333-1-133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-1-1-1-111003-1-111-3−1−i32−1−i32−1+i32−1+i32−3−3i32−3+3i323+3i323−3i321+i321+i321−i321−i32-1-1-11111+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1111−1−i32−1+i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32000000000000
χ27333-1-133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1111-1-1003-1-1-1-131−i321−i321+i321+i32−3+3i32−3−3i32−3+3i32−3−3i321−i321−i321+i321+i32-111-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32000000000000
χ28333-1-133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-111003-1-1-1-131−i321−i321+i321+i32−3+3i32−3−3i32−3+3i32−3−3i321−i321−i321+i321+i32-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-111-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32000000000000
χ29333-1-133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-1111-1-1003-1-111-3−1+i32−1+i32−1−i32−1−i32−3+3i32−3−3i323−3i323+3i321−i321−i321+i321+i32-1111-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1-1-11−i321+i3211−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ30333-1-133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-1-1-1-111003-1-111-3−1+i32−1+i32−1−i32−1−i32−3+3i32−3−3i323−3i323+3i321−i321−i321+i321+i32-1-1-11111−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1111−1+i32−1−i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32000000000000
χ3133-13-1333333333333-111-11-100-13-13-1-13-13-1-1-1-1-13-13-1-111-111-1-1-1-111111111-11-1-1-1-11-1-1-11-11-11-11-1000000000000
χ3233-13-1333333333333-1-1-11-1100-13-13-1-13-13-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1111-11-11-11-11000000000000
χ3333-13-13333-3-333-3-3-3-3-111-11-100-13-1-311-31-31-1-1113-13-1-1111-1-1-1-1111111-1-1-1-1-11-1111-11-1-11-11-1-11-11000000000000
χ3433-13-13333-3-333-3-3-3-3-1-1-11-1100-13-1-311-31-31-1-1113-13-1-1-1-1111-1-111-1-1-1-111111-11-1-1-11-111-11-111-11-1000000000000
χ3533-13-133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-111-11-100-13-13-1-1−3−3i321+i32−3+3i321−i321+i321−i321+i321−i32−3−3i321+i32−3+3i321−i32-111-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-11+i321−i321-11+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32000000000000
χ3633-13-133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-11-1100-13-13-1-1−3−3i321+i32−3+3i321−i321+i321−i321+i321−i32−3−3i321+i32−3+3i321−i32-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i321-111−1−i32−1+i32-11−1−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32000000000000
χ3733-13-133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-111-11-100-13-1-3113+3i32−1−i323−3i32−1+i321+i321−i32−1−i32−1+i32−3−3i321+i32−3+3i321−i32-1111-1-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-11−1−i32−1+i32-111+i321−i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32000000000000
χ3833-13-133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-1-1-11-1100-13-1-3113+3i32−1−i323−3i32−1+i321+i321−i32−1−i32−1+i32−3−3i321+i32−3+3i321−i32-1-1-11111+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11-11+i321−i321-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32000000000000
χ3933-13-133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-111-11-100-13-13-1-1−3+3i321−i32−3−3i321+i321−i321+i321−i321+i32−3+3i321−i32−3−3i321+i32-111-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-11−i321+i321-11−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32000000000000
χ4033-13-133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-11-1100-13-13-1-1−3+3i321−i32−3−3i321+i321−i321+i321−i321+i32−3+3i321−i32−3−3i321+i32-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i321-111−1+i32−1−i32-11−1+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32000000000000
χ4133-13-133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-111-11-100-13-1-3113−3i32−1+i323+3i32−1−i321−i321+i32−1+i32−1−i32−3+3i321−i32−3−3i321+i32-1111-1-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-11−1+i32−1−i32-111−i321+i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32000000000000
χ4233-13-133−3+3i32−3−3i32-3-3−3+3i32−3−3i323−3i323−3i323+3i323+3i32-1-1-11-1100-13-1-3113−3i32−1+i323+3i32−1−i321−i321+i32−1+i32−1−i32−3+3i321−i32−3−3i321+i32-1-1-11111−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-11-11−i321+i321-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32000000000000
χ4333-1-13333333333333-111-1-1100-1-13-13-1-13-13-1-1-1-1-13-13-111-111-1-1-1-111111111-1-11-1-1-1-11-1-1-11-11-11-11000000000000
χ4433-1-13333333333333-1-1-111-100-1-13-13-1-13-13-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1111-11-11-11-1000000000000
χ4533-1-133333-3-333-3-3-3-3-111-1-1100-1-131-311-31-3-1-111-13-13-1111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-11-111-11-1000000000000
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χ4833-1-1333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-111-100-1-13-13-11+i32−3−3i321−i32−3+3i321+i321−i321+i321−i321+i32−3−3i321−i32−3+3i32-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i3211-11−1−i32−1+i321-1−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.