Finite Group Databasebeta

← Group #11721333

Character table — Group #11721333

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111333333333334446666666666666666661212121212121212121212484848484848484848484848
order1332669918181818181826644121212123636363636363636363636364121218183636363636363366999918181818
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ31111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ511111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ611111111111111-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ7111111−1−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+i32−1+i32−1+i32−1+i32−1+i32111−1−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
χ8111111−1−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+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32
χ9111111−1−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+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i3211−1−i32−1+i321
χ10111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ11111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i321+i321−i32−1+i3211−1−i321−i32-1-11+i32
χ12111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32−1+i32−1−i321−i321+i321−1−i32−1+i321-11+i321−i32-1
χ13111111−1+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−i32−1−i32−1−i32−1−i32−1−i32111−1+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
χ14111111−1+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−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i321
χ15111111−1+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−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32
χ16111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ17111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1−i32−1+i321+i321−i321−1+i32−1−i321-11−i321+i32-1
χ18111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i321−i321+i32−1−i3211−1+i321+i32-1-11−i32
χ1933333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1000000000000
χ2033333333333333-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-3-3111111000000000000
χ21333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32333-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-1-1−3−3i32−3+3i321+i321+i321+i321−i321−i321−i32000000000000
χ22333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-3-3-3-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321113+3i323−3i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000
χ23333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32333-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-1-1−3+3i32−3−3i321−i321−i321−i321+i321+i321+i32000000000000
χ24333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-3-3-3-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321113−3i323+3i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000
χ253−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i320000000000003−3−3i32−3+3i3200000000000000000000
χ263−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i322ζ14+2ζ262ζ14+2ζ26−2ζ26−2ζ26−2ζ14−2ζ14−2ζ22−2ζ222ζ22+2ζ342ζ22+2ζ34−2ζ34−2ζ34-11+i321−i32002ζ14+2ζ26−2ζ26−2ζ14−2ζ222ζ22+2ζ34−2ζ34000000000000
χ273−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i32−2ζ26−2ζ26−2ζ14−2ζ142ζ14+2ζ262ζ14+2ζ26−2ζ34−2ζ34−2ζ22−2ζ222ζ22+2ζ342ζ22+2ζ34-11+i321−i3200−2ζ26−2ζ142ζ14+2ζ26−2ζ34−2ζ222ζ22+2ζ34000000000000
χ283−3−3i32−3+3i323−3−3i32−3+3i32000000003−3−3i32−3+3i32-1-11+i321+i321−i321−i32−2ζ14−2ζ142ζ14+2ζ262ζ14+2ζ26−2ζ26−2ζ262ζ22+2ζ342ζ22+2ζ34−2ζ34−2ζ34−2ζ22−2ζ22-11+i321−i3200−2ζ142ζ14+2ζ26−2ζ262ζ22+2ζ34−2ζ34−2ζ22000000000000
χ293−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i3233−3−3i32−3−3i32−3+3i32−3+3i32000000000000-33+3i323−3i3200000000000000000000
χ303−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i322ζ14+2ζ262ζ14+2ζ26−2ζ26−2ζ26−2ζ14−2ζ14−2ζ22−2ζ222ζ22+2ζ342ζ22+2ζ34−2ζ34−2ζ341−1−i32−1+i3200−2ζ14−2ζ262ζ262ζ142ζ22−2ζ22−2ζ342ζ34000000000000
χ313−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i32−2ζ26−2ζ26−2ζ14−2ζ142ζ14+2ζ262ζ14+2ζ26−2ζ34−2ζ34−2ζ22−2ζ222ζ22+2ζ342ζ22+2ζ341−1−i32−1+i32002ζ262ζ14−2ζ14−2ζ262ζ342ζ22−2ζ22−2ζ34000000000000
χ323−3−3i32−3+3i323−3−3i32−3+3i3200000000-33+3i323−3i32-1-11+i321+i321−i321−i32−2ζ14−2ζ142ζ14+2ζ262ζ14+2ζ26−2ζ26−2ζ262ζ22+2ζ342ζ22+2ζ34−2ζ34−2ζ34−2ζ22−2ζ221−1−i32−1+i32002ζ14−2ζ14−2ζ262ζ26−2ζ22−2ζ342ζ342ζ22000000000000
χ333−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i320000000000003−3+3i32−3−3i3200000000000000000000
χ343−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i32−2ζ22−2ζ22−2ζ34−2ζ342ζ22+2ζ342ζ22+2ζ34−2ζ26−2ζ262ζ14+2ζ262ζ14+2ζ26−2ζ14−2ζ14-11−i321+i3200−2ζ22−2ζ342ζ22+2ζ34−2ζ262ζ14+2ζ26−2ζ14000000000000
χ353−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i322ζ22+2ζ342ζ22+2ζ34−2ζ22−2ζ22−2ζ34−2ζ342ζ14+2ζ262ζ14+2ζ26−2ζ14−2ζ14−2ζ26−2ζ26-11−i321+i32002ζ22+2ζ34−2ζ22−2ζ342ζ14+2ζ26−2ζ14−2ζ26000000000000
χ363−3+3i32−3−3i323−3+3i32−3−3i32000000003−3+3i32−3−3i32-1-11−i321−i321+i321+i32−2ζ34−2ζ342ζ22+2ζ342ζ22+2ζ34−2ζ22−2ζ22−2ζ14−2ζ14−2ζ26−2ζ262ζ14+2ζ262ζ14+2ζ26-11−i321+i3200−2ζ342ζ22+2ζ34−2ζ22−2ζ14−2ζ262ζ14+2ζ26000000000000
χ373−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i3233−3+3i32−3+3i32−3−3i32−3−3i32000000000000-33−3i323+3i3200000000000000000000
χ383−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i32−2ζ22−2ζ22−2ζ34−2ζ342ζ22+2ζ342ζ22+2ζ34−2ζ26−2ζ262ζ14+2ζ262ζ14+2ζ26−2ζ14−2ζ141−1+i32−1−i32002ζ222ζ34−2ζ22−2ζ342ζ26−2ζ14−2ζ262ζ14000000000000
χ393−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i322ζ22+2ζ342ζ22+2ζ34−2ζ22−2ζ22−2ζ34−2ζ342ζ14+2ζ262ζ14+2ζ26−2ζ14−2ζ14−2ζ26−2ζ261−1+i32−1−i3200−2ζ22−2ζ342ζ222ζ34−2ζ14−2ζ262ζ142ζ26000000000000
χ403−3+3i32−3−3i323−3+3i32−3−3i3200000000-33−3i323+3i32-1-11−i321−i321+i321+i32−2ζ34−2ζ342ζ22+2ζ342ζ22+2ζ34−2ζ22−2ζ22−2ζ14−2ζ14−2ζ26−2ζ262ζ14+2ζ262ζ14+2ζ261−1+i32−1−i32002ζ34−2ζ22−2ζ342ζ222ζ142ζ26−2ζ14−2ζ26000000000000
χ41666-2-2-266-2-2-2-2-2-20002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000
χ42666-2-2-266-2-2-2-2-2-2000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000
χ43666-2-2-2−3−3i3−3+3i31+i31+i31+i31−i31−i31−i30002i−2i2i−2i2i−2i−2ζ152ζ15−2ζ152ζ15−2ζ152ζ15−2ζ32ζ3−2ζ32ζ3−2ζ32ζ300000000000000000000000
χ44666-2-2-2−3−3i3−3+3i31+i31+i31+i31−i31−i31−i3000−2i2i−2i2i−2i2i2ζ15−2ζ152ζ15−2ζ152ζ15−2ζ152ζ3−2ζ32ζ3−2ζ32ζ3−2ζ300000000000000000000000
χ45666-2-2-2−3+3i3−3−3i31−i31−i31−i31+i31+i31+i30002i−2i2i−2i2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ152ζ15−2ζ152ζ15−2ζ152ζ1500000000000000000000000
χ46666-2-2-2−3+3i3−3−3i31−i31−i31−i31+i31+i31+i3000−2i2i−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ15−2ζ152ζ15−2ζ152ζ15−2ζ1500000000000000000000000
χ476−3−3i3−3+3i3-21+i31−i3004ζ14+4ζ26−4ζ26−4ζ14−4ζ224ζ22+4ζ34−4ζ340002i−2i−2ζ152ζ15−2ζ32ζ3−2ζ232ζ232ζ23+2ζ35−2ζ23−2ζ35−2ζ352ζ352ζ7+2ζ31−2ζ7−2ζ31−2ζ72ζ7−2ζ312ζ3100000000000000000000000
χ486−3−3i3−3+3i3-21+i31−i3004ζ14+4ζ26−4ζ26−4ζ14−4ζ224ζ22+4ζ34−4ζ34000−2i2i2ζ15−2ζ152ζ3−2ζ32ζ23−2ζ23−2ζ23−2ζ352ζ23+2ζ352ζ35−2ζ35−2ζ7−2ζ312ζ7+2ζ312ζ7−2ζ72ζ31−2ζ3100000000000000000000000
χ496−3−3i3−3+3i3-21+i31−i300−4ζ26−4ζ144ζ14+4ζ26−4ζ34−4ζ224ζ22+4ζ340002i−2i−2ζ152ζ15−2ζ32ζ32ζ23+2ζ35−2ζ23−2ζ35−2ζ352ζ35−2ζ232ζ23−2ζ312ζ312ζ7+2ζ31−2ζ7−2ζ31−2ζ72ζ700000000000000000000000
χ506−3−3i3−3+3i3-21+i31−i300−4ζ26−4ζ144ζ14+4ζ26−4ζ34−4ζ224ζ22+4ζ34000−2i2i2ζ15−2ζ152ζ3−2ζ3−2ζ23−2ζ352ζ23+2ζ352ζ35−2ζ352ζ23−2ζ232ζ31−2ζ31−2ζ7−2ζ312ζ7+2ζ312ζ7−2ζ700000000000000000000000
χ516−3−3i3−3+3i3-21+i31−i300−4ζ144ζ14+4ζ26−4ζ264ζ22+4ζ34−4ζ34−4ζ220002i−2i−2ζ152ζ15−2ζ32ζ3−2ζ352ζ35−2ζ232ζ232ζ23+2ζ35−2ζ23−2ζ35−2ζ72ζ7−2ζ312ζ312ζ7+2ζ31−2ζ7−2ζ3100000000000000000000000
χ526−3−3i3−3+3i3-21+i31−i300−4ζ144ζ14+4ζ26−4ζ264ζ22+4ζ34−4ζ34−4ζ22000−2i2i2ζ15−2ζ152ζ3−2ζ32ζ35−2ζ352ζ23−2ζ23−2ζ23−2ζ352ζ23+2ζ352ζ7−2ζ72ζ31−2ζ31−2ζ7−2ζ312ζ7+2ζ3100000000000000000000000
χ536−3+3i3−3−3i3-21−i31+i300−4ζ22−4ζ344ζ22+4ζ34−4ζ264ζ14+4ζ26−4ζ140002i−2i−2ζ32ζ3−2ζ152ζ152ζ7+2ζ31−2ζ7−2ζ31−2ζ312ζ31−2ζ72ζ72ζ23+2ζ35−2ζ23−2ζ35−2ζ232ζ23−2ζ352ζ3500000000000000000000000
χ546−3+3i3−3−3i3-21−i31+i300−4ζ22−4ζ344ζ22+4ζ34−4ζ264ζ14+4ζ26−4ζ14000−2i2i2ζ3−2ζ32ζ15−2ζ15−2ζ7−2ζ312ζ7+2ζ312ζ31−2ζ312ζ7−2ζ7−2ζ23−2ζ352ζ23+2ζ352ζ23−2ζ232ζ35−2ζ3500000000000000000000000
χ556−3+3i3−3−3i3-21−i31+i3004ζ22+4ζ34−4ζ22−4ζ344ζ14+4ζ26−4ζ14−4ζ260002i−2i−2ζ32ζ3−2ζ152ζ15−2ζ72ζ72ζ7+2ζ31−2ζ7−2ζ31−2ζ312ζ31−2ζ232ζ23−2ζ352ζ352ζ23+2ζ35−2ζ23−2ζ3500000000000000000000000
χ566−3+3i3−3−3i3-21−i31+i3004ζ22+4ζ34−4ζ22−4ζ344ζ14+4ζ26−4ζ14−4ζ26000−2i2i2ζ3−2ζ32ζ15−2ζ152ζ7−2ζ7−2ζ7−2ζ312ζ7+2ζ312ζ31−2ζ312ζ23−2ζ232ζ35−2ζ35−2ζ23−2ζ352ζ23+2ζ3500000000000000000000000
χ576−3+3i3−3−3i3-21−i31+i300−4ζ344ζ22+4ζ34−4ζ22−4ζ14−4ζ264ζ14+4ζ260002i−2i−2ζ32ζ3−2ζ152ζ15−2ζ312ζ31−2ζ72ζ72ζ7+2ζ31−2ζ7−2ζ31−2ζ352ζ352ζ23+2ζ35−2ζ23−2ζ35−2ζ232ζ2300000000000000000000000
χ586−3+3i3−3−3i3-21−i31+i300−4ζ344ζ22+4ζ34−4ζ22−4ζ14−4ζ264ζ14+4ζ26000−2i2i2ζ3−2ζ32ζ15−2ζ152ζ31−2ζ312ζ7−2ζ7−2ζ7−2ζ312ζ7+2ζ312ζ35−2ζ35−2ζ23−2ζ352ζ23+2ζ352ζ23−2ζ2300000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.