Finite Group Databasebeta

← Group #72849

Character table — Group #72849

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112224444448888888888881122244444488888888888811222444444888888888888
order122442224442244888888883661212666121212661212242424242424242436612126661212126612122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1
χ411111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111
χ5111111-1-11-1-111-1-1ii−i−iii−i−i111111-1-11-1-111-1-1ii−i−iii−i−i111111-1-11-1-111-1-1ii−i−iii−i−i
χ6111111-1-11-1-111-1-1−i−iii−i−iii111111-1-11-1-111-1-1−i−iii−i−iii111111-1-11-1-111-1-1−i−iii−i−iii
χ7111111-1-11-1-1-1-111ii−i−i−i−iii111111-1-11-1-1-1-111ii−i−i−i−iii111111-1-11-1-1-1-111ii−i−i−i−iii
χ8111111-1-11-1-1-1-111−i−iiiii−i−i111111-1-11-1-1-1-111−i−iiiii−i−i111111-1-11-1-1-1-111−i−iiiii−i−i
χ9111-1-1-1111-1-11-11-1i−ii−ii−ii−i111-1-1-1111-1-11-11-1i−ii−ii−ii−i111-1-1-1111-1-11-11-1i−ii−ii−ii−i
χ10111-1-1-1111-1-11-11-1−ii−ii−ii−ii111-1-1-1111-1-11-11-1−ii−ii−ii−ii111-1-1-1111-1-11-11-1−ii−ii−ii−ii
χ11111-1-1-1111-1-1-11-11i−ii−i−ii−ii111-1-1-1111-1-1-11-11i−ii−i−ii−ii111-1-1-1111-1-1-11-11i−ii−i−ii−ii
χ12111-1-1-1111-1-1-11-11−ii−iii−ii−i111-1-1-1111-1-1-11-11−ii−iii−ii−i111-1-1-1111-1-1-11-11−ii−iii−ii−i
χ13111-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11111-1-111-1-111-1-11
χ14111-1-1-1-1-11111-1-11-111-1-111-1111-1-1-1-1-11111-1-11-111-1-111-1111-1-1-1-1-11111-1-11-111-1-111-1
χ15111-1-1-1-1-1111-111-11-1-11-111-1111-1-1-1-1-1111-111-11-1-11-111-1111-1-1-1-1-1111-111-11-1-11-111-1
χ16111-1-1-1-1-1111-111-1-111-11-1-11111-1-1-1-1-1111-111-1-111-11-1-11111-1-1-1-1-1111-111-1-111-11-1-11
χ1722222-22-2-22-200000000000022222-22-2-22-200000000000022222-22-2-22-2000000000000
χ1822222-2-22-2-2200000000000022222-2-22-2-2200000000000022222-2-22-2-22000000000000
χ19222-2-222-2-2-22000000000000222-2-222-2-2-22000000000000222-2-222-2-2-22000000000000
χ20222-2-22-22-22-2000000000000222-2-22-22-22-2000000000000222-2-22-22-22-2000000000000
χ2144-44-400000000000000000044-44-400000000000000000044-44-4000000000000000000
χ2244-4-4400000000000000000044-4-4400000000000000000044-4-44000000000000000000
χ238-80000000000000000000008-80000000000000000000008-8000000000000000000000
χ2411111111111111111111111−1+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+i32−1+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−i32−1−i32−1−i32
χ25111111111111111-1-1-1-1-1-1-1-1−1+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+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−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ2611111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ2711111111111-1-1-1-1-1-1-1-11111−1+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−i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ28111111-1-11-1-111-1-1ii−i−iii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11
χ29111111-1-11-1-111-1-1−i−iii−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11
χ30111111-1-11-1-1-1-111ii−i−i−i−iii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11
χ31111111-1-11-1-1-1-111−i−iiiii−i−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11
χ32111-1-1-1111-1-11-11-1i−ii−ii−ii−i−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ33111-1-1-1111-1-11-11-1−ii−ii−ii−ii−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ34111-1-1-1111-1-1-11-11i−ii−i−ii−ii−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11
χ35111-1-1-1111-1-1-11-11−ii−iii−ii−i−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11
χ36111-1-1-1-1-11111-1-111-1-111-1-11−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ37111-1-1-1-1-11111-1-11-111-1-111-1−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32
χ38111-1-1-1-1-1111-111-11-1-11-111-1−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32
χ39111-1-1-1-1-1111-111-1-111-11-1-11−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32
χ4022222-22-2-22-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31+i3000000000000
χ4122222-2-22-2-22000000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3000000000000
χ42222-2-222-2-2-22000000000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000000
χ43222-2-22-22-22-2000000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000
χ4444-44-4000000000000000000−2+2i3−2+2i32−2i3−2+2i32−2i3000000000000000000−2−2i3−2−2i32+2i3−2−2i32+2i3000000000000000000
χ4544-4-44000000000000000000−2+2i3−2+2i32−2i32−2i3−2+2i3000000000000000000−2−2i3−2−2i32+2i32+2i3−2−2i3000000000000000000
χ468-8000000000000000000000−4+4i34−4i3000000000000000000000−4−4i34+4i3000000000000000000000
χ4711111111111111111111111−1−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−i32−1−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+i32−1+i32−1+i32
χ48111111111111111-1-1-1-1-1-1-1-1−1−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−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+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ4911111111111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ5011111111111-1-1-1-1-1-1-1-11111−1−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+i32−1−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ51111111-1-11-1-111-1-1ii−i−iii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7
χ52111111-1-11-1-111-1-1−i−iii−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7
χ53111111-1-11-1-1-1-111ii−i−i−i−iii−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ54111111-1-11-1-1-1-111−i−iiiii−i−i−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ55111-1-1-1111-1-11-11-1i−ii−ii−ii−i−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ56111-1-1-1111-1-11-11-1−ii−ii−ii−ii−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ57111-1-1-1111-1-1-11-11i−ii−i−ii−ii−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7
χ58111-1-1-1111-1-1-11-11−ii−iii−ii−i−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7
χ59111-1-1-1-1-11111-1-111-1-111-1-11−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ60111-1-1-1-1-11111-1-11-111-1-111-1−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32
χ61111-1-1-1-1-1111-111-11-1-11-111-1−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32
χ62111-1-1-1-1-1111-111-1-111-11-1-11−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32
χ6322222-22-2-22-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31−i3000000000000
χ6422222-2-22-2-22000000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3000000000000
χ65222-2-222-2-2-22000000000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i3000000000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i3000000000000
χ66222-2-22-22-22-2000000000000−1−i3−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000−1+i3−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000
χ6744-44-4000000000000000000−2−2i3−2−2i32+2i3−2−2i32+2i3000000000000000000−2+2i3−2+2i32−2i3−2+2i32−2i3000000000000000000
χ6844-4-44000000000000000000−2−2i3−2−2i32+2i32+2i3−2−2i3000000000000000000−2+2i3−2+2i32−2i32−2i3−2+2i3000000000000000000
χ698-8000000000000000000000−4−4i34+4i3000000000000000000000−4+4i34−4i3000000000000000000000

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