Finite Group Databasebeta

← Group #13178233

Character table — Group #13178233

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122222222222222222244444444444444444444444444444444444444888888888888888888888888888888181818181818181818181818181818181818363636363636363636363636363636363636363636363636363636
order122222333444466666666633333666666666666666666666121212121212121212121212666666666612121212121212121212121212121212121212122222446666666612121212222444444666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-11-11-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111
χ5111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-111-11-11-11111-1-111-1-1-1-11111-1-1
χ7111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111-11-1-111-1-111111111-1-1-1-1-1-1
χ8111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111111111
χ91111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ101111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-11111-1-111-1-111-1-1-1-11111
χ111111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-1-111-111111-1-1-1-1-1-11111-1-111
χ121111-1-111111-1-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11-1-111-1-1-1111111-1-111-1-111-1-1
χ131111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-11-1-1-111-111-1-1-1-1-1-1-1-111-1-111-1-1
χ141111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111-11-1-1-1-11111-1-11111-1-111
χ151111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-111-1-111-1-11111-1-1-1-11111
χ161111-1-1111-1-11111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-111-1-1-1111111-1-111-1-111-1-1-1-1
χ1722222222-122222-12222-1-122-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-122-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10022000000-1-1-1-100000200020200000-1-1000000-1-1-1-100
χ1822222222-122222-12222-1-122-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-12222-1-122-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-2000000111100000-2000-20-20000011000000111100
χ1922222222-1-2-2-2-22-12222-1-122-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111110022000000-1-1-1-1000002000-20-200000-1-1000000111100
χ2022222222-1-2-2-2-22-12222-1-122-1-1-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-21111111100-2-2000000111100000-20002020000011000000-1-1-1-100
χ212222222-122222-1222-1-1222-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1220000-1-1-1-10000000020002020000-1-10000-1-1-1-1000000
χ222222222-122222-1222-1-1222-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-20000111100000000-2000-20-200001100001111000000
χ232222222-12-2-2-2-2-1222-1-1222-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111220000-1-1-1-1000000002000-20-20000-1-100001111000000
χ242222222-12-2-2-2-2-1222-1-1222-12-1-1-122-1-122-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-2-20000111100000000-20002020000110000-1-1-1-1000000
χ25222222-122222222-1-12222-1-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100002200000000-1-1-1-1002200002-1-10000-1-100000000-1-1
χ26222222-122222222-1-12222-1-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000-2-200000000111100-2-20000-2110000110000000011
χ27222222-122-2-2-2-222-1-12222-1-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-2-2-2-211-1-1-1-122-1-1-1-11111-2-211111111-2-2111100002200000000-1-1-1-100-2-2000021100001100000000-1-1
χ28222222-122-2-2-2-222-1-12222-1-1-12-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-2-2-2-2-211-1-1-1-122-1-1-1-11111-2-211111111-2-211110000-2-200000000111100220000-2-1-10000-1-10000000011
χ292222-2-222-122-2-22-12222-1-122-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-211-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-2111111110022000000-1-1-1-100000-200020-20000011000000-1-11100
χ302222-2-222-122-2-22-12222-1-122-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-211-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-21111111100-2-20000001111000002000-20200000-1-100000011-1-100
χ312222-2-222-1-2-2222-12222-1-122-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-1-122-2-211111111-2-21111111122-1-1-1-1-1-1-1-10022000000-1-1-1-100000-2000-202000001100000011-1-100
χ322222-2-222-1-2-2222-12222-1-122-1-1-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-1-122-2-211111111-2-21111111122-1-1-1-1-1-1-1-100-2-2000000111100000200020-200000-1-1000000-1-11100
χ332222-2-22-1222-2-2-1222-1-1222-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-122-1-12211-2-2-2-211-2-2111111-1-122-1-1-1-1-1-111-2-2111111220000-1-1-1-100000000-200020-20000110000-1-111000000
χ342222-2-22-1222-2-2-1222-1-1222-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-122-1-12211-2-2-2-211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-2-200001111000000002000-2020000-1-1000011-1-1000000
χ352222-2-22-12-2-222-1222-1-1222-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-1-1222211-2-211111111-2-2111111-1-122-1-1-1-1-1-1220000-1-1-1-100000000-2000-202000011000011-1-1000000
χ362222-2-22-12-2-222-1222-1-1222-12-1-1-1-2-211-2-2-12-1-1-1-1-122-1-1-1-1-1-1-2-211-2-2-1-1222211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-2-20000111100000000200020-20000-1-10000-1-111000000
χ372222-2-2-12222-2-222-1-12222-1-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-2-2-2-2111111-2-21111-1-1-1-122-1-1-1-11111-2-2111100002200000000-1-1-1-100-220000-2110000-1-10000000011
χ382222-2-2-12222-2-222-1-12222-1-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-2-2-2-2111111-2-21111-1-1-1-122-1-1-1-11111-2-211110000-2-2000000001111002-200002-1-100001100000000-1-1
χ392222-2-2-122-2-22222-1-12222-1-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-22222-1-11111-2-211111111-2-21111-1-1-1-122-1-1-1-100002200000000-1-1-1-1002-20000-2-1-10000110000000011
χ402222-2-2-122-2-22222-1-12222-1-1-12-1-111-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111-2-2-2-22222-1-11111-2-211111111-2-21111-1-1-1-122-1-1-1-10000-2-200000000111100-2200002110000-1-100000000-1-1
χ4122-2-22-22222i−2i2i−2i22-22-2-2-2-2-2222222-22-22-222222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-222-2-22i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000
χ4222-2-22-2222−2i2i−2i2i22-22-2-2-2-2-2222222-22-22-222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-222-2-2−2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000000000000000000
χ4322-2-22-222-12i−2i2i−2i2-1-22-2-211-22-1-1-1-12-22-2-112-1-1-1-1-2-2111111112i−2i2i−2i−ii2i−2i−ii2i−2i2-2-11-11-1-1112i−2i−ii−ii−i−iii2i−2i−ii−ii−i−iii0000000000−i3−i3i3i300000000000000000−i3i30000003−33−300
χ4422-2-22-222-12i−2i2i−2i2-1-22-2-211-22-1-1-1-12-22-2-112-1-1-1-1-2-2111111112i−2i2i−2i−ii2i−2i−ii2i−2i2-2-11-11-1-1112i−2i−ii−ii−i−iii2i−2i−ii−ii−i−iii0000000000i3i3−i3−i300000000000000000i3−i3000000−33−3300
χ4522-2-22-222-1−2i2i−2i2i2-1-22-2-211-22-1-1-1-12-22-2-112-1-1-1-1-2-211111111−2i2i−2i2ii−i−2i2ii−i−2i2i2-2-11-11-1-111−2i2ii−ii−iii−i−i−2i2ii−ii−iii−i−i0000000000−i3−i3i3i300000000000000000−i3i3000000−33−3300
χ4622-2-22-222-1−2i2i−2i2i2-1-22-2-211-22-1-1-1-12-22-2-112-1-1-1-1-2-211111111−2i2i−2i2ii−i−2i2ii−i−2i2i2-2-11-11-1-111−2i2ii−ii−iii−i−i−2i2ii−ii−iii−i−i0000000000i3i3−i3−i300000000000000000i3−i30000003−33−300
χ4722-2-22-22-122i−2i2i−2i-12-2211-2-2-2-12-1-1-12-2-112-2-12-1-1-111-2-21111112i−2i−ii2i−2i−ii2i−2i2i−2i-112-2-11-1-111−ii2i−2i−ii−i−iii−ii2i−2i−ii−i−iii000000−i3−i3i3i30000000000000000000−i3i300003−33−3000000
χ4822-2-22-22-122i−2i2i−2i-12-2211-2-2-2-12-1-1-12-2-112-2-12-1-1-111-2-21111112i−2i−ii2i−2i−ii2i−2i2i−2i-112-2-11-1-111−ii2i−2i−ii−i−iii−ii2i−2i−ii−i−iii000000i3i3−i3−i30000000000000000000i3−i30000−33−33000000
χ4922-2-22-22-12−2i2i−2i2i-12-2211-2-2-2-12-1-1-12-2-112-2-12-1-1-111-2-2111111−2i2ii−i−2i2ii−i−2i2i−2i2i-112-2-11-1-111i−i−2i2ii−iii−i−ii−i−2i2ii−iii−i−i000000−i3−i3i3i30000000000000000000−i3i30000−33−33000000
χ5022-2-22-22-12−2i2i−2i2i-12-2211-2-2-2-12-1-1-12-2-112-2-12-1-1-111-2-2111111−2i2ii−i−2i2ii−i−2i2i−2i2i-112-2-11-1-111i−i−2i2ii−iii−i−ii−i−2i2ii−iii−i−i000000i3i3−i3−i30000000000000000000i3−i300003−33−3000000
χ5122-2-22-2-1222i−2i2i−2i221-1-2-2-2-21-1-12-1-1-112-22-2-1-12-1-11111-2-21111−ii2i−2i2i−2i2i−2i2i−2i−ii-11-112-2-1-111−ii−ii2i−2i−i−iii−ii−ii2i−2i−i−iii0000000000000033−3−3000000000−i3i30000−i3i3000000003−3
χ5222-2-22-2-1222i−2i2i−2i221-1-2-2-2-21-1-12-1-1-112-22-2-1-12-1-11111-2-21111−ii2i−2i2i−2i2i−2i2i−2i−ii-11-112-2-1-111−ii−ii2i−2i−i−iii−ii−ii2i−2i−i−iii00000000000000−3−333000000000i3−i30000i3−i300000000−33
χ5322-2-22-2-122−2i2i−2i2i221-1-2-2-2-21-1-12-1-1-112-22-2-1-12-1-11111-2-21111i−i−2i2i−2i2i−2i2i−2i2ii−i-11-112-2-1-111i−ii−i−2i2iii−i−ii−ii−i−2i2iii−i−i0000000000000033−3−3000000000i3−i30000i3−i3000000003−3
χ5422-2-22-2-122−2i2i−2i2i221-1-2-2-2-21-1-12-1-1-112-22-2-1-12-1-11111-2-21111i−i−2i2i−2i2i−2i2i−2i2ii−i-11-112-2-1-111i−ii−i−2i2iii−i−ii−ii−i−2i2iii−i−i00000000000000−3−333000000000−i3i30000−i3i300000000−33
χ5522-2-2-222222i−2i−2i2i22-22-2-2-2-2-222222-22-22-2222222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i−2i2i−2i2i−2i2i-22-22-22-2-2222i−2i2i−2i2i−2i2i2i−2i−2i−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000000000000000000
χ5622-2-2-22222−2i2i2i−2i22-22-2-2-2-2-222222-22-22-2222222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i-22-22-22-2-222−2i2i−2i2i−2i2i−2i−2i2i2i2i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000
χ5722-2-2-2222-12i−2i−2i2i2-1-22-2-211-22-1-1-1-1-22-221-12-1-1-1-1-2-2111111112i−2i2i−2i−ii−2i2ii−i−2i2i-221-11-111-1-12i−2i−ii−ii−i−iii−2i2ii−ii−iii−i−i0000000000−i3−i3i3i300000000000000000i3−i30000003−3−3300
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χ1154-44-40044-20000-424-4-442-2-44-2-2-2-2000000-42222-442-22-222-2-200000000000000000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ1164-44-4004-2400002-44-42-2-44-4-24-2-2-20000002-42222-2-442-222-2-2000000000000000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000
χ1174-44-4004-2400002-44-42-2-44-4-24-2-2-20000002-42222-2-442-222-2-20000000000000000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ1184-44-400-2440000-4-4-22-44-442-2-24-2-200000022-4222-22-2-4422-2-20000000000000000000000000000000000000000000000000000000023−23−2323000000000000000000000000000
χ1194-44-400-2440000-4-4-22-44-442-2-24-2-200000022-4222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000−232323−23000000000000000000000000000
χ1204-4-440044-20000-42-4-44-4-2244-2-2-2-2000000-422224-4-22-22-2-222000000000000000000000000000000000000000000004-4000000-22-220000000000000000000000000000000
χ1214-4-440044-20000-42-4-44-4-2244-2-2-2-2000000-422224-4-22-22-2-22200000000000000000000000000000000000000000000-440000002-22-20000000000000000000000000000000
χ1224-4-44004-2400002-4-4-4-224-44-24-2-2-20000002-4222-224-4-22-2-2220000000000000000000000000000000000000000004-40000-22-2200000000000000000000000000000000000
χ1234-4-44004-2400002-4-4-4-224-44-24-2-2-20000002-4222-224-4-22-2-222000000000000000000000000000000000000000000-4400002-22-200000000000000000000000000000000000
χ1244-4-4400-2440000-4-4224-44-4-2-2-24-2-200000022-422-22-224-4-2-22200000000000000000000000000000000000000000000004-400000000-22-22000000000000000000000000000
χ1254-4-4400-2440000-4-4224-44-4-2-2-24-2-200000022-422-22-224-4-2-2220000000000000000000000000000000000000000000000-44000000002-22-2000000000000000000000000000
χ1268-88-8008-4-40000448-84-44-4-8-4-422200000044-2-2-24-44-4-22-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1278-88-800-48-40000-84-44-884-44-42-4220000004-24-2-24-4-224-4-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1288-88-800-4-4800004-8-444-4-8842-4-422000000-244-2-2-224-44-4-2-222000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1298-88-800-4-4-4000044-444-44-44222−1−3i3−1+3i3000000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1308-88-800-4-4-4000044-444-44-44222−1+3i3−1−3i3000000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1318-8-88008-4-4000044-8-8-44-448-4-422200000044-2-2-2-44-442-222-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-8-8800-48-40000-84448-8-44-4-42-4220000004-24-2-2-442-2-4422-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1338-8-8800-4-4800004-844-448-8-42-4-422000000-244-2-22-2-44-4422-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-8-8800-4-4-400004444-44-44-4222−1−3i3−1+3i3000000-2-2-21+3i31−3i32-22-22-2−1−3i3−1+3i31+3i31−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-8-8800-4-4-400004444-44-44-4222−1+3i3−1−3i3000000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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