Finite Group Databasebeta

← Group #13167305

Character table — Group #13167305

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363672727272108108108108
order1222223666666633336666666666666666666666663666666666444412121212121212121212121212121212121212121212121212121212121212124444444412121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ51111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-111-1-1
χ61111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111-1-111
χ71111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1111-1-111-1-111-1-1-1-111
χ81111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1-1-11111-1-1
χ911-1-11-11-111-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-11-11i−ii−i1-11-1i−ii−i1-11-1
χ1011-1-11-11-111-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i-11-11−ii−ii1-11-1−ii−ii-11-11
χ1111-1-11-11-111-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-11-11i−ii−i1-11-1i−ii−i-11-11
χ1211-1-11-11-111-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii-11-11−ii−ii1-11-1−ii−ii1-11-1
χ1311-1-1-111-1-1-111-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-111-1-1-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-111i−i−ii1-1-11i−i−ii1-1-11
χ1411-1-1-111-1-1-111-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-111-1-1-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-111−iii−i1-1-11−iii−i-111-1
χ1511-1-1-111-1-1-111-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-111-1-1-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-111i−i−ii1-1-11i−i−ii-111-1
χ1611-1-1-111-1-1-111-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-111-1-1-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1-111−iii−i1-1-11−iii−i1-1-11
χ172222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-20000-2-2-2-200000000
χ18222222-1-1-1-1-1-1-1-122-1-122-1-12-1-122-1-1-1-122-1-1-1-12-1-122-122-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-20000111100000000
χ19222222-1-1-1-1-1-1-1-122-1-122-1-12-1-122-1-1-1-122-1-1-1-12-1-122-122-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-20000111100000000
χ20222222-1-1-1-1-1-1-1-122-1-122-1-12-1-122-1-1-1-122-1-1-1-12-1-122-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122220000-1-1-1-100000000
χ21222222-1-1-1-1-1-1-1-122-1-122-1-12-1-122-1-1-1-122-1-1-1-12-1-122-122-1-1-1-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-2111122220000-1-1-1-100000000
χ222222-2-222-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2222-2-2-2-2000000000000000000000000000000000000-222-20000-2-22200000000
χ232222-2-2-1-11111-1-122-1-122-1-12-1-1-2-21111-2-211112-1-122-1-2-2-1-1-111110000−i3i3−i3i3i3−i3i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i3-222-2000011-1-100000000
χ242222-2-2-1-11111-1-122-1-122-1-12-1-1-2-21111-2-211112-1-122-1-2-2-1-1-111110000i3−i3i3−i3−i3i3−i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i3-222-2000011-1-100000000
χ252222-2-2-1-11111-1-122-1-122-1-12-1-1-2-21111-2-211112-1-122-1-2-2-1-1-1111122-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-211112-2-220000-1-11100000000
χ262222-2-2-1-11111-1-122-1-122-1-12-1-1-2-21111-2-211112-1-122-1-2-2-1-1-11111-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-12-2-220000-1-11100000000
χ2722-2-22-22-222-2-2-2222222222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222-22-2-222-2-20000000000000000000000000000000000002-22-20000-22-2200000000
χ2822-2-22-2-11-1-1111-122-1-122-1-1-21122-1-1-1-1-2-21111-211-2-2-12-2-111-1-11100003−3−333−3−330033−3−300−3−3330033−3−300−3−3332-22-200001-11-100000000
χ2922-2-22-2-11-1-1111-122-1-122-1-1-21122-1-1-1-1-2-21111-211-2-2-12-2-111-1-1110000−333−3−333−300−3−3330033−3−300−3−3330033−3−32-22-200001-11-100000000
χ3022-2-22-2-11-1-1111-122-1-122-1-1-21122-1-1-1-1-2-21111-211-2-2-12-2-111-1-1112i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii-22-220000-11-1100000000
χ3122-2-22-2-11-1-1111-122-1-122-1-1-21122-1-1-1-1-2-21111-211-2-2-12-2-111-1-111−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i-22-220000-11-1100000000
χ3222-2-2-222-2-2-222-2222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-22-222-2-2-2-22200000000000000000000000000000000000022-2-20000-222-200000000
χ3322-2-2-22-1111-1-11-122-1-122-1-1-211-2-2111122-1-1-1-1-211-2-2-1-22-11111-1-100003−3−33−333−30033−3−300−3−33300−3−3330033−3−322-2-200001-1-1100000000
χ3422-2-2-22-1111-1-11-122-1-122-1-1-211-2-2111122-1-1-1-1-211-2-2-1-22-11111-1-10000−333−33−3−3300−3−3330033−3−30033−3−300−3−33322-2-200001-1-1100000000
χ3522-2-2-22-1111-1-11-122-1-122-1-1-211-2-2111122-1-1-1-1-211-2-2-1-22-11111-1-12i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-2-2220000-111-100000000
χ3622-2-2-22-1111-1-11-122-1-122-1-1-211-2-2111122-1-1-1-1-211-2-2-1-22-11111-1-1−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-2-2220000-111-100000000
χ37444444444444441-2111-211111111111111111111-2-2-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ38444444444444441-2111-211111111111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
χ3944444444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000022220000-1-1-1-10000
χ4044444444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000000000-2-2-2-2000011110000
χ41444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-211111112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ42444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-21111111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ43444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-211111112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ44444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-21111111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ454444-4-444-4-4-4-4441-2111-211111-1-1-1-1-1-1-1-1-1-1-1-1111-2-2-222-2-2-2222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000
χ464444-4-444-4-4-4-4441-2111-211111-1-1-1-1-1-1-1-1-1-1-1-1111-2-2-222-2-2-22222-2-222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ474444-4-444-4-4-4-444-21-2-2-21-2-2-2-2-2222222222222-2-2-2111-1-1111-1-1-1-1000000000000000000000000000000000000000022-2-20000-1-1110000
χ484444-4-444-4-4-4-444-21-2-2-21-2-2-2-2-2222222222222-2-2-2111-1-1111-1-1-1-10000000000000000000000000000000000000000-2-222000011-1-10000
χ494444-4-4-2-22222-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2122111-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ504444-4-4-2-22222-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2122111-1-1-1-1-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ514444-4-4-2-22222-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2122111-1-1-1-122-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ524444-4-4-2-22222-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2122111-1-1-1-1-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ5344-4-44-44-444-4-4-441-2111-211-1-1-1111111-1-1-1-1-1-1-1-1-122-2-22-222-2-2222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii00000000000000000000
χ5444-4-44-44-444-4-4-441-2111-211-1-1-1111111-1-1-1-1-1-1-1-1-122-2-22-222-2-222−2i2i−2i2i−2i−2i2i2i−2i−2i2i2iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i00000000000000000000
χ5544-4-44-44-444-4-4-44-21-2-2-21-2-2222-2-2-2-2-2-2222222222-1-111-11-1-111-1-100000000000000000000000000000000000000002i−2i2i−2i0000−ii−ii0000
χ5644-4-44-44-444-4-4-44-21-2-2-21-2-2222-2-2-2-2-2-2222222222-1-111-11-1-111-1-10000000000000000000000000000000000000000−2i2i−2i2i0000i−ii−i0000
χ5744-4-44-4-22-2-2222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-11+3i321−3i32221-221-1-111-1-12i−2i2i−2i2ζ112ζ7−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ7−i−i−ζ11−ζ11−ζ7−ζ7iiζ11ζ11ζ7ζ7−i−i−ζ11−ζ11−ζ7−ζ7iiζ11ζ11ζ7ζ700000000000000000000
χ5844-4-44-4-22-2-2222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-11+3i321−3i32221-221-1-111-1-1−2i2i−2i2i−2ζ11−2ζ72ζ112ζ7−2ζ11−2ζ72ζ112ζ7iiζ11ζ11ζ7ζ7−i−i−ζ11−ζ11−ζ7−ζ7iiζ11ζ11ζ7ζ7−i−i−ζ11−ζ11−ζ7−ζ700000000000000000000
χ5944-4-44-4-22-2-2222-21-2−1+3i32−1−3i321-2−1+3i32−1−3i32-11−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-11−3i321+3i32221-221-1-111-1-12i−2i2i−2i2ζ72ζ11−2ζ7−2ζ112ζ72ζ11−2ζ7−2ζ11−i−i−ζ7−ζ7−ζ11−ζ11iiζ7ζ7ζ11ζ11−i−i−ζ7−ζ7−ζ11−ζ11iiζ7ζ7ζ11ζ1100000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.