Finite Group Databasebeta

← Group #13161805

Character table — Group #13161805

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size112222222222222224444444444444444444444444444444444444444444444363636363636363636363636363636363636112222222222222224444444444444444444444444444444444444444444444363636363636363636363636363636363636
order122333446666612121212333336666666666666666612121212121212121212121212121212121212121212121222666688882424242424242424222666446666612121212666666666666666666666612121212121212121212121212121212121212121212121222666688882424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1i−ii−iii−i−iii−i−i111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1i−ii−iii−i−iii−i−i
χ6111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1−ii−ii−i−iii−i−iii111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1−ii−ii−i−iii−i−iii
χ7111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111i−i−iiii−i−i−i−iii111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111i−i−iiii−i−i−i−iii
χ8111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111−iii−i−i−iiiii−i−i111111-1-111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111−iii−i−i−iiiii−i−i
χ922222-122-1-122-122222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000022222-122-1-122-122222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ1022222-122-1-122-122222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100000000000022222-122-1-122-122222-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ1122222-1-2-2-1-122-1-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-2-2-211111111111111112-2-1-11100000000000022222-1-2-2-1-122-1-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-2-2-211111111111111112-2-1-111000000000000
χ1222222-1-2-2-1-122-1-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-2-2-21111111111111111-2211-1-100000000000022222-1-2-2-1-122-1-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-2-2-21111111111111111-2211-1-1000000000000
χ132222-1222222-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-12222-1222222-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-1
χ142222-1222222-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2000011112222-1222222-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-12-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-200001111
χ152222-12-2-2222-12-2-211-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-21-2-21111-2-2-2-2111111111111000000002i−2i0000−i−iii2222-12-2-2222-12-2-211-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-21-2-21111-2-2-2-2111111111111000000002i−2i0000−i−iii
χ162222-12-2-2222-12-2-211-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-21-2-21111-2-2-2-211111111111100000000−2i2i0000ii−i−i2222-12-2-2222-12-2-211-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-21-2-21111-2-2-2-211111111111100000000−2i2i0000ii−i−i
χ17222-1222222-122-1-122-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000002200-1-1-1-10000222-1222222-122-1-122-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000002200-1-1-1-10000
χ18222-1222222-122-1-122-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000-2-20011110000222-1222222-122-1-122-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000-2-20011110000
χ19222-122-2-222-12211-2-2-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-11-2-2-211111111-2-2-2-2111111110000002i−2i00−i−iii0000222-122-2-222-12211-2-2-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-11-2-2-211111111-2-2-2-2111111110000002i−2i00−i−iii0000
χ20222-122-2-222-12211-2-2-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-11-2-2-211111111-2-2-2-211111111000000−2i2i00ii−i−i0000222-122-2-222-12211-2-2-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-11-2-2-211111111-2-2-2-211111111000000−2i2i00ii−i−i0000
χ2122-22222-2-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222-222-222-2-222-2-222-2-22222-2-2-2-200000000000000000022-22222-2-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-222222-222-222-2-222-2-222-2-22222-2-2-2-2000000000000000000
χ2222-2222-22-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22-2-222-2-222-2-222-2-2-2-2222200000000000000000022-2222-22-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22-2-222-2-222-2-222-2-2-2-22222000000000000000000
χ2322-222-12-21122-122-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-22-1122-2-2-1-111-1-111-1-1-1-1111100−i3i3−i3i300000000000022-222-12-21122-122-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-22-1122-2-2-1-111-1-111-1-1-1-1111100−i3i3−i3i3000000000000
χ2422-222-12-21122-122-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-22-1122-2-2-1-111-1-111-1-1-1-1111100i3−i3i3−i300000000000022-222-12-21122-122-2-22-1-1-1-1-2-2-2-2111111112-1-1-1-1-22-1122-2-2-1-111-1-111-1-1-1-1111100i3−i3i3−i3000000000000
χ2522-222-1-221122-1-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-12-21-1-2-22211-1-111-1-11111-1-1-1-100−i3i3i3−i300000000000022-222-1-221122-1-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-12-21-1-2-22211-1-111-1-11111-1-1-1-100−i3i3i3−i3000000000000
χ2622-222-1-221122-1-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-12-21-1-2-22211-1-111-1-11111-1-1-1-100i3−i3−i3i300000000000022-222-1-221122-1-2-2222-1-1-1-1-2-2-2-2111111112-1-1-1-12-21-1-2-22211-1-111-1-11111-1-1-1-100i3−i3−i3i3000000000000
χ2722-22-122-2-2-22-122211-12-1-1-1-2111-2-2111111-12-1-1-1-2-12-2-1-11122-2-2-1-111-1-1-1-11111000000000000003−33−322-22-122-2-2-22-122211-12-1-1-1-2111-2-2111111-12-1-1-1-2-12-2-1-11122-2-2-1-111-1-1-1-11111000000000000003−33−3
χ2822-22-122-2-2-22-122211-12-1-1-1-2111-2-2111111-12-1-1-1-2-12-2-1-11122-2-2-1-111-1-1-1-1111100000000000000−33−3322-22-122-2-2-22-122211-12-1-1-1-2111-2-2111111-12-1-1-1-2-12-2-1-11122-2-2-1-111-1-1-1-1111100000000000000−33−33
χ2922-22-12-22-2-22-12-2-2-1-1-12-1-1-1-2111-2-2111111-12-1-1-121-2211-1-1-2-22211-1-11111-1-1-1-100000000000000−i3i3i3−i322-22-12-22-2-22-12-2-2-1-1-12-1-1-1-2111-2-2111111-12-1-1-121-2211-1-1-2-22211-1-11111-1-1-1-100000000000000−i3i3i3−i3
χ3022-22-12-22-2-22-12-2-2-1-1-12-1-1-1-2111-2-2111111-12-1-1-121-2211-1-1-2-22211-1-11111-1-1-1-100000000000000i3−i3−i3i322-22-12-22-2-22-12-2-2-1-1-12-1-1-1-2111-2-2111111-12-1-1-121-2211-1-1-2-22211-1-11111-1-1-1-100000000000000i3−i3−i3i3
χ3122-2-1222-2-2-2-122-1-1-2-2-1-12-1-11-21111-2-21111-1-12-1-1122-2-1-111-1-11122-2-2-1-1-1-111110000000000−i3i3−i3i3000022-2-1222-2-2-2-122-1-1-2-2-1-12-1-11-21111-2-21111-1-12-1-1122-2-1-111-1-11122-2-2-1-1-1-111110000000000−i3i3−i3i30000
χ3222-2-1222-2-2-2-122-1-1-2-2-1-12-1-11-21111-2-21111-1-12-1-1122-2-1-111-1-11122-2-2-1-1-1-111110000000000i3−i3i3−i3000022-2-1222-2-2-2-122-1-1-2-2-1-12-1-11-21111-2-21111-1-12-1-1122-2-1-111-1-11122-2-2-1-1-1-111110000000000i3−i3i3−i30000
χ3322-2-122-22-2-2-1221122-1-12-1-11-21111-2-21111-1-12-1-1-1-2-2211-1-111-1-1-2-2221111-1-1-1-100000000003−3−33000022-2-122-22-2-2-1221122-1-12-1-11-21111-2-21111-1-12-1-1-1-2-2211-1-111-1-1-2-2221111-1-1-1-100000000003−3−330000
χ3422-2-122-22-2-2-1221122-1-12-1-11-21111-2-21111-1-12-1-1-1-2-2211-1-111-1-1-2-2221111-1-1-1-10000000000−333−3000022-2-122-22-2-2-1221122-1-12-1-11-21111-2-21111-1-12-1-1-1-2-2211-1-111-1-1-2-2221111-1-1-1-10000000000−333−30000
χ354444-2-244-2-24-2-244-2-2-2-21114-2-2-2-2-2111111-2-21114-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000004444-2-244-2-24-2-244-2-2-2-21114-2-2-2-2-2111111-2-21114-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000
χ364444-2-2-4-4-2-24-2-2-4-422-2-21114-2-2-2-2-2111111-2-2111-422222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000004444-2-2-4-4-2-24-2-2-4-422-2-21114-2-2-2-2-2111111-2-2111-422222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ37444-24-244-2-2-24-2-2-244-21-211-24-2-211-2-21111-21-211-24-2-2-2-2-2-21111-2-2-2-211111111000000000000000000444-24-244-2-2-24-2-2-244-21-211-24-2-211-2-21111-21-211-24-2-2-2-2-2-21111-2-2-2-211111111000000000000000000
χ38444-24-2-4-4-2-2-24-222-4-4-21-211-24-2-211-2-21111-21-2112-4222222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000444-24-2-4-4-2-2-24-222-4-4-21-211-24-2-211-2-21111-21-2112-4222222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ39444-2-244444-2-24-2-2-2-21-2-211-2-211-2-2-2-211111-2-211-2-2441111-2-2-2-2-2-2-2-211111111000000000000000000444-2-244444-2-24-2-2-2-21-2-211-2-211-2-2-2-211111-2-211-2-2441111-2-2-2-2-2-2-2-211111111000000000000000000
χ40444-2-24-4-444-2-2422221-2-211-2-211-2-2-2-211111-2-21122-4-4-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000000444-2-24-4-444-2-2422221-2-211-2-211-2-2-2-211111-2-21122-4-4-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000000
χ41444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111111111−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111111111−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000
χ42444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111111111−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111111111−1+3i32−1+3i32−1−3i32−1−3i32−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000
χ43444-2-2-2-4-4-2-2-2-2-22222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-1-1-1-1-1-1-11+3i321+3i321−3i321−3i321+3i321+3i321−3i321−3i32000000000000000000444-2-2-2-4-4-2-2-2-2-22222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-1-1-1-1-1-1-11+3i321+3i321−3i321−3i321+3i321+3i321−3i321−3i32000000000000000000
χ44444-2-2-2-4-4-2-2-2-2-22222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-1-1-1-1-1-1-11−3i321−3i321+3i321+3i321−3i321−3i321+3i321+3i32000000000000000000444-2-2-2-4-4-2-2-2-2-22222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-1-1-1-1-1-1-11−3i321−3i321+3i321+3i321−3i321−3i321+3i321+3i32000000000000000000
χ4544-44-2-24-4224-2-24422-2-2111-422222-1-1-1-1-1-1-2-2111-4-2-22-2-222-2-22211-1-11111-1-1-1-100000000000000000044-44-2-24-4224-2-24422-2-2111-422222-1-1-1-1-1-1-2-2111-4-2-22-2-222-2-22211-1-11111-1-1-1-1000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.