Finite Group Databasebeta

← Group #13173354

Character table — Group #13173354

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size124444449182727124444449182727124444449182727124444449182727248888881836545424888888183654542488888818365454248888881836545424888888183654542488888818365454
order133333332644266666662644266666662644266666662644412121212121212412444121212121212124124441212121212121241244412121212121212412444121212121212124124441212121212121241244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-1
χ311111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i
χ411111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii
χ52-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-100
χ62-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-2100
χ7441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000
χ844-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-2110000
χ94-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000
χ104-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000
χ114-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000
χ124-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000
χ13111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ141111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ1511111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii
χ1611111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i
χ172-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-100-21-2-21111-2100-21-2-21111-2100-21-2-21111-2100-21-2-21111-2100
χ182-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-2100-21-2-211112-100-21-2-211112-100-21-2-211112-100-21-2-211112-100
χ19441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000-4-4-12-1-1220000-4-4-12-1-1220000-4-4-12-1-1220000-4-4-12-1-1220000
χ2044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-211000044-21-2-2110000-4-42-122-1-10000-4-42-122-1-10000-4-42-122-1-10000-4-42-122-1-10000
χ214-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000
χ224-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000
χ234-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000
χ244-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000
χ25111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ261111111111-1-11111111111-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ2711111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii11111111-1-1i−i11111111-1-1i−i-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii
χ2811111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i11111111-1-1−ii11111111-1-1−ii-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i
χ292-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-100-21-2-21111-2100-21-2-21111-21002-122-1-1-1-12-1002-122-1-1-1-12-100-21-2-21111-2100-21-2-21111-2100
χ302-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-2100-21-2-211112-100-21-2-211112-1002-122-1-1-1-1-21002-122-1-1-1-1-2100-21-2-211112-100-21-2-211112-100
χ31441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000-4-4-12-1-1220000-4-4-12-1-1220000441-211-2-20000441-211-2-20000-4-4-12-1-1220000-4-4-12-1-1220000
χ3244-21-2-211000044-21-2-211000044-21-2-211000044-21-2-2110000-4-42-122-1-10000-4-42-122-1-1000044-21-2-211000044-21-2-2110000-4-42-122-1-10000-4-42-122-1-10000
χ334-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000
χ344-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000
χ354-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000
χ364-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000
χ37111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111
χ381111111111-1-11111111111-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1
χ3911111111-1-1i−i11111111-1-1i−i11111111-1-1i−i11111111-1-1i−i-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii-1-1-1-1-1-1-1-111−ii11111111-1-1i−i11111111-1-1i−i
χ4011111111-1-1−ii11111111-1-1−ii11111111-1-1−ii11111111-1-1−ii-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i-1-1-1-1-1-1-1-111i−i11111111-1-1−ii11111111-1-1−ii
χ412-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-1002-122-1-1-1-12-100-21-2-21111-2100-21-2-21111-2100-21-2-21111-2100-21-2-21111-21002-122-1-1-1-12-1002-122-1-1-1-12-100
χ422-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-21002-122-1-1-1-1-2100-21-2-211112-100-21-2-211112-100-21-2-211112-100-21-2-211112-1002-122-1-1-1-1-21002-122-1-1-1-1-2100
χ43441-211-2-20000441-211-2-20000441-211-2-20000441-211-2-20000-4-4-12-1-1220000-4-4-12-1-1220000-4-4-12-1-1220000-4-4-12-1-1220000441-211-2-20000441-211-2-20000
χ4444-21-2-211000044-21-2-211000044-21-2-211000044-21-2-2110000-4-42-122-1-10000-4-42-122-1-10000-4-42-122-1-10000-4-42-122-1-1000044-21-2-211000044-21-2-2110000
χ454-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-10000-42-121+3i321−3i32-1-100004-21-2−1−3i32−1+3i321100004-21-2−1−3i32−1+3i32110000
χ464-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-10000-42-121−3i321+3i32-1-100004-21-2−1+3i32−1−3i321100004-21-2−1+3i32−1−3i32110000
χ474-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i320000-422-1-1-11+3i321−3i3200004-2-2111−1−3i32−1+3i3200004-2-2111−1−3i32−1+3i320000
χ484-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i320000-422-1-1-11−3i321+3i3200004-2-2111−1+3i32−1−3i3200004-2-2111−1+3i32−1−3i320000
χ49111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i
χ501111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii
χ5111111111-1-1i−i-1-1-1-1-1-1-1-111−ii11111111-1-1i−i-1-1-1-1-1-1-1-111−ii11111111-1-1i−i-1-1-1-1-1-1-1-111−iiiiiiiiii−i−i-11−i−i−i−i−i−i−i−iii1-1iiiiiiii−i−i-11−i−i−i−i−i−i−i−iii1-1
χ5211111111-1-1−ii-1-1-1-1-1-1-1-111i−i11111111-1-1−ii-1-1-1-1-1-1-1-111i−i11111111-1-1−ii-1-1-1-1-1-1-1-111i−iiiiiiiii−i−i1-1−i−i−i−i−i−i−i−iii-11iiiiiiii−i−i1-1−i−i−i−i−i−i−i−iii-11
χ532-122-1-1-1-12-100-21-2-21111-21002-122-1-1-1-12-100-21-2-21111-21002-122-1-1-1-12-100-21-2-21111-21002i−i2i2i−i−i−i−i2i−i00−2ii−2i−2iiiii−2ii002i−i2i2i−i−i−i−i2i−i00−2ii−2i−2iiiii−2ii00
χ542-122-1-1-1-1-2100-21-2-211112-1002-122-1-1-1-1-2100-21-2-211112-1002-122-1-1-1-1-2100-21-2-211112-1002i−i2i2i−i−i−i−i−2ii00−2ii−2i−2iiiii2i−i002i−i2i2i−i−i−i−i−2ii00−2ii−2i−2iiiii2i−i00
χ55441-211-2-20000-4-4-12-1-1220000441-211-2-20000-4-4-12-1-1220000441-211-2-20000-4-4-12-1-12200004i4ii−2iii−2i−2i0000−4i−4i−i2i−i−i2i2i00004i4ii−2iii−2i−2i0000−4i−4i−i2i−i−i2i2i0000
χ5644-21-2-2110000-4-42-122-1-1000044-21-2-2110000-4-42-122-1-1000044-21-2-2110000-4-42-122-1-100004i4i−2ii−2i−2iii0000−4i−4i2i−i2i2i−i−i00004i4i−2ii−2i−2iii0000−4i−4i2i−i2i2i−i−i0000
χ574-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-100004-21-2−1−3i32−1+3i32110000-42-121+3i321−3i32-1-100004i−2ii−2i−ζ7+2ζ112ζ7−ζ11ii0000−4i2i−i2iζ7−2ζ11−2ζ7+ζ11−i−i00004i−2ii−2i−ζ7+2ζ112ζ7−ζ11ii0000−4i2i−i2iζ7−2ζ11−2ζ7+ζ11−i−i0000
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χ1188-42-4−1+3i3−1−3i3220000-84-241−3i31+3i3-2-20000-84-241−3i31+3i3-2-200008-42-4−1+3i3−1−3i3220000000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-4-4222−1−3i3−1+3i30000-844-2-2-21+3i31−3i30000-844-2-2-21+3i31−3i300008-4-4222−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1208-4-4222−1+3i3−1−3i30000-844-2-2-21−3i31+3i30000-844-2-2-21−3i31+3i300008-4-4222−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000000000000000000000000

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