Finite Group Databasebeta

← Group #13144502

Character table — Group #13144502

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222222222222222666666666666666688888812121212121212121212121212121212121212121212121218181818181818181818181818181818181818181818181824242424242424242424242424242424727272727272
order12223366666644444412121212121212121212121233336666666666662466121212121212121212121212121212121212121212121212121288888888242424242424242424242424242424246666666612121212121212124412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1
χ6111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111
χ7111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111
χ8111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-1
χ92222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1000000
χ102222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000-2-2111111-2-2111111000000
χ11222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000000000000000-1-122-1-1-1-1-1-122-1-1-1-1000000
χ12222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000000000000011-2-2111111-2-21111000000
χ13222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1000000000000000000000000-1-1-1-122-1-1-1-1-1-122-1-1000000
χ14222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-10000000000000000000000001111-2-2111111-2-211000000
χ15222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122000000000000000000000000-1-1-1-1-1-122-1-1-1-1-1-122000000
χ16222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122000000000000000000000000111111-2-2111111-2-2000000
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2-2-2222222222222222200000022-2-222-2-222-2-222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-100000022-2-2-1-111-1-111-1-111-2-211111100000000000000000000000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000
χ1922222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-100000022-2-2-1-111-1-111-1-111-2-211111100000000000000000000000000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000
χ2022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1000000-1-11122-2-2-1-111-1-11111-2-21111000000000000000000000000−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000
χ2122222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1000000-1-11122-2-2-1-111-1-11111-2-21111000000000000000000000000i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000
χ2222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1000000-1-111-1-11122-2-2-1-1111111-2-211000000000000000000000000−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000
χ2322222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1000000-1-111-1-11122-2-2-1-1111111-2-211000000000000000000000000i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000
χ2422222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000-1-111-1-111-1-11122-2-2111111-2-2000000000000000000000000−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000
χ2522222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000-1-111-1-111-1-11122-2-2111111-2-2000000000000000000000000i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000
χ26222222222222-2-222-2-2-2-2-2-22222-2-2-2-22222222222222222000000-2-222-2-222-2-222-2-222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ27222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-22211-1-111-1-111-1-1-2-211111100000000000000000000000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000
χ28222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1000000-2-22211-1-111-1-111-1-1-2-211111100000000000000000000000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000
χ29222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-1-1-2-22211-1-111-1-111-2-21111000000000000000000000000−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000
χ30222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-100000011-1-1-2-22211-1-111-1-111-2-21111000000000000000000000000i3−i300i3−i3−i3i3−i3i300−i3i3i3−i3000000
χ31222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-100000011-1-111-1-1-2-22211-1-11111-2-211000000000000000000000000−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000
χ32222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-100000011-1-111-1-1-2-22211-1-11111-2-211000000000000000000000000i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000
χ33222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-1200000011-1-111-1-111-1-1-2-222111111-2-2000000000000000000000000−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300000000
χ34222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-1200000011-1-111-1-111-1-1-2-222111111-2-2000000000000000000000000i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300000000
χ35222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-12-222-2-2-2-2-2-211111111111122-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-1-2-2111111000000
χ36222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-1-22-2-222-2-2-2-211111111111122-1-1-1-1-1-1000000000000000000000000-2-211111122-1-1-1-1-1-1000000
χ37222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-12-222-2-21111-2-2-2-211111111-1-122-1-1-1-1000000000000000000000000-1-122-1-1-1-111-2-21111000000
χ38222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-22-2-2221111-2-2-2-211111111-1-122-1-1-1-100000000000000000000000011-2-21111-1-122-1-1-1-1000000
χ39222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-12-222-2-211111111-2-2-2-21111-1-1-1-122-1-1000000000000000000000000-1-1-1-122-1-11111-2-211000000
χ40222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-22-2-22211111111-2-2-2-21111-1-1-1-122-1-10000000000000000000000001111-2-211-1-1-1-122-1-1000000
χ41222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-122-222-2-2111111111111-2-2-2-2-1-1-1-1-1-122000000000000000000000000-1-1-1-1-1-122111111-2-2000000
χ42222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-22-2-222111111111111-2-2-2-2-1-1-1-1-1-122000000000000000000000000111111-2-2-1-1-1-1-1-122000000
χ4322-2-22222-2-2-2-200002-20000000022-2-22222-2-2-2-2-2-2-2-2222200000000000000000000002-22-22-22-200002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ4422-2-22222-2-2-2-200002-20000000022-2-22222-2-2-2-2-2-2-2-2222200000000000000000000002-22-22-22-20000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ4522-2-22222-2-2-2-20000-2200000000-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000-22-22-22-222i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000
χ4622-2-22222-2-2-2-20000-2200000000-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000-22-22-22-22−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000
χ472-22-222-2-222-2-2002i−2i0000002i2i−2i−2i000022222-22-22-22-2-2-2-2-2000000002i−2i002i−2i002i−2i002i−2i000000002−22−2−i2i2−i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000000000
χ482-22-222-2-222-2-2002i−2i0000002i2i−2i−2i000022222-22-22-22-2-2-2-2-2000000002i−2i002i−2i002i−2i002i−2i00000000−22−22i2−i2i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000000000
χ492-22-222-2-222-2-200−2i2i000000−2i−2i2i2i000022222-22-22-22-2-2-2-2-200000000−2i2i00−2i2i00−2i2i00−2i2i000000002−22−2i2−i2i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000000000
χ502-22-222-2-222-2-200−2i2i000000−2i−2i2i2i000022222-22-22-22-2-2-2-2-200000000−2i2i00−2i2i00−2i2i00−2i2i00000000−22−22−i2i2−i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000000000
χ512-2-2222-2-2-2-2222i−2i00002i2i−2i−2i000000002222-22-22-22-22-2-2-2-20000002i−2i002i−2i002i−2i002i−2i0000000000−i2i2i2−i22−2−22−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000000000
χ522-2-2222-2-2-2-2222i−2i00002i2i−2i−2i000000002222-22-22-22-22-2-2-2-20000002i−2i002i−2i002i−2i002i−2i0000000000i2−i2−i2i2−222−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000000000
χ532-2-2222-2-2-2-222−2i2i0000−2i−2i2i2i000000002222-22-22-22-22-2-2-2-2000000−2i2i00−2i2i00−2i2i00−2i2i0000000000−i2i2i2−i2−222−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000000000
χ542-2-2222-2-2-2-222−2i2i0000−2i−2i2i2i000000002222-22-22-22-22-2-2-2-2000000−2i2i00−2i2i00−2i2i00−2i2i0000000000i2−i2−i2i22−2−22i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000000000
χ553333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000011111111−1−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+i32000000000000000011−1−i32−1+i32−1−i32−1+i32
χ563333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-11+i321−i321+i321−i32
χ573333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i3200000000000000000000000011111111−1−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+i320000000000000000-1-11+i321−i321+i321−i32
χ583333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i32000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32000000000000000011−1−i32−1+i32−1−i32−1+i32
χ593333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-3333+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i320000000000000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001-1−1−i32−1+i321+i321−i32
χ603333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-3333+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i32000000000000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-111+i321−i32−1−i32−1+i32
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χ1226-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3−6i6i0000−6ζ14−6ζ226ζ146ζ22000000000000000000000000000000000000000000000000000000i2−i2−i2i22−2−22−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ13ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ130000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.