Finite Group Databasebeta

← Group #13135642

Character table — Group #13135642

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size11112222222233333333444444466666666666666666666888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636363636363636363636363636
order122234444666336666664121212121212999121212121212121218181818181818181844121212121212363636363636363636363636363636363636121212123636363636363636363636368888888824242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111111−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−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+i32
χ6111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111111−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32
χ7111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1-1−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ8111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1-1−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-111111+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ9111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111111−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+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−i32
χ10111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111111−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32
χ11111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1-1−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ12111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1-1−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-111111−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ1311111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ1411111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ1511111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11-1-111-1-111-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii
χ1611111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11-1-111-1-111-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i
χ1711111-1-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-111-1-1−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ii−i−iii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14
χ1811111-1-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-111-1-1−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−i−iii−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14
χ1911111-1-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-111−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32ii−i−i−i−iiiζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14
χ2011111-1-1-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-1111−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-111−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−i−iiiii−i−i−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14
χ2111111-1-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-111-1-1−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32ii−i−iii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22
χ2211111-1-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-111-1-1−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−i−iii−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22
χ2311111-1-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-111−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32ii−i−i−i−iiiζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22
χ2411111-1-1-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1-1111−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-111−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−i−iiiii−i−i−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22
χ25222222222222222222222222222-1-1-122222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ26222222222222222222222222222-1-1-122222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000000000
χ27222222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i32222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32222222−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i32−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000000000
χ28222222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i32222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-2-2-2-2-2-2−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321+i321−i321−i321+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000000000
χ29222222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i32222222-11−i321+i32−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32222222−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i32−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000000000
χ30222222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i32222222-11−i321+i32−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-2-2-2-2-2-2−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321−i321+i321+i321−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000000000
χ31222222-22-222222222222-222-2-2-2-22222-22-22-22-2222222222000000-2-222-2-222-2-222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ32222222-22-222222222222-222-2-2-2-2-1-1-12-22-22-22-2-1-1-1-1-1-1-1-1-1000000-2-2-1-111-1-111-1-1111111110000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000
χ33222222-22-222222222222-222-2-2-2-2-1-1-12-22-22-22-2-1-1-1-1-1-1-1-1-1000000-2-2-1-111-1-111-1-1111111110000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000
χ34222222-22-2222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-222-2-2-2-22−1−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i322−1−i3−1−i3−1+i3−1+i32−1−i3−1+i30000001+i31−i322-2-2−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3-2-21+i31+i31−i31−i30000000000000000000000000000000000000000
χ35222222-22-2222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-222-2-2-2-2-11+i321−i32−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3-1-11+i321+i321−i321−i32-11+i321−i320000001+i31−i3-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32000000000000000000000000
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χ1081212-12-12-60120-12-66600000000000-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1091212-12-12-60-12012-666000000000006-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11012-1212-12-6120-1206-66000000000-66000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11112-1212-12-6-1201206-660000000006-6000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11212-12-1212-6000066-60000000000000−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11312-12-1212-6000066-600000000000006i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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