Finite Group Databasebeta

← Group #13146904

Character table — Group #13146904

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222333333336666661212121212121818181818181818181818182424242424242424242424243636363636361111222233333333666666121212121212181818181818181818181818242424242424242424242424363636363636
order1222366633666666441212121212121212121288882424242424242424333666666666441212121222226666666666664412121212121212121212888824242424242424246666666666664412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ311111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ411111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ511111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ611111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ71-11-11-1-1111-1-111-1-11-111-1-11-11-11-1ii−i−iii−i−iii−i−i1111-1-11-1-11-1-1i−ii−ii−i1-11-11-1-1111-1-111-1-11-111-1-11-11-11-1ii−i−iii−i−iii−i−i1111-1-11-1-11-1-1i−ii−ii−i
χ81-11-11-1-1111-1-111-1-11-111-1-11-11-11-1−i−iii−i−iii−i−iii1111-1-11-1-11-1-1−ii−ii−ii1-11-11-1-1111-1-111-1-11-111-1-11-11-11-1−i−iii−i−iii−i−iii1111-1-11-1-11-1-1−ii−ii−ii
χ91-11-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i321-1−1−i321+i32−1+i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32i−iζ22−ζ22ζ14−ζ141-11-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i321-1−1−i321+i32−1+i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ141−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32i−iζ22−ζ22ζ14−ζ14
χ101-11-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i321-1−1−i321+i32−1+i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ141−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32−ii−ζ22ζ22−ζ14ζ141-11-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i321-1−1−i321+i32−1+i321−i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ141−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32−ii−ζ22ζ22−ζ14ζ14
χ111-11-11-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i321-1−1+i321−i32−1−i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32i−iζ14−ζ14ζ22−ζ221-11-11-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i321-1−1+i321−i32−1−i321+i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ221−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32i−iζ14−ζ14ζ22−ζ22
χ121-11-11-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i321-1−1+i321−i32−1−i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ221−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32−ii−ζ14ζ14−ζ22ζ221-11-11-1-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i321-1−1+i321−i32−1−i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ221−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32−ii−ζ14ζ14−ζ22ζ22
χ132222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000002222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ1422222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i3200000022222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i322−1−i3−1−i3−1+i3−1+i3000000000000-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000
χ1522222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i3200000022222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i322−1+i3−1+i3−1−i3−1−i3000000000000-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32000000
χ1622-2-222-2-22222-2-2-2-20000000000002−22−22−22−22−22−2-1-1-111-111-111-100000022-2-222-2-22222-2-2-2-20000000000002−22−22−22−22−22−2-1-1-111-111-111-1000000
χ1722-2-222-2-22222-2-2-2-2000000000000−22−22−22−22−22−22-1-1-111-111-111-100000022-2-222-2-22222-2-2-2-2000000000000−22−22−22−22−22−22-1-1-111-111-111-1000000
χ1822-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000002−22−2−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23-11+i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i3200000022-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000002−22−2−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23-11+i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i32000000
χ1922-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000000000−22−22ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23-11+i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i3200000022-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000000000−22−22ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23-11+i321−i3211-1−1−i32−1−i321+i32−1+i32−1+i321−i32000000
χ2022-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000002−22−2ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13-11−i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i3200000022-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000002−22−2ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13-11−i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i32000000
χ2122-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000000000−22−22−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13-11−i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i3200000022-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000000000−22−22−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13-11−i321+i3211-1−1+i32−1+i321−i32−1−i32−1−i321+i32000000
χ222-22-22-2-2222-2-222-2-22-222-2-22-22-22-2000000000000-1-1-1-111-111-1110000002-22-22-2-2222-2-222-2-22-222-2-22-22-22-2000000000000-1-1-1-111-111-111000000
χ232-22-22-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i32-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000-11+i321−i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i320000002-22-22-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i32-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000-11+i321−i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i32000000
χ242-22-22-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i32-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000-11−i321+i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i320000002-22-22-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i32-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000-11−i321+i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i32000000
χ252-2-222-22-222-2-2-2-222000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2-1-1-11-111-111-110000002-2-222-22-222-2-2-2-222000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2-1-1-11-111-111-11000000
χ262-2-222-22-222-2-2-2-222000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2-1-1-11-111-111-110000002-2-222-22-222-2-2-2-222000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2-1-1-11-111-111-11000000
χ272-2-222-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000000000−i2i2i2−i2ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23-11+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i320000002-2-222-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000000000−i2i2i2−i2ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23-11+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32000000
χ282-2-222-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000000000i2−i2−i2i2−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23-11+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i320000002-2-222-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000000000i2−i2−i2i2−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23-11+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32000000
χ292-2-222-22-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000000000−i2i2i2−i2ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13-11−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i320000002-2-222-22-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000000000−i2i2i2−i2ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13-11−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32000000
χ302-2-222-22-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000000000i2−i2−i2i2−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13-11−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i320000002-2-222-22-2−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i3000000000000i2−i2−i2i2−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13-11−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32000000
χ313333333333333333-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-13333333333333333-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
χ323333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000001111113333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111
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χ3433333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000011−1−i32−1−i32−1+i32−1+i3233333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000011−1−i32−1−i32−1+i32−1+i32
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χ983-33-33-3-33−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32-111+i321−i32−1−i32−1+i32-111+i32−1−i321−i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14000000000000i−iζ22−ζ22ζ14−ζ14-33-33-333-33+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i321-1−1−i32−1+i321+i321−i321-1−1−i321+i32−1+i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14000000000000−ii−ζ22ζ22−ζ14ζ14
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χ11612-12-1212-66-6600000000000000000000000000000000000000000000000000-121212-126-66-600000000000000000000000000000000000000000000000000

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