Finite Group Databasebeta

← Group #13147071

Character table — Group #13147071

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111111111111111166666666666666666666121212121212121212121212181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424363636363636363636363636
order122233444466666612121212121212122234466666661212121212121212666666121212121212888888882424242424242424242424242424242433366666666612121212121212121212121244441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511-1-11111-1-111-1-1-1-11111-1-1-1-11-111-111-1-1-1-111111-1-1-1-1111-1-1-1111-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i111-1-1-1-1-1-1111111111-1-1-1-1-1-1i−ii−iii−i−iii−i−i
χ611-1-11111-1-111-1-1-1-11111-1-1-1-11-111-111-1-1-1-111111-1-1-1-1111-1-1-1111-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii111-1-1-1-1-1-1111111111-1-1-1-1-1-1−ii−ii−i−iii−i−iii
χ711-1-111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-111-1-1111-1-111-1-1-1-1-1111111-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii111-1-1-1-1-1-1111-1-1-1-1-1-1111111i−i−iiii−i−i−i−iii
χ811-1-111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-111-1-1111-1-111-1-1-1-1-1111111-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i111-1-1-1-1-1-1111-1-1-1-1-1-1111111−iii−i−i−iiiii−i−i
χ922222222222222222222222222222222222222222222222222222222000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1022222222222222222222222222-1222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1000000000000
χ1122222222222222222222222222-1222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1000000000000
χ1222222222222222222222222222-1222222-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122000000000000
χ13222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222-2-2-2-222222-2-2-2-222-2-2-2-2-2-2222222000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ14222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-122-2-2-2-2-1-1-122111122111111-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-12-1-1-2-21111-2-21111000000000000
χ15222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-122-2-2-2-2-1-1-122111122111111-1-1-1-1-1-1000000000000000000000000-12-1-1-122-1-1-12-111-2-21111-2-211000000000000
χ16222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-122-2-2-2-2-1-1-122111122111111-1-1-1-1-1-1000000000000000000000000-1-12-1-1-1-122-1-121111-2-21111-2-2000000000000
χ1722-2-22222-2-222-2-2-2-22222-2-2-2-22-222-222-2-2-2-222222-2-2-2-2222-2-2-2222-2-2-2000000000000000000000000-1-1-1111111-1-1-1-1-1-1-1-1-1111111000000000000
χ1822-2-22222-2-222-2-2-2-22222-2-2-2-22-2-12-222-2-211-122-1-111-2-2-1-1-1111-1-1-11110000000000000000000000002-1-1-2-211112-1-122-1-1-1-1-2-21111000000000000
χ1922-2-22222-2-222-2-2-2-22222-2-2-2-22-2-12-222-2-211-122-1-111-2-2-1-1-1111-1-1-1111000000000000000000000000-12-111-2-211-12-1-1-122-1-111-2-211000000000000
χ2022-2-22222-2-222-2-2-2-22222-2-2-2-22-2-12-222-2-211-122-1-111-2-2-1-1-1111-1-1-1111000000000000000000000000-1-121111-2-2-1-12-1-1-1-1221111-2-2000000000000
χ2122-2-222-2-22222-2-2-2-2-2-2-2-22222-2222-2-2-222-2-2222-2-222-2-2-2-2-2222222-2-2-2000000000000000000000000-1-1-1111111-1-1-1111111-1-1-1-1-1-1000000000000
χ2222-2-222-2-22222-2-2-2-2-2-2-2-22222-22-12-2-2-22211-12211-1-1-2-2111-1-1-1-1-1-11110000000000000000000000002-1-1-2-211112-1-1-2-2111122-1-1-1-1000000000000
χ2322-2-222-2-22222-2-2-2-2-2-2-2-22222-22-12-2-2-22211-12211-1-1-2-2111-1-1-1-1-1-1111000000000000000000000000-12-111-2-211-12-111-2-211-1-122-1-1000000000000
χ2422-2-222-2-22222-2-2-2-2-2-2-2-22222-22-12-2-2-22211-12211-1-1-2-2111-1-1-1-1-1-1111000000000000000000000000-1-121111-2-2-1-121111-2-2-1-1-1-122000000000000
χ252-22-2222i−2i2i−2i-2-222-2-22i2i−2i−2i2i2i−2i−2i0020000002-2-2002i−2i2i−2i000000000000002−22−2−i2i2−i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2-1-1-11-11-11-1111i−ii−ii−ii−ii−ii−i000000000000
χ262-22-2222i−2i2i−2i-2-222-2-22i2i−2i−2i2i2i−2i−2i0020000002-2-2002i−2i2i−2i00000000000000−22−22i2−i2i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i2-1-1-11-11-11-1111i−ii−ii−ii−ii−ii−i000000000000
χ272-22-222−2i2i−2i2i-2-222-2-2−2i−2i2i2i−2i−2i2i2i0020000002-2-200−2i2i−2i2i000000000000002−22−2i2−i2i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2-1-1-11-11-11-1111−ii−ii−ii−ii−ii−ii000000000000
χ282-22-222−2i2i−2i2i-2-222-2-2−2i−2i2i2i−2i−2i2i2i0020000002-2-200−2i2i−2i2i00000000000000−22−22−i2i2−i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i2-1-1-11-11-11-1111−ii−ii−ii−ii−ii−ii000000000000
χ292-2-22222i−2i−2i2i-2-2-2-2222i2i−2i−2i−2i−2i2i2i002000000-22-2002i−2i−2i2i00000000000000−i2i2i2−i2−222−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−2-1-1-1-11-11-11111i−ii−ii−i−ii−ii−ii000000000000
χ302-2-22222i−2i−2i2i-2-2-2-2222i2i−2i−2i−2i−2i2i2i002000000-22-2002i−2i−2i2i00000000000000i2−i2−i2i22−2−22i2i2−i2−i2−i2−i2i2i222−2−2−2−222-1-1-1-11-11-11111i−ii−ii−i−ii−ii−ii000000000000
χ312-2-2222−2i2i2i−2i-2-2-2-222−2i−2i2i2i2i2i−2i−2i002000000-22-200−2i2i2i−2i00000000000000−i2i2i2−i22−2−22−i2−i2i2i2i2i2−i2−i222−2−2−2−222-1-1-1-11-11-11111−ii−ii−iii−ii−ii−i000000000000
χ322-2-2222−2i2i2i−2i-2-2-2-222−2i−2i2i2i2i2i−2i−2i002000000-22-200−2i2i2i−2i00000000000000i2−i2−i2i2−222−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−2-1-1-1-11-11-11111−ii−ii−iii−ii−ii−i000000000000
χ33333333333333333333333333-1-13-1-1-1-1-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1
χ34333333333333333333333333-1-13-1-1-1-1-1-1333-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111
χ35333333-3-3-3-3333333-3-3-3-3-3-3-3-3113-1-11111333-1-1-3-3-3-3-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000000000000000-1-111-1-1-1-11111
χ36333333-3-3-3-3333333-3-3-3-3-3-3-3-3113-1-11111333-1-1-3-3-3-3-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000000011-1-11111-1-1-1-1
χ373333−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233033−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+3i320000−3−3i32−3+3i3200000000000011111111−1−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+i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ383333−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233033−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+3i320000−3−3i32−3+3i32000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ393333−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-10-1-11+i321−i321+i321−i320001+i321−i3200001+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i311111111−1−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+i32000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ403333−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-10-1-11+i321−i321+i321−i320001+i321−i3200001+i321−i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ413333−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32110-1-1−1−i32−1+i32−1−i32−1+i320001+i321−i3200001+i321−i32-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i31111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ423333−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32110-1-1−1−i32−1+i32−1−i32−1+i320001+i321−i3200001+i321−i32-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ433333−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-3-30333+3i323−3i323+3i323−3i32000−3−3i32−3+3i320000−3−3i32−3+3i320000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ443333−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-3-30333+3i323−3i323+3i323−3i32000−3−3i32−3+3i320000−3−3i32−3+3i32000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ453333−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233033−3+3i32−3−3i32−3+3i32−3−3i32000−3+3i32−3−3i320000−3+3i32−3−3i3200000000000011111111−1+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−i320000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ463333−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233033−3+3i32−3−3i32−3+3i32−3−3i32000−3+3i32−3−3i320000−3+3i32−3−3i32000000000000-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ473333−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-10-1-11−i321+i321−i321+i320001−i321+i3200001−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i311111111−1+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−i32000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ483333−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-10-1-11−i321+i321−i321+i320001−i321+i3200001−i321+i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i320000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
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χ503333−3+3i32−3−3i32-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32110-1-1−1+i32−1−i32−1+i32−1−i320001−i321+i3200001−i321+i32-21−i31+i3-21−i31+i32−1+i3−1−i32−1+i3−1−i3-1-1-1-111111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.