Finite Group Databasebeta

← Group #13147355

Character table — Group #13147355

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111112222222229999991212121212121212121212121212121218181818181818181836363636363636363636363611111122222222299999912121212121212121212121212121212181818181818181818363636363636363636363636
order1233664881212242424244412121212336612121212242424242424242426688242424248888242424242424242422666648812122424242444121212126666121212122424242424242424266882424242488882424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i
χ4111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii
χ51111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11-111-1-111-1-11111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11-111-1-111-1-1
χ61111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-11-1-111-1-1111111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11-11-1-111-1-111
χ71111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111i−i−iiii−i−i−i−iii1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111i−i−iiii−i−i−i−iii
χ81111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−i−iiiii−i−i1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111−iii−i−i−iiiii−i−i
χ9222222-200-2-200002222222222-2-2-2-200000000-2-2-2000000000000000000222222-200-2-200002222222222-2-2-2-200000000-2-2-2000000000000000000
χ10222222-200-2-20000-2-2-2-2-2-22222-2-2-2-200000000222000000000000000000222222-200-2-20000-2-2-2-2-2-22222-2-2-2-200000000222000000000000000000
χ112-222-2-20−i2i200−i2−i2i2i22i−2i2i2i−2i−2i22-2-20000−i2−i2−i2−i2i2i2i2i20002−222−2−20000000000002-222-2-20−i2i200−i2−i2i2i22i−2i2i2i−2i−2i22-2-20000−i2−i2−i2−i2i2i2i2i20002−222−2−2000000000000
χ122-222-2-20−i2i200−i2−i2i2i2−2i2i−2i−2i2i2i22-2-20000−i2−i2−i2−i2i2i2i2i2000−22−2−2220000000000002-222-2-20−i2i200−i2−i2i2i2−2i2i−2i−2i2i2i22-2-20000−i2−i2−i2−i2i2i2i2i2000−22−2−222000000000000
χ132-222-2-20i2−i200i2i2−i2−i22i−2i2i2i−2i−2i22-2-20000i2i2i2i2−i2−i2−i2−i2000−22−2−2220000000000002-222-2-20i2−i200i2i2−i2−i22i−2i2i2i−2i−2i22-2-20000i2i2i2i2−i2−i2−i2−i2000−22−2−222000000000000
χ142-222-2-20i2−i200i2i2−i2−i2−2i2i−2i−2i2i2i22-2-20000i2i2i2i2−i2−i2−i2−i20002−222−2−20000000000002-222-2-20i2−i200i2i2−i2−i2−2i2i−2i−2i2i2i22-2-20000i2i2i2i2−i2−i2−i2−i20002−222−2−2000000000000
χ1533−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ2233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ1633−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ2233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ1733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i32-1-11+i321−i321+i321−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i32-1-11+i321−i321+i321−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i32-1-11+i321−i321+i321−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i32-1-11+i321−i321+i321−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ1933−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i32-1-11+i321−i321+i321−i32i−i−iiζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ2233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i32-1-11+i321−i321+i321−i32i−i−iiζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22
χ2033−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i32-1-11+i321−i321+i321−i32−iii−i−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ2233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3211−1−i32−1+i32−1−i32−1+i3200000000000000001−1−i32−1+i32-1-11+i321−i321+i321−i32−iii−i−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22
χ2133−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i321-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i321-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ2233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i32-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3233−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320000000000000000-11+i321−i3211−1−i32−1+i32−1−i32−1+i32-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ1433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
χ2433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ1433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
χ2533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i32-1-11−i321+i321−i321+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i32-1-11−i321+i321−i321+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i32-1-11−i321+i321−i321+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i32-1-11−i321+i321−i321+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ2733−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i32-1-11−i321+i321−i321+i32i−i−iiζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ1433−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i32-1-11−i321+i321−i321+i32i−i−iiζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14
χ2833−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i32-1-11−i321+i321−i321+i32−iii−i−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ1433−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3211−1+i32−1−i32−1+i32−1−i3200000000000000001−1+i32−1−i32-1-11−i321+i321−i321+i32−iii−i−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14
χ2933−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i321-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3233−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i321-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ3033−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i32-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3233−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i32-1-11−i321+i321−i321+i320000000000000000-11−i321+i3211−1+i32−1−i32−1+i32−1−i32-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
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χ344444444-4-444-4-4-4-4000000-21-21-2-21122-1-122-1-10000000000000000000004444444-4-444-4-4-4-4000000-21-21-2-21122-1-122-1-1000000000000000000000
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χ1166-6−3+3i3−3−3i33−3i33+3i303i2−3i200−3ζ5−3ζ23−3ζ7−3ζ133ζ5+3ζ233ζ7+3ζ13−2i2i−2ζ14−2ζ222ζ142ζ2200000000000000000002−2ζ5−ζ23−ζ7+ζ13−ζ5+ζ23ζ7−ζ13000000000000-663−3i33+3i3−3+3i3−3−3i30−3i23i2003ζ5+3ζ233ζ7+3ζ13−3ζ5−3ζ23−3ζ7−3ζ132i−2i2ζ142ζ22−2ζ14−2ζ220000000000000000000−22−ζ5+ζ23ζ7−ζ13ζ5−ζ23−ζ7+ζ13000000000000

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