Finite Group Databasebeta

← Group #13144766

Character table — Group #13144766

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222222222222222666666666666666688888812121212121212121212121212121212121212121212121218181818181818181818181818181818181818181818181824242424242424242424242424242424727272727272
order12223366666644888812121212242424242424242433336666666666664412121212121212121212121224242424242424242424242424242424224466668888121212122424242424242424121212121212121212121212121212124412121212
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
χ511111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-1
χ92222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1000000
χ102222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2-2-22-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2111111-2-2111111000000
χ11222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000-1-122-1-1-1-1-1-122-1-1-1-1000000
χ12222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-2-2-2-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000000000011-2-2111111-2-21111000000
χ13222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1000000000000000000000000-1-1-1-122-1-1-1-1-1-122-1-1000000
χ14222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-10000000000000000000000001111-2-2111111-2-211000000
χ15222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000000000-1-1-1-1-1-122-1-1-1-1-1-122000000
χ16222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000000000111111-2-2111111-2-2000000
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12-222-2-22-1-1-12-1-1-1-2-2-2-211111111111100000000000000000000000022-1-1-1-1-1-1-2-2111111000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1-22-2-2222-1-1-12-1-1-1-2-2-2-2111111111111000000000000000000000000-2-211111122-1-1-1-1-1-1000000
χ1922222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-12-222-2-2-12-1-1-12-1-11111-2-2-2-211111111000000000000000000000000-1-122-1-1-1-111-2-21111000000
χ2022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-22-2-222-12-1-1-12-1-11111-2-2-2-21111111100000000000000000000000011-2-21111-1-122-1-1-1-1000000
χ2122222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-12-222-2-2-1-12-1-1-12-111111111-2-2-2-21111000000000000000000000000-1-1-1-122-1-11111-2-211000000
χ2222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-22-2-222-1-12-1-1-12-111111111-2-2-2-211110000000000000000000000001111-2-211-1-1-1-122-1-1000000
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χ25222222222222-2-20000-2-2-2-2000000002222222222222222000000-2-2-2-2-2-2-2-2000000000000000022-2-222220000-2-2-2-2000000000000000000000000000000
χ26222222222222-2-20000-2-2-2-2000000002222222222222222000000-2-2-2-2-2-2-2-20000000000000000-2-222-2-2-2-200002222000000000000000000000000000000
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χ332-22-222-2-222-2-2-222-22-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-22222000000-2-2-2-222222-22-22-22-22-22-22-22-20000000000000000000000000000000000000000000000
χ342-22-222-2-222-2-2-222-22-2-2-22222-2-222-2-22-1-1-1-2-21111112-1-1-1000000-21112-1-1-12-22-2-11-11-11-11-11-1100000000000000000000000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000
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χ372-22-222-2-222-2-2-222-22-2-2-22222-2-222-2-2-12-1-111-2-21111-12-1-10000001-211-12-1-1-11-112-22-2-11-11-11-11000000000000000000000000i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000
χ382-22-222-2-222-2-2-222-22-2-2-22222-2-222-2-2-1-12-11111-2-211-1-12-100000011-21-1-12-1-11-11-11-112-22-2-11-11000000000000000000000000−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000
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χ402-22-222-2-222-2-2-222-22-2-2-22222-2-222-2-2-1-1-12111111-2-2-1-1-12000000111-2-1-1-12-11-11-11-11-11-112-22-2000000000000000000000000−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000
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χ432-22-222-2-222-2-2-22-22-22-2-222-2-222-2-2222-1-1-1-2-21111112-1-1-1000000-21112-1-1-1-22-221-11-11-11-11-11-100000000000000000000000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000
χ442-22-222-2-222-2-2-22-22-22-2-222-2-222-2-2222-1-1-1-2-21111112-1-1-1000000-21112-1-1-1-22-221-11-11-11-11-11-100000000000000000000000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000
χ452-22-222-2-222-2-2-22-22-22-2-222-2-222-2-222-12-1-111-2-21111-12-1-10000001-211-12-1-11-11-1-22-221-11-11-11-1000000000000000000000000−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000
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χ472-22-222-2-222-2-2-22-22-22-2-222-2-222-2-222-1-12-11111-2-211-1-12-100000011-21-1-12-11-11-11-11-1-22-221-11-1000000000000000000000000−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000
χ482-22-222-2-222-2-2-22-22-22-2-222-2-222-2-222-1-12-11111-2-211-1-12-100000011-21-1-12-11-11-11-11-1-22-221-11-1000000000000000000000000i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000
χ492-22-222-2-222-2-2-22-22-22-2-222-2-222-2-222-1-1-12111111-2-2-1-1-12000000111-2-1-1-121-11-11-11-11-11-1-22-22000000000000000000000000−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300000000
χ502-22-222-2-222-2-2-22-22-22-2-222-2-222-2-222-1-1-12111111-2-2-1-1-12000000111-2-1-1-121-11-11-11-11-11-1-22-22000000000000000000000000i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300000000
χ512-2-2222-2-2-2-222002−2−22000022−2−2−2−2222222-22-22-22-22-2-2-2-2000000000000002−2−222−2−222−2−222−2−22002i−2i0000−i2i2i2−i22i2i−2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000000000
χ522-2-2222-2-2-2-222002−2−22000022−2−2−2−2222222-22-22-22-22-2-2-2-2000000000000002−2−222−2−222−2−222−2−2200−2i2i0000i2−i2−i2i2−2i−2i2i2ii2i2−i2−i2−i2−i2i2i20000000000000000000000
χ532-2-2222-2-2-2-22200−222−20000−2−22222−2−22222-22-22-22-22-2-2-2-200000000000000−222−2−222−2−222−2−222−2002i−2i0000i2−i2−i2i22i2i−2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000000000
χ542-2-2222-2-2-2-22200−222−20000−2−22222−2−22222-22-22-22-22-2-2-2-200000000000000−222−2−222−2−222−2−222−200−2i2i0000−i2i2i2−i2−2i−2i2i2i−i2−i2i2i2i2i2−i2−i20000000000000000000000
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+3i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−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+3i32000000000000000000000000-1-1-1-11+i321−i321+i321−i32-1-1-1-11+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+3i323−3i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−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+3i323−3i32000000000000000000000000-1-1-1-11+i321−i321+i321−i32-1-1-1-11+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+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−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+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000003-3−3−3i32−3+3i323+3i323−3i32000000000000000000000000-1-1-1-11+i321−i321+i321−i3211111+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
χ613333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i320000000000000000-333+3i323−3i32−3−3i32−3+3i320000000000000000000000001111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-111+i321−i32−1−i32−1+i32
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χ1226-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i300−323232−320000−3ζ5+3ζ233ζ7−3ζ133ζ5−3ζ23−3ζ7+3ζ133ζ5−3ζ23−3ζ7+3ζ13−3ζ5+3ζ233ζ7−3ζ13000000000000000000000000000000000000000000000000−2i2i0000−i2i2i2−i2−2ζ14−2ζ222ζ142ζ22ζ5+ζ23ζ7+ζ13−ζ5−ζ23−ζ7−ζ13−ζ5−ζ23−ζ7−ζ13ζ5+ζ23ζ7+ζ130000000000000000000000

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