Finite Group Databasebeta

← Group #13144033

Character table — Group #13144033

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222444444444444444444666666666666666612121212121212121212121212121212121212121212121218181818181818181818181824242424242424242424242424242424363636363636363636363636363636363636
order123344661212121224661212244466881212121212122424242433336666121212121212121266661212121212121212121212121212121212121212224466661212121266661212121224242424242424242444668812121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111
χ5111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1111111-1-1-1-1
χ91111-1-111-1-1-1-1-11-1-1111-1i−i11i−i-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-1i−i11i−i-1-1ii−i−iii−i−i
χ101111-1-111-1-1-1-1-11-1-1111-1i−i11i−i-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-11−ii-1-1−ii11−i−iii−i−iii
χ111111-1-111-1-1-1-1-11-1-1111-1−ii11−ii-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii11−ii-1-1−i−iii−i−iii
χ121111-1-111-1-1-1-1-11-1-1111-1−ii11−ii-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-11i−i-1-1i−i11ii−i−iii−i−i
χ131111-1-111-1-1-1-1-11-1-111-11i−i-1-1−ii11ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11i−i-1-1−ii11ii−i−i−i−iii
χ141111-1-111-1-1-1-1-11-1-111-11i−i-1-1−ii11ii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-1-111-1-1-1-11111−i−i−i−iiiii1-1−ii11i−i-1-1−i−iiiii−i−i
χ151111-1-111-1-1-1-1-11-1-111-11−ii-1-1i−i11−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11−ii-1-1i−i11−i−iiiii−i−i
χ161111-1-111-1-1-1-1-11-1-111-11−ii-1-1i−i11−i−iiiii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-1-111-1-1-1-11111iiii−i−i−i−i1-1i−i11−ii-1-1ii−i−i−i−iii
χ172222222222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000002-1-1-12-1-1-12-1-1-12-1-1-1000000000000000000
χ18222222222222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000-12-1-1-12-1-1-12-1-1-12-1-1000000000000000000
χ19222222222222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000-1-12-1-1-12-1-1-12-1-1-12-1000000000000000000
χ20222222222222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000
χ2122222222222222222222-2-222-2-222-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-21111110000000000002-1-1-12-1-1-1-2111-2111000000000000000000
χ2222222222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000-12-1-1-12-1-11-2111-211000000000000000000
χ2322222222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-11111-2-2111111-2-211000000000000-1-12-1-1-12-111-2111-21000000000000000000
χ2422222222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111111-2-2111111-2-2000000000000-1-1-12-1-1-12111-2111-2000000000000000000
χ25222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2111-2111-2111-2111000000000000000000
χ26222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000001-2111-2111-2111-211000000000000000000
χ27222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-100000000000011-2111-2111-2111-21000000000000000000
χ28222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000111-2111-2111-2111-2000000000000000000
χ29222222222222222222-2-2-2-2-2-222-2-2-2-2-2-222222-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000-2111-21112-1-1-12-1-1-1000000000000000000
χ30222222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-111-2-2111111-2-211110000000000001-2111-211-12-1-1-12-1-1000000000000000000
χ31222222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-11111-2-2111111-2-21100000000000011-2111-21-1-12-1-1-12-1000000000000000000
χ32222222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12111111-2-2111111-2-2000000000000111-2111-2-1-1-12-1-1-12000000000000000000
χ33222222222222-2-2-2-2-2-20000000000000000002222222222222222-2-2-2-2-2-2-2-200000000000000002-2-2222-2-2-2-2220000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-20000000000000000002222222222222222-2-2-2-2-2-2-2-20000000000000000-222-2-2-22222-2-20000000000000000000000000000000000
χ352222-2-222-2-2-2-22-222-2-200000000000000000022222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-22222-2-2-2-20000000000000000000000000000000000
χ362222-2-222-2-2-2-22-222-2-200000000000000000022222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-222-2-2-2-222220000000000000000000000000000000000
χ372222-2-222-2-2-2-2-22-2-2222-22i−2i222i−2i-2-22i2i−2i−2i2i2i−2i−2i2-1-1-12-1-1-1-2-2111111-21112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000002-1-1-1-21112i−i−i−i−2iiii000000000000000000
χ382222-2-222-2-2-2-2-22-2-2222-22i−2i222i−2i-2-22i2i−2i−2i2i2i−2i−2i-12-1-1-12-1-111-2-211111-211-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000-12-1-11-211−i2i−i−ii−2iii000000000000000000
χ392222-2-222-2-2-2-2-22-2-2222-22i−2i222i−2i-2-22i2i−2i−2i2i2i−2i−2i-1-12-1-1-12-11111-2-21111-21-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000-1-12-111-21−i−i2i−iii−2ii000000000000000000
χ402222-2-222-2-2-2-2-22-2-2222-22i−2i222i−2i-2-22i2i−2i−2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2111-2-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000-1-1-12111-2−i−i−i2iiii−2i000000000000000000
χ412222-2-222-2-2-2-2-22-2-2222-2−2i2i22−2i2i-2-2−2i−2i2i2i−2i−2i2i2i2-1-1-12-1-1-1-2-2111111-21112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000002-1-1-1-2111−2iiii2i−i−i−i000000000000000000
χ422222-2-222-2-2-2-2-22-2-2222-2−2i2i22−2i2i-2-2−2i−2i2i2i−2i−2i2i2i-12-1-1-12-1-111-2-211111-211-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000-12-1-11-211i−2iii−i2i−i−i000000000000000000
χ432222-2-222-2-2-2-2-22-2-2222-2−2i2i22−2i2i-2-2−2i−2i2i2i−2i−2i2i2i-1-12-1-1-12-11111-2-21111-21-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000-1-12-111-21ii−2ii−i−i2i−i000000000000000000
χ442222-2-222-2-2-2-2-22-2-2222-2−2i2i22−2i2i-2-2−2i−2i2i2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2111-2-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000-1-1-12111-2iii−2i−i−i−i2i000000000000000000
χ452222-2-222-2-2-2-2-22-2-222-222i−2i-2-2−2i2i222i2i−2i−2i−2i−2i2i2i2-1-1-12-1-1-1-2-2111111-21112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000-21112-1-1-1−2iiii2i−i−i−i000000000000000000
χ462222-2-222-2-2-2-2-22-2-222-222i−2i-2-2−2i2i222i2i−2i−2i−2i−2i2i2i-12-1-1-12-1-111-2-211111-211-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000001-211-12-1-1i−2iii−i2i−i−i000000000000000000
χ472222-2-222-2-2-2-2-22-2-222-222i−2i-2-2−2i2i222i2i−2i−2i−2i−2i2i2i-1-12-1-1-12-11111-2-21111-21-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii00000000000011-21-1-12-1ii−2ii−i−i2i−i000000000000000000
χ482222-2-222-2-2-2-2-22-2-222-222i−2i-2-2−2i2i222i2i−2i−2i−2i−2i2i2i-1-1-12-1-1-12111111-2-2111-2-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000111-2-1-1-12iii−2i−i−i−i2i000000000000000000
χ492222-2-222-2-2-2-2-22-2-222-22−2i2i-2-22i−2i22−2i−2i2i2i2i2i−2i−2i2-1-1-12-1-1-1-2-2111111-21112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000-21112-1-1-12i−i−i−i−2iiii000000000000000000
χ502222-2-222-2-2-2-2-22-2-222-22−2i2i-2-22i−2i22−2i−2i2i2i2i2i−2i−2i-12-1-1-12-1-111-2-211111-211-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000001-211-12-1-1−i2i−i−ii−2iii000000000000000000
χ512222-2-222-2-2-2-2-22-2-222-22−2i2i-2-22i−2i22−2i−2i2i2i2i2i−2i−2i-1-12-1-1-12-11111-2-21111-21-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i00000000000011-21-1-12-1−i−i2i−iii−2ii000000000000000000
χ522222-2-222-2-2-2-2-22-2-222-22−2i2i-2-22i−2i22−2i−2i2i2i2i2i−2i−2i-1-1-12-1-1-12111111-2-2111-2-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000111-2-1-1-12−i−i−i2iiii−2i000000000000000000
χ5333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000001111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011-1-1−1−i32−1+i32-1-1−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1111+i321−i32111+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1111+i321−i32-1-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
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χ11912-12−6−6i3−6+6i312i−12i6+6i36−6i312ζ11−12ζ1112ζ7−12ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12012-12−6−6i3−6+6i3−12i12i6+6i36−6i3−12ζ1112ζ11−12ζ712ζ700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12112-12−6+6i3−6−6i312i−12i6−6i36+6i312ζ7−12ζ712ζ11−12ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12212-12−6+6i3−6−6i3−12i12i6−6i36+6i3−12ζ712ζ7−12ζ1112ζ1100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.