Finite Group Databasebeta

← Group #14277081

Character table — Group #14277081

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222444444444444444444444444444448888888888888888888888888888888888888888881010101010102020202020202020204040404040406060606060606060120120120120
order1222344446661212121225661010101212151520202020303030303030606060606060606088101020202424242430303030404040404040404060606060120120120120120120120120120120120120120120120120444444412121212121212128824242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ91111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1i−i-1-111ii−i−i-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-11111-1-1-1-1i−iii−i−i11-1-111-1-1i−ii−i
χ101111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1i−i-1-111ii−i−i-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-11111-1-1-1-1i−iii−i−i-1-111-1-111−ii−ii
χ111111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1i−i-1-111ii−i−i-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-1-1-11111−ii−i−iiiii−i−i−i−iii-111-1
χ121111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1i−i-1-111ii−i−i-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1111-1-1-1-11111−ii−i−iii−i−iiiii−i−i1-1-11
χ131111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1−ii-1-111−i−iii-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-11111-1-1-1-1−ii−i−iii11-1-111-1-1−ii−ii
χ141111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1−ii-1-111−i−iii-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-11111-1-1-1-1−ii−i−iii-1-111-1-111i−ii−i
χ151111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1−ii-1-111−i−iii-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-1-1-11111i−iii−i−iii−i−i−i−iii1-1-11
χ161111111-1-1111-1-1-1-1-11-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1−ii-1-111−i−iii-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1111-1-1-1-11111i−iii−i−i−i−iiiii−i−i-111-1
χ1722222-2-2222222222-22-2-2222-2-22222222222222222222200-2-2-2-20000-2-2-2-200000000-2-2-2-2000000000000000022-2-222-222-2-222-2-2000000000000000000
χ1822222-2-2222222222-22-2-2222-2-22222222222222222222200-2-2-2-20000-2-2-2-200000000-2-2-2-20000000000000000-2-222-2-22-2-222-2-222000000000000000000
χ1922222-2-2-2-2222-2-2-2-22222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20022-2-20000222200000000-2-2-2-2000000000000000022-2-2-2-2222-2-2-2-222000000000000000000
χ2022222-2-2-2-2222-2-2-2-22222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20022-2-20000222200000000-2-2-2-20000000000000000-2-22222-2-2-22222-2-2000000000000000000
χ212222-12222-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ222222-12222-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111-2-21111000000000000
χ232222-12222-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222222-1-1-1-1-1-1-1-1-2-21111000000000000
χ242222-12222-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2-2-2-21111111122-1-1-1-1000000000000
χ252222-122-2-2-1-1-11111-2211222-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111112i−2i-2-222−i−iii11112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii2222-2-2-2-1-1-1-111112i−2i−i−iii000000000000
χ262222-122-2-2-1-1-11111-2211222-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111112i−2i-2-222−i−iii11112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-2-2-22221111-1-1-1-1−2i2iii−i−i000000000000
χ272222-122-2-2-1-1-11111-2211222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111−2i2i-2-222ii−i−i1111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i2222-2-2-2-1-1-1-11111−2i2iii−i−i000000000000
χ282222-122-2-2-1-1-11111-2211222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111−2i2i-2-222ii−i−i1111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-2-2-22221111-1-1-1-12i−2i−i−iii000000000000
χ292222-1-2-222-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2−i3i3−i3i31111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-222-2-1-111-1-11100−i3i3−i3i3000000000000
χ302222-1-2-222-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2−i3i3−i3i31111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-222-2-2211-1-111-1-100i3−i3i3−i3000000000000
χ312222-1-2-222-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2i3−i3i3−i31111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-222-2-1-111-1-11100i3−i3i3−i3000000000000
χ322222-1-2-222-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2i3−i3i3−i31111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-222-2-2211-1-111-1-100−i3i3−i3i3000000000000
χ332222-1-2-2-2-2-1-1-1111122-1-122211-1-1-2-2-2-2-1-1-1-1-1-1111111110022-2-23−3−33-1-1-1-10000000011113333−3−3−3−3−3−3−3−3333322-2-2-2-22-1-11111-1-1003−3−33000000000000
χ342222-1-2-2-2-2-1-1-1111122-1-122211-1-1-2-2-2-2-1-1-1-1-1-1111111110022-2-23−3−33-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333-2-22222-211-1-1-1-11100−333−3000000000000
χ352222-1-2-2-2-2-1-1-1111122-1-122211-1-1-2-2-2-2-1-1-1-1-1-1111111110022-2-2−333−3-1-1-1-1000000001111−3−3−3−333333333−3−3−3−322-2-2-2-22-1-11111-1-100−333−3000000000000
χ362222-1-2-2-2-2-1-1-1111122-1-122211-1-1-2-2-2-2-1-1-1-1-1-1111111110022-2-2−333−3-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3-2-22222-211-1-1-1-111003−3−33000000000000
χ372-22-22002i−2i-22-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000002i−2i002-202i−2i002-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ382-22-22002i−2i-22-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000002i−2i002-202i−2i002-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ392-22-22002i−2i-22-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000−2i2i00-220−2i2i00-22000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ402-22-22002i−2i-22-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000−2i2i00-220−2i2i00-2200000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ412-22-2200−2i2i-22-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000002i−2i00-2202i−2i00-22000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ422-22-2200−2i2i-22-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000002i−2i00-2202i−2i00-2200000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ432-22-2200−2i2i-22-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000−2i2i002-20−2i2i002-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ442-22-2200−2i2i-22-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000−2i2i002-20−2i2i002-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ4544444444444444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ4644444444444444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-1-1-1-1-4-4-4-4-1-1-1-111111111-1-1-1-11111111111111111000000000000000000000000000000000
χ474444444-4-4444-4-4-4-4-4-1-4-4-1-1-144-1-11111-1-1-1-1-1-1111111114i−4i11-1-14i4i−4i−4i1111−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii000000000000000000000000000000000
χ484444444-4-4444-4-4-4-4-4-1-4-4-1-1-144-1-11111-1-1-1-1-1-111111111−4i4i11-1-1−4i−4i4i4i1111iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i000000000000000000000000000000000
χ4944444-4-4444444444-4-1-4-4-1-1-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100111100001111−5−555−5−5551111−5−555−5−555−5−555−5−555000000000000000000000000000000000
χ5044444-4-4444444444-4-1-4-4-1-1-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10011110000111155−5−555−5−5111155−5−555−5−555−5−555−5−5000000000000000000000000000000000
χ5144444-4-4-4-4444-4-4-4-44-144-1-1-1-4-4-1-11111-1-1-1-1-1-11111111100-1-1110000-1-1-1-1−i5−i5i5i5i5i5−i5−i51111−i5−i5i5i5−i5−i5i5i5i5i5−i5−i5i5i5−i5−i5000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-44-144-1-1-1-4-4-1-11111-1-1-1-1-1-11111111100-1-1110000-1-1-1-1i5i5−i5−i5−i5−i5i5i51111i5i5−i5−i5i5i5−i5−i5−i5−i5i5i5−i5−i5i5i5000000000000000000000000000000000
χ534444-24444-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15244-1-1-1-1-2-2-2-21−i1521−i1521+i1521+i152-1-1-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i152000000000000000000000000000000000
χ544444-24444-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152-4-4-1-1-1-122221−i1521−i1521+i1521+i152111111111−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152000000000000000000000000000000000
χ554444-24444-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15244-1-1-1-1-2-2-2-21+i1521+i1521−i1521−i152-1-1-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i152000000000000000000000000000000000
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χ11488-8-8-40000-4444i3−4i34i3−4i30-20022-2001+i151−i1525−25−2525−1−i15−1+i15−1−i15−1+i151+i151−i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116000000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-88008i−8i-88-88i8i−8i−8i0-200-22200-2-2−2i−2i2i2i-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-88-8800−8i8i-88-8−8i−8i8i8i0-200-22200-2-22i2i−2i−2i-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-88-8-4008i−8i4-44−4i−4i4i4i0-200-222001−i151+i15−2i−2i2i2i1−i151+i15−1+i15−1−i15−1+i15−1−i152ζ14+2ζ22+2ζ86+2ζ1182ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ38+2ζ46+2ζ62+2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ94−2ζ38−2ζ46−2ζ62−2ζ94000000000000000000000000000000000000000000000000000000000000000000000000000
χ1188-88-8-4008i−8i4-44−4i−4i4i4i0-200-222001+i151−i15−2i−2i2i2i1+i151−i15−1−i15−1+i15−1−i15−1+i152ζ38+2ζ46+2ζ62+2ζ942ζ38+2ζ46+2ζ62+2ζ942ζ14+2ζ22+2ζ86+2ζ1182ζ14+2ζ22+2ζ86+2ζ118−2ζ38−2ζ46−2ζ62−2ζ94−2ζ38−2ζ46−2ζ62−2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ14−2ζ22−2ζ86−2ζ118000000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-88-8-400−8i8i4-444i4i−4i−4i0-200-222001−i151+i152i2i−2i−2i1−i151+i15−1+i15−1−i15−1+i15−1−i15−2ζ14−2ζ22−2ζ86−2ζ118−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ94−2ζ38−2ζ46−2ζ62−2ζ942ζ14+2ζ22+2ζ86+2ζ1182ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ38+2ζ46+2ζ62+2ζ94000000000000000000000000000000000000000000000000000000000000000000000000000
χ1208-88-8-400−8i8i4-444i4i−4i−4i0-200-222001+i151−i152i2i−2i−2i1+i151−i15−1−i15−1+i15−1−i15−1+i15−2ζ38−2ζ46−2ζ62−2ζ94−2ζ38−2ζ46−2ζ62−2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ14−2ζ22−2ζ86−2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ38+2ζ46+2ζ62+2ζ942ζ14+2ζ22+2ζ86+2ζ1182ζ14+2ζ22+2ζ86+2ζ118000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.