Finite Group Databasebeta

← Group #14277176

Character table — Group #14277176

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11111111222222224444444444444444444444444444448888888888888888888888888888888888888888881010101010101010202020202020202040404040404060606060606060606060606060606060
order1222222236666666445101010101010101212121215153030303030303030303030303030441212121220202020202020202020202060606060606060606060606060606060606060606060606044444444121212121212121244121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i
χ91-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111-1-1-11-11111-1-1-1-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111-1-1-11-11111-1-1-1-1i−iii−i−i-1-111−i−iii-1-111−i−iii
χ111-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111-11-1-1-1-11111−ii−i−iiiii−i−i-1-111−i−iii11-1-1
χ121-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111-11-1-1-1-11111−ii−i−iii−i−iii11-1-1ii−i−i-1-111
χ131-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111-1-1-11-11111-1-1-1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111-1-1-11-11111-1-1-1-1−ii−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111-11-1-1-1-11111i−iii−i−iii−i−i11-1-1−i−iii-1-111
χ161-1-1-1111-11-1-1-1111-11-1111-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1−ii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111-11-1-1-1-11111i−iii−i−i−i−iii-1-111ii−i−i11-1-1
χ172222222222222222-2-222222222-2-2-2-22222222222222222000000-2-2-2-200000000-2-2-2-2-2-2-2-2000000000000000022-22-2-2-2222-2-222-2-20000000000000000000000
χ182222222222222222-2-222222222-2-2-2-22222222222222222000000-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-2-22-2222-2-2-222-2-2220000000000000000000000
χ1922222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ2022222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-211110000000000000000
χ2122222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122222222-1-1-1-1-1-1-1-1-2-211110000000000000000
χ2222222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2-2-2-2-21111111122-1-1-1-10000000000000000
χ2322222222-1-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3−i3i3-2-2-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-22-2-2-22-1-111-1-11100−i3i3−i3i30000000000000000
χ2422222222-1-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3−i3i3-2-2-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-22-2222-211-1-111-1-100i3−i3i3−i30000000000000000
χ2522222222-1-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3i3−i3-2-2-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-22-2-2-22-1-111-1-11100i3−i3i3−i30000000000000000
χ2622222222-1-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3i3−i3-2-2-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-22-2222-211-1-111-1-100−i3i3−i3i30000000000000000
χ27222-2-22-2-2222-2-22-2-20022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000202-2-20002-2002-200000000002−22−200002−22−2
χ28222-2-22-2-2222-2-22-2-20022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000202-2-20002-2002-20000000000−22−220000−22−22
χ29222-2-22-2-2222-2-22-2-20022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000-20-222000-2200-220000000000−i2i2−i2i20000i2−i2i2−i2
χ30222-2-22-2-2222-2-22-2-20022-222-2-2-200002222-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000000-20-222000-2200-220000000000i2−i2i2−i20000−i2i2−i2i2
χ3122-22-2-22-222-22-2-22-2002-222-22-2-2000022-2-22222-2-222-2-2-2-20000000000000000000000000000000000000000002-202000-22-2002-2000000002−22−200002−22−20000
χ3222-22-2-22-222-22-2-22-2002-222-22-2-2000022-2-22222-2-222-2-2-2-20000000000000000000000000000000000000000002-202000-22-2002-200000000−22−220000−22−220000
χ3322-22-2-22-222-22-2-22-2002-222-22-2-2000022-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000-220-20002-2200-2200000000−i2i2−i2i20000i2−i2i2−i20000
χ3422-22-2-22-222-22-2-22-2002-222-22-2-2000022-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000-220-20002-2200-2200000000i2−i2i2−i20000−i2i2−i2i20000
χ352-22-2-2-2222-22-2-2-222002-22-22-2-22000022-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000002-20-200022-200-22000000002−2−2200002−2−220000
χ362-22-2-2-2222-22-2-2-222002-22-22-2-22000022-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000002-20-200022-200-2200000000−222−20000−222−20000
χ372-22-2-2-2222-22-2-2-222002-22-22-2-22000022-2-222-2-222-2-2-2-222000000000000000000000000000000000000000000-2202000-2-22002-200000000−i2i2i2−i20000i2−i2−i2i20000
χ382-22-2-2-2222-22-2-2-222002-22-22-2-22000022-2-222-2-222-2-2-2-222000000000000000000000000000000000000000000-2202000-2-22002-200000000i2−i2−i2i20000−i2i2i2−i20000
χ392-2-22-22-222-2-22-22-220022-2-2-22-2200002222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000020-22-20002-200-220000000000−i2i2i2−i20000−i2i2i2−i2
χ402-2-22-22-222-2-22-22-220022-2-2-22-2200002222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000020-22-20002-200-220000000000i2−i2−i2i20000i2−i2−i2i2
χ412-2-22-22-222-2-22-22-220022-2-2-22-2200002222-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000-202-22000-22002-200000000002−2−220000−222−2
χ422-2-22-22-222-2-22-22-220022-2-2-22-2200002222-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000-202-22000-22002-20000000000−222−200002−2−22
χ432-2-2-2222-22-2-2-2222-2-22222-2-2-22-2-2-222222222-2-2-2-2-2-222-2-2000000-2-22200000000-2-2-2-22222000000000000000022-2-222-2-222-2-2-2-2220000000000000000000000
χ442-2-2-2222-22-2-2-2222-2-22222-2-2-22-2-2-222222222-2-2-2-2-2-222-2-2000000-2-22200000000-2-2-2-222220000000000000000-2-222-2-222-2-22222-2-20000000000000000000000
χ452-2-2-2222-2-1111-1-1-112-2222-2-2-22-2-1-111-1-1-1-1-1-1111111-1-1112i−2i−i−iii22-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii222-2-2-22-2-1-1-1-111112i−2i−i−iii0000000000000000
χ462-2-2-2222-2-1111-1-1-112-2222-2-2-22-2-1-111-1-1-1-1-1-1111111-1-1112i−2i−i−iii22-2-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-2-2222-221111-1-1-1-1−2i2iii−i−i0000000000000000
χ472-2-2-2222-2-1111-1-1-112-2222-2-2-22-2-1-111-1-1-1-1-1-1111111-1-111−2i2iii−i−i22-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i222-2-2-22-2-1-1-1-11111−2i2iii−i−i0000000000000000
χ482-2-2-2222-2-1111-1-1-112-2222-2-2-22-2-1-111-1-1-1-1-1-1111111-1-111−2i2iii−i−i22-2-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2-2222-221111-1-1-1-12i−2i−i−iii0000000000000000
χ492-2-2-2222-2-1111-1-1-11-22222-2-2-22-211-1-1-1-1-1-1-1-1111111-1-111003−3−33-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333322-2-222-2-2-1-11111-1-1003−3−330000000000000000
χ502-2-2-2222-2-1111-1-1-11-22222-2-2-22-211-1-1-1-1-1-1-1-1111111-1-111003−3−33-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-2-222-2-22211-1-1-1-11100−333−30000000000000000
χ512-2-2-2222-2-1111-1-1-11-22222-2-2-22-211-1-1-1-1-1-1-1-1111111-1-11100−333−3-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−322-2-222-2-2-1-11111-1-100−333−30000000000000000
χ522-2-2-2222-2-1111-1-1-11-22222-2-2-22-211-1-1-1-1-1-1-1-1111111-1-11100−333−3-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-2-222-2-22211-1-1-1-111003−3−330000000000000000
χ53444444444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ54444444444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-4-4-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000000000000000
χ554444444444444444-4-4-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000001111−5−555−5−55511111111−5−555−5−555−5−555−5−55500000000000000000000000000000000000000
χ564444444444444444-4-4-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000111155−5−555−5−51111111155−5−555−5−555−5−555−5−500000000000000000000000000000000000000
χ5744444444-2-2-2-2-2-2-2-244-1-1-1-1-1-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15244-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i15200000000000000000000000000000000000000
χ5844444444-2-2-2-2-2-2-2-244-1-1-1-1-1-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-4-42222-1-1-1-1111111111−i1521−i1521+i1521+i1521−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+i15200000000000000000000000000000000000000
χ5944444444-2-2-2-2-2-2-2-244-1-1-1-1-1-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15244-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i15200000000000000000000000000000000000000
χ6044444444-2-2-2-2-2-2-2-244-1-1-1-1-1-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-4-42222-1-1-1-1111111111+i1521+i1521−i1521−i1521+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−i15200000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.