Finite Group Databasebeta

← Group #72221727

Character table — Group #72221727

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size112222244444448888888888888888888810101010202020202020202020202525404040404040404040404040404050100100100100100112222244444448888888888888888888810101010202020202020202020202525404040404040404040404040404050100100100100100
order122551010251010101010551010101010101010101010101010101010102222444444101010102210102020202020202020202020202244442221010101021010101010101010101010101010101010101010101010101010222244444410101010221010202020202020202020202020224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1ii−i−i-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1ii−i−i111111111111111111111111111111111111-1-11-1ii−i−i-1-1-1-1-1-111-1-111iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111-1-11-1−i−iii-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1−i−iii111111111111111111111111111111111111-1-11-1−i−iii-1-1-1-1-1-111-1-111−i−i−i−iiiii-1-1−i−iii
χ51111111111111111111111111111111111-1-111-1111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111111111111111111111111111111111-1-111-1111111111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-111-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-111-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii1111111111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i1111111111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ91111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-11-111111111-1-1-1-111-1-111-1-11-11-11-11111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-11-111111111-1-1-1-111-1-111-1-11-11-11-1
χ101111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111111111-1-1-1-1-1-111-1-1111-1-11-111111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111111111-1-1-1-1-1-111-1-1111-1-11-11
χ111111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11i−i−ii-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii1111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11i−i−ii-1-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii
χ121111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11−iii−i-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i1111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11−iii−i-1-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i
χ131111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-11-11-11111-1-1-1-1-1-11111-1-111-1-1-11-11-111111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-11-11-11111-1-1-1-1-1-11111-1-111-1-1-11-11-11
χ141111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-11-111111-1-1-1-1-1-111-1-111-1-111-111-11-11111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-11-111111-1-1-1-1-1-111-1-111-1-111-111-11-1
χ151111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-111-1-11111ii−i−i−i−iii1-1−iii−i1111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-111-1-11111ii−i−i−i−iii1-1−iii−i
χ161111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-111-1-11111−i−iiiii−i−i1-1i−i−ii1111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-111-1-11111−i−iiiii−i−i1-1i−i−ii
χ17222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520022022222−1+52−1+52−1−52−1−520000−1+52−1−5200−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520022022222−1+52−1+52−1−52−1−520000−1+52−1−5200−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000
χ18222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002202-2-2-2-2−1+52−1+52−1−52−1−520000−1+52−1−52001−521+521−521+521−521+521−521+52000000222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002202-2-2-2-2−1+52−1+52−1−52−1−520000−1+52−1−52001−521+521−521+521−521+521−521+52000000
χ19222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-22i2i−2i−2i1−521−521+521+5200001−521+5200−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-22i2i−2i−2i1−521−521+521+5200001−521+5200−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000
χ20222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-2−2i−2i2i2i1−521−521+521+5200001−521+5200ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000222−1+52−1−52−1+52−1−5222−1+52−1−52222−1+52−1−52−1+52−1−5222−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-20-2−2i−2i2i2i1−521−521+521+5200001−521+5200ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000
χ21222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200220-22-22-2−1+52−1+52−1−52−1−5200001−521+5200−1+52−1−521−521+52−1+52−1−521−521+52000000222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200220-22-22-2−1+52−1+52−1−52−1−5200001−521+5200−1+52−1−521−521+52−1+52−1−521−521+52000000
χ22222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200220-2-22-22−1+52−1+52−1−52−1−5200001−521+52001−521+52−1+52−1−521−521+52−1+52−1−52000000222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200220-2-22-22−1+52−1+52−1−52−1−5200001−521+52001−521+52−1+52−1−521−521+52−1+52−1−52000000
χ23222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200-2-2022i−2i−2i2i1−521−521+521+520000−1+52−1−5200−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200-2-2022i−2i−2i2i1−521−521+521+520000−1+52−1−5200−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000
χ24222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200-2-202−2i2i2i−2i1−521−521+521+520000−1+52−1−5200ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000222−1+52−1−52−1+52−1−52-22−1+52−1−52222−1+52−1−521−521+52-2-2−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+5200-2-202−2i2i2i−2i1−521−521+521+520000−1+52−1−5200ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000
χ25222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520022022222−1−52−1−52−1+52−1+520000−1−52−1+5200−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520022022222−1−52−1−52−1+52−1+520000−1−52−1+5200−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000
χ26222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002202-2-2-2-2−1−52−1−52−1+52−1+520000−1−52−1+52001+521−521+521−521+521−521+521−52000000222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002202-2-2-2-2−1−52−1−52−1+52−1+520000−1−52−1+52001+521−521+521−521+521−521+521−52000000
χ27222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-22i2i−2i−2i1+521+521−521−5200001+521−5200−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-22i2i−2i−2i1+521+521−521−5200001+521−5200−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000
χ28222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-2−2i−2i2i2i1+521+521−521−5200001+521−5200ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000222−1−52−1+52−1−52−1+5222−1−52−1+52222−1−52−1+52−1−52−1+5222−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-20-2−2i−2i2i2i1+521+521−521−5200001+521−5200ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000
χ29222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200220-22-22-2−1−52−1−52−1+52−1+5200001+521−5200−1−52−1+521+521−52−1−52−1+521+521−52000000222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200220-22-22-2−1−52−1−52−1+52−1+5200001+521−5200−1−52−1+521+521−52−1−52−1+521+521−52000000
χ30222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200220-2-22-22−1−52−1−52−1+52−1+5200001+521−52001+521−52−1−52−1+521+521−52−1−52−1+52000000222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200220-2-22-22−1−52−1−52−1+52−1+5200001+521−52001+521−52−1−52−1+521+521−52−1−52−1+52000000
χ31222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200-2-2022i−2i−2i2i1+521+521−521−520000−1−52−1+5200−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200-2-2022i−2i−2i2i1+521+521−521−520000−1−52−1+5200−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000
χ32222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200-2-202−2i2i2i−2i1+521+521−521−520000−1−52−1+5200ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000222−1−52−1+52−1−52−1+52-22−1−52−1+52222−1−52−1+521+521−52-2-2−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200-2-202−2i2i2i−2i1+521+521−521−520000−1−52−1+5200ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000
χ3322-2222202-2-2-2-222200002-2-22-2-2000000002-22-20000002-22-2222-2000000000000-20000022-2222202-2-2-2-222200002-2-22-2-2000000002-22-20000002-22-2222-2000000000000-200000
χ3422-2222202-2-2-2-222200002-2-22-2-2000000002-2-22000000-22-22-2-22-200000000000020000022-2222202-2-2-2-222200002-2-22-2-2000000002-2-22000000-22-22-2-22-2000000000000200000
χ3522-2222202-2-2-2-222200002-2-22-2-200000000-222-20000002-22-2-2-2-2200000000000020000022-2222202-2-2-2-222200002-2-22-2-200000000-222-20000002-22-2-2-2-22000000000000200000
χ3622-2222202-2-2-2-222200002-2-22-2-200000000-22-22000000-22-2222-22000000000000-20000022-2222202-2-2-2-222200002-2-22-2-200000000-22-22000000-22-2222-22000000000000-200000
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χ1338-80−2+25−2−252−252+250-20025−2521−521+520000−1+525−52−5+52−1−52−5−525+52−5+525−52−5−3525+352−5+3525−352−5−525+52000000000000000000000000000000000000-8802−252+25−2+25−2−250200−2525-2−1+52−1−5200001−52−5+525−521+525+52−5−525−52−5+525+352−5−3525−352−5+3525+52−5−52000000000000000000000000000000000000
χ1348-80−2+25−2−252−252+250-200−252521−521+520000−1+52−5+525−52−1−525+52−5−525+352−5−352−5+525−52−5−525+525−352−5+352000000000000000000000000000000000000-8802−252+25−2+25−2−25020025−25-2−1+52−1−5200001−525−52−5+521+52−5−525+52−5−3525+3525−52−5+525+52−5−52−5+3525−352000000000000000000000000000000000000
χ1358-80−2+25−2−252−252+250-200−252521−521+520000−1+52−5+525−52−1−525+52−5−52−5−3525+3525−52−5+525+52−5−52−5+3525−352000000000000000000000000000000000000-8802−252+25−2+25−2−25020025−25-2−1+52−1−5200001−525−52−5+521+52−5−525+525+352−5−352−5+525−52−5−525+525−352−5+352000000000000000000000000000000000000
χ1368-80−2−25−2+252+252−25080000-8−2−25−2+2500002+25002−250000000000000000000000000000000000000000000000-8802+252−25−2−25−2+250-8000082+252−250000−2−2500−2+250000000000000000000000000000000000000000000000
χ1378-80−2−25−2+252+252−250-20025−2521+521−520000−1−52−5−525+52−1+525−52−5+525−352−5+352−5−525+52−5+525−525+352−5−352000000000000000000000000000000000000-8802+252−25−2−25−2+250200−2525-2−1−52−1+5200001+525+52−5−521−52−5+525−52−5+3525−3525+52−5−525−52−5+52−5−3525+352000000000000000000000000000000000000
χ1388-80−2−25−2+252+252−250-20025−2521+521−520000−1−52−5−525+52−1+525−52−5+52−5+3525−3525+52−5−525−52−5+52−5−3525+352000000000000000000000000000000000000-8802+252−25−2−25−2+250200−2525-2−1−52−1+5200001+525+52−5−521−52−5+525−525−352−5+352−5−525+52−5+525−525+352−5−352000000000000000000000000000000000000
χ1398-80−2−25−2+252+252−250-200−252521+521−520000−1−525+52−5−52−1+52−5+525−525+52−5−525−352−5+3525+352−5−3525−52−5+52000000000000000000000000000000000000-8802+252−25−2−25−2+25020025−25-2−1−52−1+5200001+52−5−525+521−525−52−5+52−5−525+52−5+3525−352−5−3525+352−5+525−52000000000000000000000000000000000000
χ1408-80−2−25−2+252+252−250-200−252521+521−520000−1−525+52−5−52−1+52−5+525−52−5−525+52−5+3525−352−5−3525+352−5+525−52000000000000000000000000000000000000-8802+252−25−2−25−2+25020025−25-2−1−52−1+5200001+52−5−525+521−525−52−5+525+52−5−525−352−5+3525+352−5−3525−52−5+52000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.