Finite Group Databasebeta

← Group #72221057

Character table — Group #72221057

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
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order12244885555558101010101010101010101010101010101010242020202020202020202020204040404040404040404040404040404040404040404040401010101010101010101010102020202020202020202020202224488444488888248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1ii−i−i-1-1ii−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1−i−iii-1-1−i−iii
χ511111111111111111111111111111111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1ii−i−i11−i−iii
χ811111111111111111111111111111111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−iii11ii−i−i
χ911111-1-1111111-11111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-11-11-11-1
χ1011111-1-1111111-11111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111111-1-11-11
χ1111111-1-1111111-11111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i1−i−iii-11i−i−ii
χ1211111-1-1111111-11111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii1ii−i−i-11−iii−i
χ1311111-1-1111111-1111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11111-1-1-1-1-1-11-11-11
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χ1168-8000−4i24i2-2-2−2−253+53−5−2+250−252525−25005−5−5+5−5−55+500222+25−3−5−3+52−2500000000000000i2−i2i2−i2−2ζ21−2ζ29−2ζ31−2ζ392ζ21+2ζ29+2ζ31+2ζ39ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ392ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ39−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+2ζ23+2ζ37i10−i10−i10i10003ζ7+3ζ13+2ζ21+3ζ23+2ζ29+2ζ31+3ζ37+2ζ39−3ζ7−3ζ13−2ζ21−3ζ23−2ζ29−2ζ31−3ζ37−2ζ39−2ζ7−2ζ13−3ζ21−2ζ23−3ζ29−3ζ31−2ζ37−3ζ392ζ7+2ζ13+3ζ21+2ζ23+3ζ29+3ζ31+2ζ37+3ζ39000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.