Finite Group Databasebeta

← Group #72223197

Character table — Group #72223197

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166
size112222222444444444444444444448888888888888888888888888888888888888888888888888888888888888888888888888888888888888888252540404040404040405050505050505080808080808080808080808080808080100100100100200200200200200200200200400400400400
order1224488884455881010202020204040404040404040551010101010101010202020202020202020202020202020202020202020202020202020202020202020204040404040404040404040404040404040404040404040404040404040404040404040404040404040404040221616161616161616244888880808080808080808080808080808080448816161616161616164444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiii−i−i
χ911111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1-11-1
χ1011111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-11-11
χ1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i-11-11
χ1211111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii1-11-1
χ1311111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-111−iii−i
χ1411111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-11111-1-1i−i−ii
χ1511111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-111i−i−ii
χ1611111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-11111-1-1−iii−i
χ172222222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000222-2-2220000000000000000-2-22-2000000000000
χ182222222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-222-2-2000000000000000022-22000000000000
χ1922222-2-222-2-222-22222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222222220000000022222-2-20000000000000000-2-2-22000000000000
χ2022222-2-222-2-222-22222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222222222-2-200000000-2-2-2-2-2220000000000000000222-2000000000000
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χ2222-22-2002200220-22222222222222222-2-222-2-2-2-2000000000000000000000000-2-22222-2-2-2-2-2-2-2-200000000000000000000000022222222-2-2-2-2-2-2-2-22200000000-22-222000000000000000000000-2−22−22−22−220000
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χ2522-22-200-2-2002202222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-22222-2-2-2-22222000000000000000000000000-2-2-2-2-2-2-2-2222222222200000000-22-2-2-20000000000000000000002i2−i2−i2i2i2−i2−i2i20000
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χ2722-22-200-2-2002202222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-22222-2-2-2-22222000000000000000000000000-2-2-2-2-2-2-2-222222222-2-2000000002-2222000000000000000000000-22−2−22−222−20000
χ2822-22-200-2-2002202222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-22222-2-2-2-22222000000000000000000000000-2-2-2-2-2-2-2-222222222-2-2000000002-2222000000000000000000000-2−222−22−2−220000
χ2922-2-2222000022-2022-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-2-2-222220000222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222−22−22−22−2-2-22002222−2−222−2−222−2−222−2−200-20000000000000
χ3022-2-2222000022-2022-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-2-2-222220000222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022−22−22−22−22-2-220022−2−222−2−222−2−222−2−22200-20000000000000
χ3122-2-2222000022-2022-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-2-2-222220000222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-22−22−2−22−2222-200-2-222−2−222−2−2−2−222−2−2220020000000000000
χ3222-2-2222000022-2022-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-2-2-222220000222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2−22−222−22−222-200-2-2−2−222−2−22222−2−222−2−20020000000000000
χ3322-2-22-2-20000222022-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000022-2-2-2-222220000-2-2-2-2-2-2-2-2-2-2-2-2222222222222000000000000000022i2−i2−i2i2i2−i2−i2i2-2-2200-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20020000000000000
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χ37444444444444-1444-144-1-14444-1-1-1-1-1-14-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14-1-1-1-1-1-1-1-1-144-1-144-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000004444000000000000000-1-1-1-1-1-1-1-10000000000000000
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χ1638-8000−4i24i2−4i24i24-4-2-20022−2i52i52i5−2i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39-23002-3005-5−1−i51+i5−1+i51−i5−1+i51−i5−1−i51+i5−1−i5−1+i51+i51−i5-14−i51−4+i5-14+i51−4−i5−1+i5−1−i51−i51+i50000−i5i5−2i52i5i5−i50000i2−i2i2−i2−2ζ7−2ζ21−2ζ23−2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ392ζ7+2ζ21+2ζ23+2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ3910−10−101000002ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ39−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ393ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ39i2−i22ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ39ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39i2−i210−103ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ39−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ3910−100000000000000000000000000000000000000000000000000
χ1648-8000−4i24i2−4i24i24-4-2-20022−2i52i52i5−2i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39-23002-300-55−1−i51+i5−1+i51−i5−1+i51−i5−1−i51+i5−1+i5−1−i51−i51+i54−i5-1−4+i514+i5-1−4−i51−1−i5−1+i51+i51−i50000−i5i52i5−2i5−i5i50000i2−i2i2−i2−2ζ13−2ζ31−2ζ37−2ζ39−2ζ7−2ζ21−2ζ23−2ζ29ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ392ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ392ζ13+2ζ31+2ζ37+2ζ392ζ7+2ζ21+2ζ23+2ζ29−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ3910−10−10100000−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ393ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ39i2−i22ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ39ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39i2−i2−1010−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ393ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ39−10100000000000000000000000000000000000000000000000000
χ1658-8000−4i24i2−4i24i24-4-2-20022−2i52i5−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ293-200-325-500−1−i51+i5−1+i51−i5−1−i51+i5−1+i51−i5-14+i51−4−i5−1−i5−1+i51+i51−i5−1+i5−1−i51−i51+i5-14−i51−4+i500i5−i500−i5i5−2i52i50000i2−i2i2−i2ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ392ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39−2ζ7−2ζ21−2ζ23−2ζ29−2ζ13−2ζ31−2ζ37−2ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ392ζ7+2ζ21+2ζ23+2ζ292ζ13+2ζ31+2ζ37+2ζ3910−1010−103ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ39−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ390000ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39i2−i2i2−i22ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ3910−1010−10−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ393ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ390000000000000000000000000000000000000000000000000
χ1668-8000−4i24i2−4i24i24-4-2-20022−2i52i5−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ293-200-32-5500−1−i51+i5−1+i51−i5−1−i51+i5−1+i51−i54+i5-1−4−i51−1+i5−1−i51−i51+i5−1−i5−1+i51+i51−i54−i5-1−4+i5100i5−i500i5−i52i5−2i50000i2−i2i2−i22ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ39−2ζ7−2ζ21−2ζ23−2ζ29−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ392ζ7+2ζ21+2ζ23+2ζ2910−1010−10−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ393ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ39−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ390000ζ7+2ζ13+ζ21+ζ23+ζ29+2ζ31+2ζ37+2ζ39−ζ7−2ζ13−ζ21−ζ23−ζ29−2ζ31−2ζ37−2ζ39i2−i2i2−i22ζ7+ζ13+2ζ21+2ζ23+2ζ29+ζ31+ζ37+ζ39−2ζ7−ζ13−2ζ21−2ζ23−2ζ29−ζ31−ζ37−ζ39−2ζ7−3ζ13−2ζ21−2ζ23−2ζ29−3ζ31−3ζ37−3ζ392ζ7+3ζ13+2ζ21+2ζ23+2ζ29+3ζ31+3ζ37+3ζ39−1010−10103ζ7+2ζ13+3ζ21+3ζ23+3ζ29+2ζ31+2ζ37+2ζ39−3ζ7−2ζ13−3ζ21−3ζ23−3ζ29−2ζ31−2ζ37−2ζ390000000000000000000000000000000000000000000000000

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