Finite Group Databasebeta

← Group #13107630

Character table — Group #13107630

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size112224455555588810101010101010101022444881010101010101616162020202020202020202244488101010101010161616202020202020202020551010102020252525252525404040505050505050505050
order12444510448888202020222888888510202020510202040404040202020101010404040404040510202020510202040404040202020101010404040404040224441010448888202020222888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1
χ31111111-1-1ii−i−i111-1-1-1iii−i−i−i1111111-1-1ii−i−i111-1-1-1iii−i−i−i1111111-1-1ii−i−i111-1-1-1iii−i−i−i1111111-1-1ii−i−i111-1-1-1iii−i−i−i
χ41111111-1-1−i−iii111-1-1-1−i−i−iiii1111111-1-1−i−iii111-1-1-1−i−i−iiii1111111-1-1−i−iii111-1-1-1−i−i−iiii1111111-1-1−i−iii111-1-1-1−i−i−iiii
χ5111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1
χ6111-1-11111-1-1-1-11-1-11-1-1-111-111111-1-11111-1-1-1-11-1-11-1-1-111-111111-1-11111-1-1-1-11-1-11-1-1-111-111111-1-11111-1-1-1-11-1-11-1-1-111-111
χ7111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii
χ8111-1-111-1-1−i−iii1-1-1-111−iiii−i−i111-1-111-1-1−i−iii1-1-1-111−iiii−i−i111-1-111-1-1−i−iii1-1-1-111−iiii−i−i111-1-111-1-1−i−iii1-1-1-111−iiii−i−i
χ911-11-111111111-11-1-11-1-11-1-11-111-11-111111111-11-1-11-1-11-1-11-111-11-111111111-11-1-11-1-11-1-11-111-11-111111111-11-1-11-1-11-1-11-1
χ1011-11-11111-1-1-1-1-11-1-11-11-111-1111-11-11111-1-1-1-1-11-1-11-11-111-1111-11-11111-1-1-1-1-11-1-11-11-111-1111-11-11111-1-1-1-1-11-1-11-11-111-11
χ1111-11-111-1-1ii−i−i-11-11-11−ii−ii−ii11-11-111-1-1ii−i−i-11-11-11−ii−ii−ii11-11-111-1-1ii−i−i-11-11-11−ii−ii−ii11-11-111-1-1ii−i−i-11-11-11−ii−ii−ii
χ1211-11-111-1-1−i−iii-11-11-11i−ii−ii−i11-11-111-1-1−i−iii-11-11-11i−ii−ii−i11-11-111-1-1−i−iii-11-11-11i−ii−ii−i11-11-111-1-1−i−iii-11-11-11i−ii−ii−i
χ1311-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-11
χ1411-1-111111-1-1-1-1-1-11-1-1111-111-111-1-111111-1-1-1-1-1-11-1-1111-111-111-1-111111-1-1-1-1-1-11-1-1111-111-111-1-111111-1-1-1-1-1-11-1-1111-111-1
χ1511-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i11-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i11-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i11-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i
χ1611-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii11-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii11-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii11-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii
χ172-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ182-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ192-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ202-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ2144444-1-1000000-1-1-100000000044444-1-1000000-1-1-100000000044444-1-1000000-1-1-100000000044444-1-1000000-1-1-1000000000
χ22444-4-4-1-1000000-111000000000444-4-4-1-1000000-111000000000444-4-4-1-1000000-111000000000444-4-4-1-1000000-111000000000
χ2344-44-4-1-10000001-1100000000044-44-4-1-10000001-1100000000044-44-4-1-10000001-1100000000044-44-4-1-10000001-11000000000
χ2444-4-44-1-100000011-100000000044-4-44-1-100000011-100000000044-4-44-1-100000011-100000000044-4-44-1-100000011-1000000000
χ258-8000-220000000000000000008-8000-220000000000000000008-8000-220000000000000000008-8000-22000000000000000000
χ26111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ27111111111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ281111111-1-1ii−i−i111-1-1-1iii−i−i−i1111111-1-1ii−i−i111-1-1-1iii−i−i−i1111111-1-1ii−i−i111-1-1-1iii−i−i−i-1-1-1-1-1-1-111−i−iii-1-1-1111−i−i−iiii
χ291111111-1-1−i−iii111-1-1-1−i−i−iiii1111111-1-1−i−iii111-1-1-1−i−i−iiii1111111-1-1−i−iii111-1-1-1−i−i−iiii-1-1-1-1-1-1-111ii−i−i-1-1-1111iii−i−i−i
χ30111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-111-111-111-111
χ31111-1-11111-1-1-1-11-1-11-1-1-111-111111-1-11111-1-1-1-11-1-11-1-1-111-111111-1-11111-1-1-1-11-1-11-1-1-111-111-1-1-111-1-1-1-11111-111-1111-1-11-1-1
χ32111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii111-1-111-1-1ii−i−i1-1-1-111i−i−i−iii-1-1-111-1-111−i−iii-1111-1-1−iiii−i−i
χ33111-1-111-1-1−i−iii1-1-1-111−iiii−i−i111-1-111-1-1−i−iii1-1-1-111−iiii−i−i111-1-111-1-1−i−iii1-1-1-111−iiii−i−i-1-1-111-1-111ii−i−i-1111-1-1i−i−i−iii
χ3411-11-111111111-11-1-11-1-11-1-11-111-11-111111111-11-1-11-1-11-1-11-111-11-111111111-11-1-11-1-11-1-11-1-1-11-11-1-1-1-1-1-1-1-11-111-111-111-11
χ3511-11-11111-1-1-1-1-11-1-11-11-111-1111-11-11111-1-1-1-1-11-1-11-11-111-1111-11-11111-1-1-1-1-11-1-11-11-111-11-1-11-11-1-1-1-111111-111-11-11-1-11-1
χ3611-11-111-1-1ii−i−i-11-11-11−ii−ii−ii11-11-111-1-1ii−i−i-11-11-11−ii−ii−ii11-11-111-1-1ii−i−i-11-11-11−ii−ii−ii-1-11-11-1-111−i−iii1-11-11-1i−ii−ii−i
χ3711-11-111-1-1−i−iii-11-11-11i−ii−ii−i11-11-111-1-1−i−iii-11-11-11i−ii−ii−i11-11-111-1-1−i−iii-11-11-11i−ii−ii−i-1-11-11-1-111ii−i−i1-11-11-1−ii−ii−ii
χ3811-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-1111-1-1111111111-1-11-1-11-1-11-1-11-1-111-1-1-1-1-1-1-1-1-111-111-111-111-1
χ3911-1-111111-1-1-1-1-1-11-1-1111-111-111-1-111111-1-1-1-1-1-11-1-1111-111-111-1-111111-1-1-1-1-1-11-1-1111-111-1-1-111-1-1-1-1-1111111-111-1-1-11-1-11
χ4011-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i11-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i11-1-1111-1-1ii−i−i-1-1111-1−i−iiii−i-1-111-1-1-111−i−iii11-1-1-11ii−i−i−ii
χ4111-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii11-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii11-1-1111-1-1−i−iii-1-1111-1ii−i−i−ii-1-111-1-1-111ii−i−i11-1-1-11−i−iiii−i
χ422-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000002-20002-22i−2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000-22000-22−2i2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ432-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000002-20002-22i−2i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000-22000-22−2i2i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ442-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000002-20002-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000-22000-222i−2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ452-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000002-20002-2−2i2i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000-22000-222i−2i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ4644444-1-1000000-1-1-100000000044444-1-1000000-1-1-100000000044444-1-1000000-1-1-1000000000-4-4-4-4-411000000111000000000
χ47444-4-4-1-1000000-111000000000444-4-4-1-1000000-111000000000444-4-4-1-1000000-111000000000-4-4-444110000001-1-1000000000
χ4844-44-4-1-10000001-1100000000044-44-4-1-10000001-1100000000044-44-4-1-10000001-11000000000-4-44-4411000000-11-1000000000
χ4944-4-44-1-100000011-100000000044-4-44-1-100000011-100000000044-4-44-1-100000011-1000000000-4-444-411000000-1-11000000000
χ508-8000-220000000000000000008-8000-220000000000000000008-8000-22000000000000000000-880002-2000000000000000000
χ512222222222222222222222222−1+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+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000000000000000
χ52222222222-2-2-2-2222222-2-2-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+520000000000000000000000000
χ532222222-2-22i2i−2i−2i222-2-2-22i2i2i−2i−2i−2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−1+52−1+52−1+521−521−521−52−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−1−52−1−52−1−521+521+521+52−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ140000000000000000000000000
χ542222222-2-2−2i−2i2i2i222-2-2-2−2i−2i−2i2i2i2i−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−1+52−1+52−1+521−521−521−52ζ22+ζ38ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−1−52−1−52−1−521+521+521+52ζ6+ζ14ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ140000000000000000000000000
χ55222-2-2222222222-2-22-2-22-2-22-2-2−1+52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+521−521−52−1+521−521−52−1+521−521−52−1−52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−521+521+52−1−521+521+52−1−521+521+520000000000000000000000000
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χ10016-16000-44000000000000000000−4−454+450001+5−1−5000000000000000000−4+454−450001−5−1+50000000000000000000000000000000000000000000

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