Finite Group Databasebeta

← Group #13107631

Character table — Group #13107631

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size112222222444444445555555588888881010101010101010101010101010101010101010101010101616161616162020202020202020202020202020202020202020252525252525404040505050505050505050
order12444551010510202020202020444488885510102020202222228888882020202040404040404040402020202020201010101010102020404040404040404040404040228888101010444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111-1-1ii−i−i1111111111-1-1-1iii−i−i−i-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-111iiiiii−i−i−i−i−i−i-1-1ii−i−i111-1-1-1iii−i−i−i
χ41111111111111111111-1-1−i−iii1111111111-1-1-1−i−i−iiii-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-111−i−i−i−i−i−iiiiiii-1-1−i−iii111-1-1-1−i−i−iiii
χ511111111111111111-1-11111111111111-1-1-1111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ711111111111111111-1-1-1-1ii−i−i1111111-1-1-1-1-1-1iii−i−i−i-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11−i−iii-1-1-1111−i−i−iiii
χ811111111111111111-1-1-1-1−i−iii1111111-1-1-1-1-1-1−i−i−iiii-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11ii−i−i-1-1-1111iii−i−i−i
χ9111-1-111111111-1-1-1-11111111111111-1-11-1-11-1-11-1-11-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111-1-11-1-11-1-11-1-1
χ10111-1-111111111-1-1-1-11111-1-1-1-111111-1-11-1-11-1-1-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1111111-1-1-1-11-1-11-1-1-111-111
χ11111-1-111111111-1-1-1-111-1-1ii−i−i11111-1-11-1-1-111i−i−i−iii-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-1111111ii−i−i−i−i−i−iiiii-1-1ii−i−i1-1-1-111i−i−i−iii
χ12111-1-111111111-1-1-1-111-1-1−i−iii11111-1-11-1-1-111−iiii−i−i-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-1111111−i−iiiiiii−i−i−i−i-1-1−i−iii1-1-1-111−iiii−i−i
χ13111-1-111111111-1-1-1-1-1-111111111111-1-1-1111-1-11-1-11-1-111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111-111-111
χ14111-1-111111111-1-1-1-1-1-111-1-1-1-111111-1-1-1111-1-1-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111-111-1111-1-11-1-1
χ15111-1-111111111-1-1-1-1-1-1-1-1ii−i−i11111-1-1-111-111i−i−i−iii-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-1-1ii−i−i−i−i−i−iiiii11−i−iii-1111-1-1−iiii−i−i
χ16111-1-111111111-1-1-1-1-1-1-1-1−i−iii11111-1-1-111-111−iiii−i−i-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-1-1−i−iiiiiii−i−i−i−i11ii−i−i-1111-1-1i−i−i−iii
χ1711-11-1111111-1-111-1-1111111111111-11-1-11-1-11-1-11-1-11-1111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-1111111-11-1-11-1-11-1-11-1
χ1811-11-1111111-1-111-1-11111-1-1-1-11111-11-1-11-1-11-11-111-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-11111-1-1-1-1-11-1-11-11-111-11
χ1911-11-1111111-1-111-1-111-1-1ii−i−i1111-11-1-11-11-11−ii−ii−ii-1-1-1-1iiii−i−i−i−i-1-111-1-111-1-11111−i−iii−i−iii−i−iii-1-1ii−i−i-11-11-11−ii−ii−ii
χ2011-11-1111111-1-111-1-111-1-1−i−iii1111-11-1-11-11-11i−ii−ii−i-1-1-1-1−i−i−i−iiiii-1-111-1-111-1-11111ii−i−iii−i−iii−i−i-1-1−i−iii-11-11-11i−ii−ii−i
χ2111-11-1111111-1-111-1-1-1-11111111111-11-11-11-11-1-11-1-11-1111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-111-111-111-11
χ2211-11-1111111-1-111-1-1-1-111-1-1-1-11111-11-11-11-11-11-111-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111111-111-11-11-1-11-1
χ2311-11-1111111-1-111-1-1-1-1-1-1ii−i−i1111-11-11-111-11−ii−ii−ii-1-1-1-1iiii−i−i−i−i-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii11−i−iii1-11-11-1i−ii−ii−i
χ2411-11-1111111-1-111-1-1-1-1-1-1−i−iii1111-11-11-111-11i−ii−ii−i-1-1-1-1−i−i−i−iiiii-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−i11ii−i−i1-11-11-1−ii−ii−ii
χ2511-1-11111111-1-1-1-111111111111111-1-11-1-11-1-11-1-11-1-11111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-11-1-11-1-11-1-11
χ2611-1-11111111-1-1-1-1111111-1-1-1-11111-1-11-1-11-1-1111-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-11-1-1111-111-1
χ2711-1-11111111-1-1-1-11111-1-1ii−i−i1111-1-11-1-1111-1−i−iiii−i-1-1-1-1iiii−i−i−i−i-1-1-1-1111111-1-111−i−i−i−iiiiiii−i−i-1-1ii−i−i-1-1111-1−i−iiii−i
χ2811-1-11111111-1-1-1-11111-1-1−i−iii1111-1-11-1-1111-1ii−i−i−ii-1-1-1-1−i−i−i−iiiii-1-1-1-1111111-1-111iiii−i−i−i−i−i−iii-1-1−i−iii-1-1111-1ii−i−i−ii
χ2911-1-11111111-1-1-1-111-1-11111111111-1-1111-1-1-11-1-11-1-11111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-111-111-111-1
χ3011-1-11111111-1-1-1-111-1-111-1-1-1-11111-1-1111-1-1-1111-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1111111-111-1-1-11-1-11
χ3111-1-11111111-1-1-1-111-1-1-1-1ii−i−i1111-1-1111-111-1−i−iiii−i-1-1-1-1iiii−i−i−i−i-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiii−i−i11−i−iii11-1-1-11ii−i−i−ii
χ3211-1-11111111-1-1-1-111-1-1-1-1−i−iii1111-1-1111-111-1ii−i−i−ii-1-1-1-1−i−i−i−iiiii-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−iii11ii−i−i11-1-1-11−i−iiii−i
χ3322222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5200222222−1+52−1−52−1+52−1−52222000222222222−1+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+52−1−5200−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ3422222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−520022-2-2-2-2−1+52−1−52−1+52−1−52222000222-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52001−521+521−521+521−521+521−521+521−521+521−521+52000000000000000000
χ3522222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5200-2-22i2i−2i−2i−1+52−1−52−1+52−1−52222000-2-2-22i2i2i−2i−2i−2i1−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+521−521+5200−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14000000000000000000
χ3622222−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52−1+52−1−5200-2-2−2i−2i2i2i−1+52−1−52−1+52−1−52222000-2-2-2−2i−2i−2i2i2i2i1−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+521−521+5200ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14000000000000000000
χ3722222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5200222222−1−52−1+52−1−52−1+52222000222222222−1−52−1−52−1+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+5200−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ3822222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+520022-2-2-2-2−1−52−1+52−1−52−1+52222000222-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52001+521−521+521−521+521−521+521−521+521−521+521−52000000000000000000
χ3922222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5200-2-22i2i−2i−2i−1−52−1+52−1−52−1+52222000-2-2-22i2i2i−2i−2i−2i1+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−521+521−5200−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38000000000000000000
χ4022222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+5200-2-2−2i−2i2i2i−1−52−1+52−1−52−1+52222000-2-2-2−2i−2i−2i2i2i2i1+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−521+521−5200ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38000000000000000000
χ41222-2-2−1+52−1−52−1+52−1−5222−1+52−1−521−521+521−521+5200222222−1+52−1−52−1+52−1−522-2-20002-2-22-2-22-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+5200−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+52000000000000000000
χ42222-2-2−1+52−1−52−1+52−1−5222−1+52−1−521−521+521−521+520022-2-2-2-2−1+52−1−52−1+52−1−522-2-20002-2-2-222-222−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+52001−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ43222-2-2−1+52−1−52−1+52−1−5222−1+52−1−521−521+521−521+5200-2-22i2i−2i−2i−1+52−1−52−1+52−1−522-2-2000-2222i−2i−2i−2i2i2i1−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1−521−521+521−521+521−521+52−1+52−1−52−1+52−1−5200−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14000000000000000000
χ44222-2-2−1+52−1−52−1+52−1−5222−1+52−1−521−521+521−521+5200-2-2−2i−2i2i2i−1+52−1−52−1+52−1−522-2-2000-222−2i2i2i2i−2i−2i1−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−1+52−1−521−521+521−521+521−521+52−1+52−1−52−1+52−1−5200ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14000000000000000000
χ45222-2-2−1−52−1+52−1−52−1+5222−1−52−1+521+521−521+521−5200222222−1−52−1+52−1−52−1+522-2-20002-2-22-2-22-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−5200−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−52000000000000000000
χ46222-2-2−1−52−1+52−1−52−1+5222−1−52−1+521+521−521+521−520022-2-2-2-2−1−52−1+52−1−52−1+522-2-20002-2-2-222-222−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−52001+521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ47222-2-2−1−52−1+52−1−52−1+5222−1−52−1+521+521−521+521−5200-2-22i2i−2i−2i−1−52−1+52−1−52−1+522-2-2000-2222i−2i−2i−2i2i2i1+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−1−52−1+521+521−521+521−521+521−52−1−52−1+52−1−52−1+5200−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38000000000000000000
χ48222-2-2−1−52−1+52−1−52−1+5222−1−52−1+521+521−521+521−5200-2-2−2i−2i2i2i−1−52−1+52−1−52−1+522-2-2000-222−2i2i2i2i−2i−2i1+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−1−52−1+521+521−521+521−521+521−52−1−52−1+52−1−52−1+5200ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38ζ6+ζ14ζ22+ζ38000000000000000000
χ4922-22-2−1+52−1−52−1+52−1−52221−521+52−1+52−1−521−521+5200222222−1+52−1−52−1+52−1−52-22-2000-22-2-22-2-22-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+52001−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+52000000000000000000
χ5022-22-2−1+52−1−52−1+52−1−52221−521+52−1+52−1−521−521+520022-2-2-2-2−1+52−1−52−1+52−1−52-22-2000-22-22-222-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−521−521+521−521+52−1+52−1−521−521+5200−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−52000000000000000000
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χ9688-8-88−2−25−2+25−2−25−2+25-2-22+252−252+252−25−2−25−2+25000000001+521−521+521−5222-2000000000000000000000000−1−52−1+52−1−52−1+521+521−5200000000000000000000000000000000000000
χ978-800088-8-8-220000008i−8i000000-2-222000000000000000000000000000000000000000−2i2i000000000000000000000000000000
χ988-800088-8-8-22000000−8i8i000000-2-2220000000000000000000000000000000000000002i−2i000000000000000000000000000000
χ9916-16000−4+45−4−454−454+45-44000000000000001−51+5−1+5−1−500000000000000000000000000000000000000000000000000000000000000000000000
χ10016-16000−4−45−4+454+454−45-44000000000000001+51−5−1−5−1+500000000000000000000000000000000000000000000000000000000000000000000000

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