Finite Group Databasebeta

← Group #72221774

Character table — Group #72221774

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11222222244444444445588888888888888810101010101010161616161616161616161616161620202020202020202020202020204040404040404040404040404040404040404040404040404040408080100100100100100100100100200200
order122445510105101010101020202020222551010101010101010101020202441010101010101010101010101010202020202244444410102020202028810101010202020202020202020202020404040404040404010102244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ6111111111111111111111-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ7111111111111111111111-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111111111111-1-1111111111111111-1-1-1-1-1-1-1111111111111111111ii−i−i-1-1-1-1-1-1-1i−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1ii−i−ii−i
χ101111111111111111111-1-1111111111111111-1-1-1-1-1-1-1111111111111111111−i−iii-1-1-1-1-1-1-1−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1−i−iii−ii
χ111111111111111111111-1-1111111111111111-1-1-1-1-1-1-111111111111111-1-1-1-1ii−i−i-1-1-1-1-1-1-1i−i-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111−i−iii−ii
χ121111111111111111111-1-1111111111111111-1-1-1-1-1-1-111111111111111-1-1-1-1−i−iii-1-1-1-1-1-1-1−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111ii−i−ii−i
χ131111111111111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1-1-1-1-11−ii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111ii−i−i−ii
χ141111111111111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii-1-1-1-1-1-11i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111−i−iiii−i
χ151111111111111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i-1-1-1-1-1-11−ii11111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1−i−iiii−i
χ161111111111111111111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii-1-1-1-1-1-11i−i11111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1ii−i−i−ii
χ1722222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222−1+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+52−1−52−1−5200002222−1+52−1−52−1+52−1−52−1+52−1−52222−1+52−1+52−1−52−1−520000−1+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+52−1−52−1−52000000000000
χ1822222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222222−1+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+52−1−52−1−520000-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−522-2-2−1+52−1+52−1−52−1−5200001−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000
χ1922222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−5222-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−5222222−1+52−1+52−1−52−1−52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−5200002222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-21−521−521+521+520000−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000
χ2022222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−5222-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−5222222−1+52−1+52−1−52−1−52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−520000-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2221−521−521+521+5200001−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ2122222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-21−521−521+521+5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−5200002i2i−2i−2i1−521+521−521+521−521+52-22i−2i1−521−521+521+520000−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7000000000000
χ2222222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-21−521−521+521+5222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−520000−2i−2i2i2i1−521+521−521+521−521+52-2−2i2i1−521−521+521+520000ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7000000000000
χ2322222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52-2-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-21−521−521+521+52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−5200002i2i−2i−2i1−521+521−521+521−521+522−2i2i−1+52−1+52−1−52−1−520000−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7000000000000
χ2422222−1+52−1−52−1+52−1−522−1+52−1−52222−1+52−1+52−1−52−1−52-2-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-21−521−521+521+52-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−520000−2i−2i2i2i1−521+521−521+521−521+5222i−2i−1+52−1+52−1−52−1−520000ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7000000000000
χ2522222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222−1−52−1−52−1+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+5200002222−1−52−1+52−1−52−1+52−1−52−1+52222−1−52−1−52−1+52−1+520000−1−52−1−52−1+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+52000000000000
χ2622222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222222−1−52−1−52−1+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+520000-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+522-2-2−1−52−1−52−1+52−1+5200001+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000
χ2722222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+5222-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+5222222−1−52−1−52−1+52−1+52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+5200002222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-21+521+521−521−520000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000
χ2822222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+5222-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+5222222−1−52−1−52−1+52−1+52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+520000-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2221+521+521−521−5200001+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ2922222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52-2-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-21+521+521−521−5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+5200002i2i−2i−2i1+521−521+521−521+521−52-22i−2i1+521+521−521−520000−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19000000000000
χ3022222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52-2-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-21+521+521−521−5222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+520000−2i−2i2i2i1+521−521+521−521+521−52-2−2i2i1+521+521−521−520000ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19000000000000
χ3122222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52-2-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-21+521+521−521−52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+5200002i2i−2i−2i1+521−521+521−521+521−522−2i2i−1−52−1−52−1+52−1+520000−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19000000000000
χ3222222−1−52−1+52−1−52−1+522−1−52−1+52222−1−52−1−52−1+52−1+52-2-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-21+521+521−521−52-2-21+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+520000−2i−2i2i2i1+521−521+521−521+521−5222i−2i−1−52−1−52−1+52−1+520000ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19000000000000
χ33222-2-22222222222-2-2-2-2220220000222222-2-22-2-222220000000000-2-2-2-22-200000022-2-2-2-20000000000000000000000000002-22-200000000
χ34222-2-22222222222-2-2-2-2220220000222222-2-22-2-222220000000000-2-2-2-2-2200000022-2-2-2-2000000000000000000000000000-22-2200000000
χ35222-2-22222222222-2-2-2-2-2-20220000222222-2-2-222-2-2-2-20000000000-2-2-2-22-2000000-2-222220000000000000000000000000002-2-2200000000
χ36222-2-22222222222-2-2-2-2-2-20220000222222-2-2-222-2-2-2-20000000000-2-2-2-2-22000000-2-22222000000000000000000000000000-222-200000000
χ3722-22-222222-2-22-2-22-22-2220220000-2-2-2-2222-2-22-2222200000000002-22-200002-22-2-2-2-2-222000000000002-22-22-22-200000000000000000000
χ3822-22-222222-2-22-2-22-22-2220220000-2-2-2-2222-2-22-2222200000000002-22-20000-22-22-2-2-2-22200000000000-22-22-22-2200000000000000000000
χ3922-22-222222-2-22-2-22-22-2-2-20220000-2-2-2-2222-22-22-2-2-2-200000000002-22-200002i−2i−2i2i2222-2-2000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ4022-22-222222-2-22-2-22-22-2-2-20220000-2-2-2-2222-22-22-2-2-2-200000000002-22-20000−2i2i2i−2i2222-2-200000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4122-22-2−1+52−1−52−1+52−1−5221−521+522-2-2−1+521−52−1−521+52220−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−1+52−1−522-2-22-2−1+52−1+52−1−52−1−5200ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+521−52−1−521+5200002-22-21−521+521−521+52−1+52−1−52000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000−1+521−52−1−521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000000000
χ4222-22-2−1+52−1−52−1+52−1−5221−521+522-2-2−1+521−52−1−521+52220−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−1+52−1−522-2-22-2−1+52−1+52−1−52−1−5200ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−1+521−52−1−521+520000-22-221−521+521−521+52−1+52−1−52000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800001−52−1+521+52−1−521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000000000
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χ9688-8-88−2+25−2−25−2+25−2−25-22−252+25-2222−25−2+252+25−2−250001−521+520000−1+52−1+52−1−52−1−521−521+522-20000000002ζ2+ζ6−ζ14−2ζ18−2ζ2−ζ6+ζ14+2ζ18−2ζ2−ζ6+ζ14+2ζ182ζ2+ζ6−ζ14−2ζ18ζ2−2ζ6+2ζ14−ζ18−ζ2+2ζ6−2ζ14+ζ18−ζ2+2ζ6−2ζ14+ζ18ζ2−2ζ6+2ζ14−ζ18−1+521−52−1−521+5200000000000000000000000000000000000000000000000000000
χ9788-8-88−2−25−2+25−2−25−2+25-22+252−25-2222+25−2−252−25−2+250001+521−520000−1−52−1−52−1+52−1+521+521−522-2000000000−ζ2+2ζ6−2ζ14+ζ18ζ2−2ζ6+2ζ14−ζ18ζ2−2ζ6+2ζ14−ζ18−ζ2+2ζ6−2ζ14+ζ182ζ2+ζ6−ζ14−2ζ18−2ζ2−ζ6+ζ14+2ζ18−2ζ2−ζ6+ζ14+2ζ182ζ2+ζ6−ζ14−2ζ18−1−521+52−1+521−5200000000000000000000000000000000000000000000000000000
χ9888-8-88−2−25−2+25−2−25−2+25-22+252−25-2222+25−2−252−25−2+250001+521−520000−1−52−1−52−1+52−1+521+521−522-2000000000ζ2−2ζ6+2ζ14−ζ18−ζ2+2ζ6−2ζ14+ζ18−ζ2+2ζ6−2ζ14+ζ18ζ2−2ζ6+2ζ14−ζ18−2ζ2−ζ6+ζ14+2ζ182ζ2+ζ6−ζ14−2ζ182ζ2+ζ6−ζ14−2ζ18−2ζ2−ζ6+ζ14+2ζ18−1−521+52−1+521−5200000000000000000000000000000000000000000000000000000
χ998-800088-8-8-200225−250000000-2-2000025−2525−252200000000000000000000000004-400000000000000000−1+51−5−1−51+50000000000000000000000000000
χ1008-800088-8-8-200225−250000000-2-2000025−2525−25220000000000000000000000000-44000000000000000001−5−1+51+5−1−50000000000000000000000000000
χ1018-800088-8-8-2002−25250000000-2-20000−2525−25252200000000000000000000000004-400000000000000000−1−51+5−1+51−50000000000000000000000000000
χ1028-800088-8-8-2002−25250000000-2-20000−2525−2525220000000000000000000000000-44000000000000000001+5−1−51−5−1+50000000000000000000000000000
χ1038-8000−2+25−2−252−252+25800-80000008-80−2+25−2−25000000002−252+2500000−2+252−25−2−252+250000000000000000000000000000000000000000000000000000000000000000000
χ1048-8000−2+25−2−252−252+25800-8000000-880−2+25−2−25000000002−252+25000002−25−2+252+25−2−250000000000000000000000000000000000000000000000000000000000000000000
χ1058-8000−2−25−2+252+252−25800-80000008-80−2−25−2+25000000002+252−2500000−2−252+25−2+252−250000000000000000000000000000000000000000000000000000000000000000000
χ1068-8000−2−25−2+252+252−25800-8000000-880−2−25−2+25000000002+252−25000002+25−2−252−25−2+250000000000000000000000000000000000000000000000000000000000000000000
χ10716-16000−4+45−4−454−454+45-400445−4500000001−51+500005−5−5+5−5−55+5−1+5−1−50000000000000000000000000000000000000000000000000000000000000000000000000000
χ10816-16000−4+45−4−454−454+45-4004−454500000001−51+50000−5+55−55+5−5−5−1+5−1−50000000000000000000000000000000000000000000000000000000000000000000000000000
χ10916-16000−4−45−4+454+454−45-400445−4500000001+51−50000−5−55+55−5−5+5−1−5−1+50000000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000−4−45−4+454+454−45-4004−454500000001+51−500005+5−5−5−5+55−5−1−5−1+50000000000000000000000000000000000000000000000000000000000000000000000000000

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