Finite Group Databasebeta

← Group #13104315

Character table — Group #13104315

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11244444444444444444888888888888888820202020202040404040404040404040404040404040405050100200200
order12245555101010101010101020202020510101010102020202020202020202022444441010101020202020202020202020202044488
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-11111-1-1-1-11111-1-1-1-1111-1-1
χ3111111111111111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-111-111-1-1111111-1-1-1-1-1-111-11-1
χ6111-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1111-1-1-1-1-1-111-1-1111111-1-11
χ7111-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1111111-1-111-1-1-1-111-1-11
χ8111-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-111-1-1-1-1-1-111111111-11-1
χ922222222222222222222222222222222222200000000000000000000000-2-2-200
χ10222-2222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-200000000000000000000000-2-2200
χ1122-202222-2-2-2-2222200002-2-2-2-220000000000020-20000022000000-2-200002-2000
χ1222-202222-2-2-2-2222200002-2-2-2-2200000000000-20200000-2-20000002200002-2000
χ1322-202222-2-2-2-2222200002-2-2-2-22000000000020-2000022000000-2-2000000-22000
χ1422-202222-2-2-2-2222200002-2-2-2-220000000000-2020000-2-200000022000000-22000
χ154444−1+5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1−53−523+523−523−523+523+52-13−523+52-1-1-1−1+5−1+53−523+52−1−5−1−5-1-1-1-12222000−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−52000000000
χ164444−1+5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1−53−523+523−523−523+523+52-13−523+52-1-1-1−1+5−1+53−523+52−1−5−1−5-1-1-1-1-2-2-2-20001−521+521−521+5200001−521+521−521+52000000000
χ1744443−523+52−1−5−1+53−523+523−523+523−523+52−1−5−1+5−1−5−1−5−1+5−1+5-1−1−5−1+5-1-1-13−523−52−1−5−1+53+523+52-1-1-1-100002220000−1+52−1+52−1−52−1−520000−1+52−1+52−1−52−1−5200000
χ1844443−523+52−1−5−1+53−523+523−523+523−523+52−1−5−1+5−1−5−1−5−1+5−1+5-1−1−5−1+5-1-1-13−523−52−1−5−1+53+523+52-1-1-1-10000-2-2-200001−521−521+521+5200001−521−521+521+5200000
χ1944443+523−52−1+5−1−53+523−523+523−523+523−52−1+5−1−5−1+5−1+5−1−5−1−5-1−1+5−1−5-1-1-13+523+52−1+5−1−53−523−52-1-1-1-100002220000−1−52−1−52−1+52−1+520000−1−52−1−52−1+52−1+5200000
χ2044443+523−52−1+5−1−53+523−523+523−523+523−52−1+5−1−5−1+5−1+5−1−5−1−5-1−1+5−1−5-1-1-13+523+52−1+5−1−53−523−52-1-1-1-10000-2-2-200001+521+521−521−5200001+521+521−521−5200000
χ214444−1−5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1+53+523−523+523+523−523−52-13+523−52-1-1-1−1−5−1−53+523−52−1+5−1+5-1-1-1-12222000−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+52000000000
χ224444−1−5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1+53+523−523+523+523−523−52-13+523−52-1-1-1−1−5−1−53+523−52−1+5−1+5-1-1-1-1-2-2-2-20001+521−521+521−5200001+521−521+521−52000000000
χ23444-4−1+5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1−53−523+52−3+52−3+52−3−52−3−52-13−523+52-1-1-11−51−5−3+52−3−521+51+511112-22-2000−1+52−1−521−521+520000−1+52−1−521−521+52000000000
χ24444-4−1+5−1−53−523+52−1+5−1−5−1+5−1−5−1+5−1−53−523+52−3+52−3+52−3−52−3−52-13−523+52-1-1-11−51−5−3+52−3−521+51+51111-22-220001−521+52−1+52−1−5200001−521+52−1+52−1−52000000000
χ25444-43−523+52−1−5−1+53−523+523−523+523−523+52−1−5−1+51+51+51−51−5-1−1−5−1+5-1-1-1−3+52−3+521+51−5−3−52−3−521111000022-20000−1+52−1+52−1−52−1−5200001−521−521+521+5200000
χ26444-43−523+52−1−5−1+53−523+523−523+523−523+52−1−5−1+51+51+51−51−5-1−1−5−1+5-1-1-1−3+52−3+521+51−5−3−52−3−5211110000-2-2200001−521−521+521+520000−1+52−1+52−1−52−1−5200000
χ27444-43+523−52−1+5−1−53+523−523+523−523+523−52−1+5−1−51−51−51+51+5-1−1+5−1−5-1-1-1−3−52−3−521−51+5−3+52−3+521111000022-20000−1−52−1−52−1+52−1+5200001+521+521−521−5200000
χ28444-43+523−52−1+5−1−53+523−523+523−523+523−52−1+5−1−51−51−51+51+5-1−1+5−1−5-1-1-1−3−52−3−521−51+5−3+52−3+5211110000-2-2200001+521+521−521−520000−1−52−1−52−1+52−1+5200000
χ29444-4−1−5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1+53+523−52−3−52−3−52−3+52−3+52-13+523−52-1-1-11+51+5−3−52−3+521−51−511112-22-2000−1−52−1+521+521−520000−1−52−1+521+521−52000000000
χ30444-4−1−5−1+53+523−52−1−5−1+5−1−5−1+5−1−5−1+53+523−52−3−52−3−52−3+52−3+52-13+523−52-1-1-11+51+5−3−52−3+521−51−51111-22-220001+521−52−1−52−1+5200001+521−52−1−52−1+52000000000
χ3144-40−1+5−1−53−523+521−51+51−51+5−1+5−1−53−523+525+525+525−525−52-1−3+52−3−5211-100−5−52−5+520055−5−522-2-2000−1+52−1−52−1+52−1−5200001−521+521−521+52000000000
χ3244-40−1+5−1−53−523+521−51+51−51+5−1+5−1−53−523+525+525+525−525−52-1−3+52−3−5211-100−5−52−5+520055−5−5-2-2220001−521+521−521+520000−1+52−1−52−1+52−1−52000000000
χ3344-40−1+5−1−53−523+521−51+51−51+5−1+5−1−53−523+52−5−52−5−52−5+52−5+52-1−3+52−3−5211-1005+525−5200−5−5552-2-22000−1+52−1−521−521+5200001−521+52−1+52−1−52000000000
χ3444-40−1+5−1−53−523+521−51+51−51+5−1+5−1−53−523+52−5−52−5−52−5+52−5+52-1−3+52−3−5211-1005+525−5200−5−555-222-20001−521+52−1+52−1−520000−1+52−1−521−521+52000000000
χ3544-40−1−5−1+53+523−521+51−51+51−5−1−5−1+53+523−525−525−525+525+52-1−3−52−3+5211-100−5+52−5−5200−5−55522-2-2000−1−52−1+52−1−52−1+5200001+521−521+521−52000000000
χ3644-40−1−5−1+53+523−521+51−51+51−5−1−5−1+53+523−525−525−525+525+52-1−3−52−3+5211-100−5+52−5−5200−5−555-2-2220001+521−521+521−520000−1−52−1+52−1−52−1+52000000000
χ3744-40−1−5−1+53+523−521+51−51+51−5−1−5−1+53+523−52−5+52−5+52−5−52−5−52-1−3−52−3+5211-1005−525+520055−5−52-2-22000−1−52−1+521+521−5200001+521−52−1−52−1+52000000000
χ3844-40−1−5−1+53+523−521+51−51+51−5−1−5−1+53+523−52−5+52−5+52−5−52−5−52-1−3−52−3+5211-1005−525+520055−5−5-222-20001+521−52−1−52−1+520000−1−52−1+521+521−52000000000
χ394-40044440000-4-4-4-4000040000-4000000000000002-2000002-22-20000000000000
χ404-40044440000-4-4-4-4000040000-400000000000000-2200000-22-220000000000000
χ414-4003−523+52−1−5−1+55+525−52−5−52−5+52−3+52−3−521+51−52ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19-1005−51ζ3−ζ7−ζ3+ζ700−ζ11+ζ19ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ1900002-200000−1+521−52−1−521+520000−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000
χ424-4003−523+52−1−5−1+55+525−52−5−52−5+52−3+52−3−521+51−52ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19-1005−51ζ3−ζ7−ζ3+ζ700−ζ11+ζ19ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000-22000001−52−1+521+52−1−520000ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000
χ434-4003−523+52−1−5−1+55+525−52−5−52−5+52−3+52−3−521+51−5−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19-1005−51−ζ3+ζ7ζ3−ζ700ζ11−ζ19−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ1900002-200000−1+521−52−1−521+520000ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000
χ444-4003−523+52−1−5−1+55+525−52−5−52−5+52−3+52−3−521+51−5−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19-1005−51−ζ3+ζ7ζ3−ζ700ζ11−ζ19−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000-22000001−52−1+521+52−1−520000−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000
χ454-4003+523−52−1+5−1−55−525+52−5+52−5−52−3−52−3+521−51+5−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7-100−551−ζ11+ζ19ζ11−ζ1900−ζ3+ζ7ζ3−ζ7−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ1900002-200000−1−521+52−1+521−520000−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000
χ464-4003+523−52−1+5−1−55−525+52−5+52−5−52−3−52−3+521−51+5−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7-100−551−ζ11+ζ19ζ11−ζ1900−ζ3+ζ7ζ3−ζ7−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000-22000001+52−1−521−52−1+520000ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000
χ474-4003+523−52−1+5−1−55−525+52−5+52−5−52−3−52−3+521−51+52ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7-100−551ζ11−ζ19−ζ11+ζ1900ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ1900002-200000−1−521+52−1+521−520000ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000
χ484-4003+523−52−1+5−1−55−525+52−5+52−5−52−3−52−3+521−51+52ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7-100−551ζ11−ζ19−ζ11+ζ1900ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000-22000001+52−1−521−52−1+520000−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000
χ498888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-2-2333-2-2-2-2-2-233330000000000000000000000000000
χ50888-8-2-2-2-2-2-2-2-2-2-2-2-222223-2-2333222222-3-3-3-30000000000000000000000000000
χ5188-80-2-2-2-22222-2-2-2-22525−25−25322-3-3300−252500−5−5550000000000000000000000000000
χ5288-80-2-2-2-22222-2-2-2-2−25−252525322-3-330025−250055−5−50000000000000000000000000000
χ5388-803−53+5−2−25−2+25−3+5−3−5−3+5−3−53−53+5−2−25−2+250000-22+252−2522-200000000000000000000000000000000000000
χ5488-803+53−5−2+25−2−25−3−5−3+5−3−5−3+53+53−5−2+25−2−250000-22−252+2522-200000000000000000000000000000000000000
χ558-800-2-2-2-225−25−25252222−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19300−55-32ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ190000000000000000000000000000
χ568-800-2-2-2-225−25−252522222ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ19300−55-3−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ190000000000000000000000000000
χ578-800-2-2-2-2−252525−2522222ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ193005−5-32ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ7ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ190000000000000000000000000000
χ588-800-2-2-2-2−252525−252222−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ193005−5-3−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ7−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ190000000000000000000000000000
χ598-800−2+25−2−253−53+500002−252+25−3+5−3−52ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ19-200002−2ζ11+2ζ192ζ11−2ζ1900−2ζ3+2ζ72ζ3−2ζ72ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000
χ608-800−2+25−2−253−53+500002−252+25−3+5−3−5−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19-2000022ζ11−2ζ19−2ζ11+2ζ19002ζ3−2ζ7−2ζ3+2ζ7−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000
χ618-8003−53+5−2−25−2+25−5−5−5+55+55−5−3+5−3−52+252−250000-200−2525200000000000000000000000000000000000000
χ628-8003+53−5−2+25−2−25−5+5−5−55−55+5−3−5−3+52−252+250000-20025−25200000000000000000000000000000000000000
χ638-800−2−25−2+253+53−500002+252−25−3−5−3+5−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7-200002−2ζ3+2ζ72ζ3−2ζ7002ζ11−2ζ19−2ζ11+2ζ19−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000
χ648-800−2−25−2+253+53−500002+252−25−3−5−3+52ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ7-2000022ζ3−2ζ7−2ζ3+2ζ700−2ζ11+2ζ192ζ11−2ζ192ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000

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