Finite Group Databasebeta

← Group #13107681

Character table — Group #13107681

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222444444448888888888888810101010161616202020202020202020202020202025254040404040404040404040405050505050100100100
order12224555510101010510101010101010101020202020444410102022444420202020202020202210101010202020202020202022444444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11111-111-1-11111-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-1
χ3111111111111111111111111111-1-111111-11-1-111-1-1-1-1111111-1-111-1-1-1-11111111-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111-1-11111111111111-1-1-1-11-1-1-1-111111-1-1-1-11-11-11111111111-1-1-1-111-1-111-1-11-1-111-11-1
χ6111-1-11111111111111-1-1-1-11-1-1-1-111-1-11-1-1-111-1-111111-1-1-1-111-1-11111-1-1-1-1111-1-1-1-11-11
χ7111-1-11111111111111-1-1-1-11-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-111111111-1-1-1-11111-1-11-1-1-1-11-11
χ8111-1-11111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-111-11-11-1-1-1-1-1-1-1-1111111-1-111-1-1111-1-111-11-1
χ911-11-1111111111-1-1-1-111111-1-1-1-11111-11-1-1-1-11-111111111111-1-1-1-1-1-111-1-111-11-111-1-11
χ1011-11-1111111111-1-1-1-111111-1-1-1-111-1-1-11-1-11-111-11111-1-1-1-111-1-111-1-11111-1-1-11-1-1-111-1
χ1111-11-1111111111-1-1-1-111111-1-1-1-1-1-111-11-11-11-1-11-1-1-1-111111111-1-111-1-1-1-111-11-1-1-111-1
χ1211-11-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11-1111-11-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-111-1-11
χ1311-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1411-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111
χ1511-1-11111111111-1-1-1-1-1-1-1-111111-1-111-1-11-1111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-11-1-1-111
χ1611-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ17222222222222222222222222222000022200000000000000-2-2000000000000-2-2-200000
χ18222-2-22222222222222-2-2-2-22-2-2-2-200002-2-200000000000000-2-2000000000000-22200000
χ1922-22-2222222222-2-2-2-222222-2-2-2-20000-22-200000000000000-2-20000000000002-2200000
χ2022-2-22222222222-2-2-2-2-2-2-2-2222220000-2-2200000000000000-2-200000000000022-200000
χ212-20002222-2-2-2-2200000000-200002i−2i2i−2i0000000002i2i−2i−2i2i2i−2i−2i-220000000000000002-2000
χ222-20002222-2-2-2-2200000000-200002i−2i−2i2i0000000002i2i−2i−2i−2i−2i2i2i-22000000000000000-22000
χ232-20002222-2-2-2-2200000000-20000−2i2i2i−2i000000000−2i−2i2i2i2i2i−2i−2i-22000000000000000-22000
χ242-20002222-2-2-2-2200000000-20000−2i2i−2i2i000000000−2i−2i2i2i−2i−2i2i2i-220000000000000002-2000
χ2544444−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−50022-1-1-10200220000−1+52−1−52−1+52−1−520000−1+52−1−520000−1+52−1−52−1+52−1−5200000000
χ2644444−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−500-2-2-1-1-10-200-2-200001−521+521−521+5200001−521+5200001−521+521−521+5200000000
χ27444443−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+522200-1-1-1202200−1+52−1−52−1+52−1−52000000−1+52−1−5200−1+52−1−52−1+52−1−52000000000000
χ28444443−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+52-2-200-1-1-1-20-2-2001−521+521−521+520000001−521+52001−521+521−521+52000000000000
χ29444443+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−522200-1-1-1202200−1−52−1+52−1−52−1+52000000−1−52−1+5200−1−52−1+52−1−52−1+52000000000000
χ30444443+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−52-2-200-1-1-1-20-2-2001+521−521+521−520000001+521−52001+521−521+521−52000000000000
χ3144444−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+50022-1-1-10200220000−1−52−1+52−1−52−1+520000−1−52−1+520000−1−52−1+52−1−52−1+5200000000
χ3244444−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+500-2-2-1-1-10-200-2-200001+521−521+521−5200001+521−5200001+521−521+521−5200000000
χ33444-4-4−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−51−5−3+52−3−521+5-11−5−3+52−3−521+50022-1110-2002-20000−1+52−1−52−1+52−1−5200001−521+520000−1+52−1−521−521+5200000000
χ34444-4-4−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−51−5−3+52−3−521+5-11−5−3+52−3−521+500-2-2-1110200-2200001−521+521−521+520000−1+52−1−5200001−521+52−1+52−1−5200000000
χ35444-4-43−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+52−3+521+51−5−3−52-1−3+521+51−5−3−522200-111-202-200−1+52−1−52−1+52−1−520000001−521+5200−1+52−1−521−521+52000000000000
χ36444-4-43−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+52−3+521+51−5−3−52-1−3+521+51−5−3−52-2-200-11120-22001−521+521−521+52000000−1+52−1−52001−521+52−1+52−1−52000000000000
χ37444-4-43+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−52−3−521−51+5−3+52-1−3−521−51+5−3+522200-111-202-200−1−52−1+52−1−52−1+520000001+521−5200−1−52−1+521+521−52000000000000
χ38444-4-43+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−52−3−521−51+5−3+52-1−3−521−51+5−3+52-2-200-11120-22001+521−521+521−52000000−1−52−1+52001+521−52−1−52−1+52000000000000
χ39444-4-4−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+51+5−3−52−3+521−5-11+5−3−52−3+521−50022-1110-2002-20000−1−52−1+52−1−52−1+5200001+521−520000−1−52−1+521+521−5200000000
χ40444-4-4−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+51+5−3−52−3+521−5-11+5−3−52−3+521−500-2-2-1110200-2200001+521−521+521−520000−1−52−1+5200001+521−52−1−52−1+5200000000
χ4144-44-4−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+5−1+53−523+52−1−5-11−5−3+52−3−521+500221-110-200-220000−1+52−1−52−1+52−1−5200001−521+5200001−521+52−1+52−1−5200000000
χ4244-44-4−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+5−1+53−523+52−1−5-11−5−3+52−3−521+500-2-21-1102002-200001−521+521−521+520000−1+52−1−520000−1+52−1−521−521+5200000000
χ4344-44-43−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−523−52−1−5−1+53+52-1−3+521+51−5−3−5222001-11-20-2200−1+52−1−52−1+52−1−520000001−521+52001−521+52−1+52−1−52000000000000
χ4444-44-43−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−523−52−1−5−1+53+52-1−3+521+51−5−3−52-2-2001-11202-2001−521+521−521+52000000−1+52−1−5200−1+52−1−521−521+52000000000000
χ4544-44-43+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+523+52−1+5−1−53−52-1−3−521−51+5−3+5222001-11-20-2200−1−52−1+52−1−52−1+520000001+521−52001+521−52−1−52−1+52000000000000
χ4644-44-43+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+523+52−1+5−1−53−52-1−3−521−51+5−3+52-2-2001-11202-2001+521−521+521−52000000−1−52−1+5200−1−52−1+521+521−52000000000000
χ4744-44-4−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−5−1−53+523−52−1+5-11+5−3−52−3+521−500221-110-200-220000−1−52−1+52−1−52−1+5200001+521−5200001+521−52−1−52−1+5200000000
χ4844-44-4−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−5−1−53+523−52−1+5-11+5−3−52−3+521−500-2-21-1102002-200001+521−521+521−520000−1−52−1+520000−1−52−1+521+521−5200000000
χ4944-4-44−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+51−5−3+52−3−521+5-1−1+53−523+52−1−5002211-10200-2-20000−1+52−1−52−1+52−1−520000−1+52−1−5200001−521+521−521+5200000000
χ5044-4-44−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+51−5−3+52−3−521+5-1−1+53−523+52−1−500-2-211-10-2002200001−521+521−521+5200001−521+520000−1+52−1−52−1+52−1−5200000000
χ5144-4-443−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−52−3+521+51−5−3−52-13−52−1−5−1+53+52220011-120-2-200−1+52−1−52−1+52−1−52000000−1+52−1−52001−521+521−521+52000000000000
χ5244-4-443−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−52−3+521+51−5−3−52-13−52−1−5−1+53+52-2-20011-1-2022001−521+521−521+520000001−521+5200−1+52−1−52−1+52−1−52000000000000
χ5344-4-443+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+52−3−521−51+5−3+52-13+52−1+5−1−53−52220011-120-2-200−1−52−1+52−1−52−1+52000000−1−52−1+52001+521−521+521−52000000000000
χ5444-4-443+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+52−3−521−51+5−3+52-13+52−1+5−1−53−52-2-20011-1-2022001+521−521+521−520000001+521−5200−1−52−1+52−1−52−1+52000000000000
χ5544-4-44−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−51+5−3−52−3+521−5-1−1−53+523−52−1+5002211-10200-2-20000−1−52−1+52−1−52−1+520000−1−52−1+5200001+521−521+521−5200000000
χ5644-4-44−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−51+5−3−52−3+521−5-1−1−53+523−52−1+500-2-211-10-2002200001+521−521+521−5200001+521−520000−1−52−1+52−1−52−1+5200000000
χ574-40004444-4-4-4-4400000000-400000000000000000000000004-400000000000000000000
χ5888888-2-2-2-2-2-2-2-23-2-2-2-2-2-2-2-23-2-2-2-20000333000000000000000000000000000000000000
χ59888-8-8-2-2-2-2-2-2-2-23-2-2-2-222223222200003-3-3000000000000000000000000000000000000
χ6088-88-8-2-2-2-2-2-2-2-232222-2-2-2-2322220000-33-3000000000000000000000000000000000000
χ6188-8-88-2-2-2-2-2-2-2-23222222223-2-2-2-20000-3-33000000000000000000000000000000000000
χ628-8000−2+253−53+5−2−252−25−3+5−3−52+25-20000000020000004i−4i0000000000000−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ70000000000000000000000
χ638-8000−2+253−53+5−2−252−25−3+5−3−52+25-2000000002000000−4i4i00000000000002ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ70000000000000000000000
χ648-80003−5−2−25−2+253+5−3+52+252−25−3−5-200000000200004i−4i00000000000−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ700000000000000000000000000
χ658-80003−5−2−25−2+253+5−3+52+252−25−3−5-20000000020000−4i4i000000000002ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ700000000000000000000000000
χ668-80003+5−2+25−2−253−5−3−52−252+25−3+5-200000000200004i−4i00000000000−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ1900000000000000000000000000
χ678-80003+5−2+25−2−253−5−3−52−252+25−3+5-20000000020000−4i4i000000000002ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ1900000000000000000000000000
χ688-8000−2−253+53−5−2+252+25−3−5−3+52−25-20000000020000004i−4i0000000000000−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ190000000000000000000000
χ698-8000−2−253+53−5−2+252+25−3−5−3+52−25-2000000002000000−4i4i00000000000002ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ190000000000000000000000
χ7016-16000-4-4-4-44444600000000-600000000000000000000000000000000000000000000000

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