Finite Group Databasebeta

← Group #13107686

Character table — Group #13107686

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222444444448888888888888810101010161616202020202020202020202020202025254040404040404040404040405050505050100100100
order12444555510101010510202020202020202020202020224420202022244410101010202020202210101010101020202020202044444444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1111-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1-1
χ3111111111111111111111111111-1-111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-1-1
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
χ5111-1-1111111111111-1-1-1-111-1-1-1-111111-1-11-1-11-1-1111111111111-1-1-1-111-1-1-1-11-1-1111-1-1
χ6111-1-1111111111111-1-1-1-111-1-1-1-111-1-11-1-1-1111-1-11111-1-1-1-111-1-1111111-1-1-1-11-1-1-1-1-111
χ7111-1-1111111111111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1-111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-111
χ8111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-111-1-1-1-1-1-1-1-111-1-11111-1-111111-1-1111-1-1
χ911-11-11111111111-1-111-1-1-1-111-1-11111-11-1-11-1-11-11111111111-1-111-1-1-1-111-1-1-11-111-11-1
χ1011-11-11111111111-1-111-1-1-1-111-1-111-1-1-11-11-11-11-11111-1-1-1-11111-1-111-1-111-1-1-11-1-1-11-11
χ1111-11-11111111111-1-111-1-1-1-111-1-1-1-111-11-1-11-11-11-1-1-1-1111111-1-111-1-111-1-111-11-1-1-11-11
χ1211-11-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-11-11-111-11-1-1-1-1-1-1-1-11111-1-11111-1-111-11-111-11-1
χ1311-1-111111111111-1-1-1-111-1-1-1-1111111-1-11-1-11-1-111111111111-1-1-1-111-1-1-1-111-1-1111-1-11
χ1411-1-111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111111-1-1-1-1111111-1-1-1-1-1-111-1-11-1-111-1
χ1511-1-111111111111-1-1-1-111-1-1-1-111-1-111-1-11-1-1111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-111-1
χ1611-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-11
χ17222222222222222222222222222000022200000000000000-2-2000000000000-2-2-200000
χ18222-2-2222222222222-2-2-2-222-2-2-2-200002-2-200000000000000-2-2000000000000-22200000
χ1922-22-22222222222-2-222-2-2-2-222-2-20000-22-200000000000000-2-20000000000002-2200000
χ2022-2-222222222222-2-2-2-222-2-2-2-2220000-2-2200000000000000-2-200000000000022-200000
χ212-20002222-2-2-2-22-20000000000002-22i−2i00000000022-2-22i2i−2i−2i-220000000000000002i−2i000
χ222-20002222-2-2-2-22-20000000000002-2−2i2i00000000022-2-2−2i−2i2i2i-22000000000000000−2i2i000
χ232-20002222-2-2-2-22-2000000000000-222i−2i000000000-2-2222i2i−2i−2i-22000000000000000−2i2i000
χ242-20002222-2-2-2-22-2000000000000-22−2i2i000000000-2-222−2i−2i2i2i-220000000000000002i−2i000
χ2544444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+523−523+523−523+52−1+5−1−5−1+5−1−5−1+5−1−50022-1-1-12220000000−1+52−1−52−1+52−1−5200−1+52−1−52−1+52−1−52−1+52−1−5200000000000000
χ2644444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+523−523+523−523+52−1+5−1−5−1+5−1−5−1+5−1−500-2-2-1-1-1-2-2-200000001−521+521−521+52001−521+521−521+521−521+5200000000000000
χ27444443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+5−1−5−1+5−1−5−1+53−523+523−523+523−523+522200-1-1-1000222−1+52−1−52−1+52−1−52000000000000−1+52−1−52−1+52−1−52−1+52−1−5200000000
χ28444443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+5−1−5−1+5−1−5−1+53−523+523−523+523−523+52-2-200-1-1-1000-2-2-21−521+521−521+520000000000001−521+521−521+521−521+5200000000
χ29444443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−5−1+5−1−5−1+5−1−53+523−523+523−523+523−522200-1-1-1000222−1−52−1+52−1−52−1+52000000000000−1−52−1+52−1−52−1+52−1−52−1+5200000000
χ30444443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−5−1+5−1−5−1+5−1−53+523−523+523−523+523−52-2-200-1-1-1000-2-2-21+521−521+521−520000000000001+521−521+521−521+521−5200000000
χ3144444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−523+523−523+523−52−1−5−1+5−1−5−1+5−1−5−1+50022-1-1-12220000000−1−52−1+52−1−52−1+5200−1−52−1+52−1−52−1+52−1−52−1+5200000000000000
χ3244444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−523+523−523+523−52−1−5−1+5−1−5−1+5−1−5−1+500-2-2-1-1-1-2-2-200000001+521−521+521−52001+521−521+521−521+521−5200000000000000
χ33444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−3+52−3−52−3+52−3−52−1+5−1−51−51+51−51+50022-1112-2-20000000−1+52−1−52−1+52−1−5200−1+52−1−521−521+521−521+5200000000000000
χ34444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−3+52−3−52−3+52−3−52−1+5−1−51−51+51−51+500-2-2-111-22200000001−521+521−521+52001−521+52−1+52−1−52−1+52−1−5200000000000000
χ35444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+51+51−51+51−53−523+52−3+52−3−52−3+52−3−522200-1110002-2-2−1+52−1−52−1+52−1−52000000000000−1+52−1−521−521+521−521+5200000000
χ36444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+51+51−51+51−53−523+52−3+52−3−52−3+52−3−52-2-200-111000-2221−521+521−521+520000000000001−521+52−1+52−1−52−1+52−1−5200000000
χ37444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−51−51+51−51+53+523−52−3−52−3+52−3−52−3+522200-1110002-2-2−1−52−1+52−1−52−1+52000000000000−1−52−1+521+521−521+521−5200000000
χ38444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−51−51+51−51+53+523−52−3−52−3+52−3−52−3+52-2-200-111000-2221+521−521+521−520000000000001+521−52−1−52−1+52−1−52−1+5200000000
χ39444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−3−52−3+52−3−52−3+52−1−5−1+51+51−51+51−50022-1112-2-20000000−1−52−1+52−1−52−1+5200−1−52−1+521+521−521+521−5200000000000000
χ40444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−3−52−3+52−3−52−3+52−1−5−1+51+51−51+51−500-2-2-111-22200000001+521−521+521−52001+521−52−1−52−1+52−1−52−1+5200000000000000
χ4144-44-4−1+5−1−53−523+523−523+52−1+5−1−5-1-1−3+52−3−523−523+52−3+52−3−521−51+5−1+5−1−51−51+500221-11-22-20000000−1+52−1−52−1+52−1−52001−521+52−1+52−1−521−521+5200000000000000
χ4244-44-4−1+5−1−53−523+523−523+52−1+5−1−5-1-1−3+52−3−523−523+52−3+52−3−521−51+5−1+5−1−51−51+500-2-21-112-2200000001−521+521−521+5200−1+52−1−521−521+52−1+52−1−5200000000000000
χ4344-44-43−523+52−1−5−1+5−1−5−1+53−523+52-1-11+51−5−1−5−1+51+51−5−3+52−3−523−523+52−3+52−3−5222001-11000-22-2−1+52−1−52−1+52−1−520000000000001−521+52−1+52−1−521−521+5200000000
χ4444-44-43−523+52−1−5−1+5−1−5−1+53−523+52-1-11+51−5−1−5−1+51+51−5−3+52−3−523−523+52−3+52−3−52-2-2001-110002-221−521+521−521+52000000000000−1+52−1−521−521+52−1+52−1−5200000000
χ4544-44-43+523−52−1+5−1−5−1+5−1−53+523−52-1-11−51+5−1+5−1−51−51+5−3−52−3+523+523−52−3−52−3+5222001-11000-22-2−1−52−1+52−1−52−1+520000000000001+521−52−1−52−1+521+521−5200000000
χ4644-44-43+523−52−1+5−1−5−1+5−1−53+523−52-1-11−51+5−1+5−1−51−51+5−3−52−3+523+523−52−3−52−3+52-2-2001-110002-221+521−521+521−52000000000000−1−52−1+521+521−52−1−52−1+5200000000
χ4744-44-4−1−5−1+53+523−523+523−52−1−5−1+5-1-1−3−52−3+523+523−52−3−52−3+521+51−5−1−5−1+51+51−500221-11-22-20000000−1−52−1+52−1−52−1+52001+521−52−1−52−1+521+521−5200000000000000
χ4844-44-4−1−5−1+53+523−523+523−52−1−5−1+5-1-1−3−52−3+523+523−52−3−52−3+521+51−5−1−5−1+51+51−500-2-21-112-2200000001+521−521+521−5200−1−52−1+521+521−52−1−52−1+5200000000000000
χ4944-4-44−1+5−1−53−523+523−523+52−1+5−1−5-1-1−3+52−3−52−3+52−3−523−523+521−51+51−51+5−1+5−1−5002211-1-2-220000000−1+52−1−52−1+52−1−52001−521+521−521+52−1+52−1−5200000000000000
χ5044-4-44−1+5−1−53−523+523−523+52−1+5−1−5-1-1−3+52−3−52−3+52−3−523−523+521−51+51−51+5−1+5−1−500-2-211-122-200000001−521+521−521+5200−1+52−1−52−1+52−1−521−521+5200000000000000
χ5144-4-443−523+52−1−5−1+5−1−5−1+53−523+52-1-11+51−51+51−5−1−5−1+5−3+52−3−52−3+52−3−523−523+52220011-1000-2-22−1+52−1−52−1+52−1−520000000000001−521+521−521+52−1+52−1−5200000000
χ5244-4-443−523+52−1−5−1+5−1−5−1+53−523+52-1-11+51−51+51−5−1−5−1+5−3+52−3−52−3+52−3−523−523+52-2-20011-100022-21−521+521−521+52000000000000−1+52−1−52−1+52−1−521−521+5200000000
χ5344-4-443+523−52−1+5−1−5−1+5−1−53+523−52-1-11−51+51−51+5−1+5−1−5−3−52−3+52−3−52−3+523+523−52220011-1000-2-22−1−52−1+52−1−52−1+520000000000001+521−521+521−52−1−52−1+5200000000
χ5444-4-443+523−52−1+5−1−5−1+5−1−53+523−52-1-11−51+51−51+5−1+5−1−5−3−52−3+52−3−52−3+523+523−52-2-20011-100022-21+521−521+521−52000000000000−1−52−1+52−1−52−1+521+521−5200000000
χ5544-4-44−1−5−1+53+523−523+523−52−1−5−1+5-1-1−3−52−3+52−3−52−3+523+523−521+51−51+51−5−1−5−1+5002211-1-2-220000000−1−52−1+52−1−52−1+52001+521−521+521−52−1−52−1+5200000000000000
χ5644-4-44−1−5−1+53+523−523+523−52−1−5−1+5-1-1−3−52−3+52−3−52−3+523+523−521+51−51+51−5−1−5−1+500-2-211-122-200000001+521−521+521−5200−1−52−1+52−1−52−1+521+521−5200000000000000
χ574-40004444-4-4-4-44-40000000000000000000000000000000004-400000000000000000000
χ5888888-2-2-2-2-2-2-2-233-2-2-2-2-2-2-2-2-2-2-2-20000333000000000000000000000000000000000000
χ59888-8-8-2-2-2-2-2-2-2-233-2-22222-2-2222200003-3-3000000000000000000000000000000000000
χ6088-88-8-2-2-2-2-2-2-2-23322-2-22222-2-2220000-33-3000000000000000000000000000000000000
χ6188-8-88-2-2-2-2-2-2-2-2332222-2-22222-2-20000-3-33000000000000000000000000000000000000
χ628-8000−2+25−2−253−53+5−3+5−3−52−252+25-22000000000000004i−4i0000000000000−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ70000000000000000000000
χ638-8000−2+25−2−253−53+5−3+5−3−52−252+25-2200000000000000−4i4i00000000000002ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ70000000000000000000000
χ648-80003−53+5−2−25−2+252+252−25−3+5−3−5-220000000000004-400000000000−1+5−1−51−51+500000000000000000000000000
χ658-80003−53+5−2−25−2+252+252−25−3+5−3−5-22000000000000-44000000000001−51+5−1+5−1−500000000000000000000000000
χ668-80003+53−5−2+25−2−252−252+25−3−5−3+5-220000000000004-400000000000−1−5−1+51+51−500000000000000000000000000
χ678-80003+53−5−2+25−2−252−252+25−3−5−3+5-22000000000000-44000000000001+51−5−1−5−1+500000000000000000000000000
χ688-8000−2−25−2+253+53−5−3−5−3+52+252−25-22000000000000004i−4i0000000000000−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ190000000000000000000000
χ698-8000−2−25−2+253+53−5−3−5−3+52+252−25-2200000000000000−4i4i00000000000002ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ190000000000000000000000
χ7016-16000-4-4-4-444446-60000000000000000000000000000000000000000000000000000000

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