Finite Group Databasebeta

← Group #13107676

Character table — Group #13107676

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size11222444444448888888888888816161620202020202020202020202020202020404040404040404040404040505050505050100100100
order12224555510101010510101010101010101020202020101020222244441010101020202020101010101010202020202020244488888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111-1-1-11-1111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111
χ5111-1-111111111111-1-111-1-11-1-1-1-11-1-111-11-11-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11-1-111-1
χ6111-1-111111111111-1-111-1-11-1-1-1-11-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-111-11-1111-1-11
χ7111-1-111111111111-1-111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-11-1111-1-11
χ8111-1-111111111111-1-111-1-11-1-1-1-11-1-1-1-11-11-111-1-1-1-11111-1-1-1-11111-1-111-11-11-1-111-1
χ911-11-1111111111-1-111-1-1111-1-1-1-1-11-11-111-1-11-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-11-11
χ1011-11-1111111111-1-111-1-1111-1-1-1-1-11-11-11-1-11-1111111111-1-1-1-111-1-111-1-1-1-11111-11-1
χ1111-11-1111111111-1-111-1-1111-1-1-1-1-11-1-11-111-11-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-11-1
χ1211-11-1111111111-1-111-1-1111-1-1-1-1-11-1-11-1-111-11-1-1-1-11111-1-111-1-11111-1-1-1-111-1-11-11
χ1311-1-11111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111111111111-1-1-1-111-1-1-1-11-1-11111-1-1
χ1411-1-11111111111-1-1-1-1-1-1-1-111111-1-111-1-1-1111-11111-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-111
χ1511-1-11111111111-1-1-1-1-1-1-1-111111-1-11-1111-1-1-11-1-1-1-11111111111-1-1-1-1-1-11-1-11-1-1-111
χ1611-1-11111111111-1-1-1-1-1-1-1-111111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11111-1-1
χ172222222222222222222222222222220000000000000000000000000000-2-2-2-200000
χ18222-2-222222222222-2-222-2-22-2-2-2-22-2-200000000000000000000000000002-22-200000
χ1922-22-2222222222-2-222-2-2222-2-2-2-2-22-2000000000000000000000000000022-2-200000
χ2022-2-22222222222-2-2-2-2-2-2-2-222222-2-220000000000000000000000000000-222-200000
χ2144444−1+5−1−53−523+523−523+52−1+5−1−5-1−1+5−1−5−1+5−1−53−523+523−523+52-13−523+52−1+5−1−5-1-1-122202000−1+52−1+52−1−52−1−52000000−1+52−1−52−1+52−1−52−1+52−1−520000000000000
χ2244444−1+5−1−53−523+523−523+52−1+5−1−5-1−1+5−1−5−1+5−1−53−523+523−523+52-13−523+52−1+5−1−5-1-1-1-2-2-20-20001−521−521+521+520000001−521+521−521+521−521+520000000000000
χ23444443−523+52−1−5−1+5−1−5−1+53−523+52-13−523+523−523+52−1−5−1+5−1−5−1+5-1−1−5−1+53−523+52-1-1-1000202220000−1+52−1+52−1−52−1−52−1+52−1−52000000−1+52−1−52−1+52−1−52000000000
χ24444443−523+52−1−5−1+5−1−5−1+53−523+52-13−523+523−523+52−1−5−1+5−1−5−1+5-1−1−5−1+53−523+52-1-1-1000-20-2-2-200001−521−521+521+521−521+520000001−521+521−521+52000000000
χ25444443+523−52−1+5−1−5−1+5−1−53+523−52-13+523−523+523−52−1+5−1−5−1+5−1−5-1−1+5−1−53+523−52-1-1-1000202220000−1−52−1−52−1+52−1+52−1−52−1+52000000−1−52−1+52−1−52−1+52000000000
χ26444443+523−52−1+5−1−5−1+5−1−53+523−52-13+523−523+523−52−1+5−1−5−1+5−1−5-1−1+5−1−53+523−52-1-1-1000-20-2-2-200001+521+521−521−521+521−520000001+521−521+521−52000000000
χ2744444−1−5−1+53+523−523+523−52−1−5−1+5-1−1−5−1+5−1−5−1+53+523−523+523−52-13+523−52−1−5−1+5-1-1-122202000−1−52−1−52−1+52−1+52000000−1−52−1+52−1−52−1+52−1−52−1+520000000000000
χ2844444−1−5−1+53+523−523+523−52−1−5−1+5-1−1−5−1+5−1−5−1+53+523−523+523−52-13+523−52−1−5−1+5-1-1-1-2-2-20-20001+521+521−521−520000001+521−521+521−521+521−520000000000000
χ29444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1−1+5−1−51−51+53−523+52−3+52−3−52-1−3+52−3−521−51+5-11122-20-2000−1+52−1+52−1−52−1−52000000−1+52−1−521−521+521−521+520000000000000
χ30444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1−1+5−1−51−51+53−523+52−3+52−3−52-1−3+52−3−521−51+5-111-2-22020001−521−521+521+520000001−521+52−1+52−1−52−1+52−1−520000000000000
χ31444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-13−523+52−3+52−3−52−1−5−1+51+51−5-11+51−5−3+52−3−52-111000202-2-200001−521−521+521+52−1+52−1−52000000−1+52−1−521−521+52000000000
χ32444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-13−523+52−3+52−3−52−1−5−1+51+51−5-11+51−5−3+52−3−52-111000-20-2220000−1+52−1+52−1−52−1−521−521+520000001−521+52−1+52−1−52000000000
χ33444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-13+523−52−3−52−3+52−1+5−1−51−51+5-11−51+5−3−52−3+52-111000202-2-200001+521+521−521−52−1−52−1+52000000−1−52−1+521+521−52000000000
χ34444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-13+523−52−3−52−3+52−1+5−1−51−51+5-11−51+5−3−52−3+52-111000-20-2220000−1−52−1−52−1+52−1+521+521−520000001+521−52−1−52−1+52000000000
χ35444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1−1−5−1+51+51−53+523−52−3−52−3+52-1−3−52−3+521+51−5-11122-20-2000−1−52−1−52−1+52−1+52000000−1−52−1+521+521−521+521−520000000000000
χ36444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1−1−5−1+51+51−53+523−52−3−52−3+52-1−3−52−3+521+51−5-111-2-22020001+521+521−521−520000001+521−52−1−52−1+52−1−52−1+520000000000000
χ3744-44-4−1+5−1−53−523+523−523+52−1+5−1−5-11−51+5−1+5−1−5−3+52−3−523−523+52-1−3+52−3−521−51+51-112-220-2000−1+52−1+52−1−52−1−520000001−521+52−1+52−1−521−521+520000000000000
χ3844-44-4−1+5−1−53−523+523−523+52−1+5−1−5-11−51+5−1+5−1−5−3+52−3−523−523+52-1−3+52−3−521−51+51-11-22-2020001−521−521+521+52000000−1+52−1−521−521+52−1+52−1−520000000000000
χ3944-44-43−523+52−1−5−1+5−1−5−1+53−523+52-1−3+52−3−523−523+521+51−5−1−5−1+5-11+51−5−3+52−3−521-1100020-22-200001−521−521+521+52−1+52−1−520000001−521+52−1+52−1−52000000000
χ4044-44-43−523+52−1−5−1+5−1−5−1+53−523+52-1−3+52−3−523−523+521+51−5−1−5−1+5-11+51−5−3+52−3−521-11000-202-220000−1+52−1+52−1−52−1−521−521+52000000−1+52−1−521−521+52000000000
χ4144-44-43+523−52−1+5−1−5−1+5−1−53+523−52-1−3−52−3+523+523−521−51+5−1+5−1−5-11−51+5−3−52−3+521-1100020-22-200001+521+521−521−52−1−52−1+520000001+521−52−1−52−1+52000000000
χ4244-44-43+523−52−1+5−1−5−1+5−1−53+523−52-1−3−52−3+523+523−521−51+5−1+5−1−5-11−51+5−3−52−3+521-11000-202-220000−1−52−1−52−1+52−1+521+521−52000000−1−52−1+521+521−52000000000
χ4344-44-4−1−5−1+53+523−523+523−52−1−5−1+5-11+51−5−1−5−1+5−3−52−3+523+523−52-1−3−52−3+521+51−51-112-220-2000−1−52−1−52−1+52−1+520000001+521−52−1−52−1+521+521−520000000000000
χ4444-44-4−1−5−1+53+523−523+523−52−1−5−1+5-11+51−5−1−5−1+5−3−52−3+523+523−52-1−3−52−3+521+51−51-11-22-2020001+521+521−521−52000000−1−52−1+521+521−52−1−52−1+520000000000000
χ4544-4-44−1+5−1−53−523+523−523+52−1+5−1−5-11−51+51−51+5−3+52−3−52−3+52−3−52-13−523+52−1+5−1−511-12-2-202000−1+52−1+52−1−52−1−520000001−521+521−521+52−1+52−1−520000000000000
χ4644-4-44−1+5−1−53−523+523−523+52−1+5−1−5-11−51+51−51+5−3+52−3−52−3+52−3−52-13−523+52−1+5−1−511-1-2220-20001−521−521+521+52000000−1+52−1−52−1+52−1−521−521+520000000000000
χ4744-4-443−523+52−1−5−1+5−1−5−1+53−523+52-1−3+52−3−52−3+52−3−521+51−51+51−5-1−1−5−1+53−523+5211-100020-2-220000−1+52−1+52−1−52−1−52−1+52−1−520000001−521+521−521+52000000000
χ4844-4-443−523+52−1−5−1+5−1−5−1+53−523+52-1−3+52−3−52−3+52−3−521+51−51+51−5-1−1−5−1+53−523+5211-1000-2022-200001−521−521+521+521−521+52000000−1+52−1−52−1+52−1−52000000000
χ4944-4-443+523−52−1+5−1−5−1+5−1−53+523−52-1−3−52−3+52−3−52−3+521−51+51−51+5-1−1+5−1−53+523−5211-100020-2-220000−1−52−1−52−1+52−1+52−1−52−1+520000001+521−521+521−52000000000
χ5044-4-443+523−52−1+5−1−5−1+5−1−53+523−52-1−3−52−3+52−3−52−3+521−51+51−51+5-1−1+5−1−53+523−5211-1000-2022-200001+521+521−521−521+521−52000000−1−52−1+52−1−52−1+52000000000
χ5144-4-44−1−5−1+53+523−523+523−52−1−5−1+5-11+51−51+51−5−3−52−3+52−3−52−3+52-13+523−52−1−5−1+511-12-2-202000−1−52−1−52−1+52−1+520000001+521−521+521−52−1−52−1+520000000000000
χ5244-4-44−1−5−1+53+523−523+523−52−1−5−1+5-11+51−51+51−5−3−52−3+52−3−52−3+52-13+523−52−1−5−1+511-1-2220-20001+521+521−521−52000000−1−52−1+52−1−52−1+521+521−520000000000000
χ534-40004444-4-4-4-4400000000-40000000000000000000000000000000000000002i2−2i2000
χ544-40004444-4-4-4-4400000000-4000000000000000000000000000000000000000−2i22i2000
χ5588888-2-2-2-2-2-2-2-23-2-2-2-2-2-2-2-23-2-2-2-23330000000000000000000000000000000000000
χ56888-8-8-2-2-2-2-2-2-2-23-2-222-2-222322223-3-30000000000000000000000000000000000000
χ5788-88-8-2-2-2-2-2-2-2-2322-2-222-2-232222-33-30000000000000000000000000000000000000
χ5888-8-88-2-2-2-2-2-2-2-23222222223-2-2-2-2-3-330000000000000000000000000000000000000
χ598-8000−2+25−2−253−53+5−3+5−3−52−252+25-20000000020000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000
χ608-8000−2+25−2−253−53+5−3+5−3−52−252+25-2000000002000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000
χ618-80003−53+5−2−25−2+252+252−25−3+5−3−5-20000000020000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000
χ628-80003−53+5−2−25−2+252+252−25−3+5−3−5-200000000200000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000
χ638-80003+53−5−2+25−2−252−252+25−3−5−3+5-200000000200000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000
χ648-80003+53−5−2+25−2−252−252+25−3−5−3+5-20000000020000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000
χ658-8000−2−25−2+253+53−5−3−5−3+52+252−25-2000000002000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000
χ668-8000−2−25−2+253+53−5−3−5−3+52+252−25-20000000020000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000
χ6716-16000-4-4-4-44444600000000-600000000000000000000000000000000000000000000

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