Finite Group Databasebeta

← Group #12253884

Character table — Group #12253884

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size112222222224444444444444444444444444444444888888888888888888888810101010161616162020202020202020202020202020323232323232323280808080
order12244558810102488810101616161616161616202020204040404080808080808080801010202040404040404080808080808080808080808022442488248888161616161616161610102020404040402288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ911111111111-1-11-1-1111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111-1-11-1-1111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1111111111111-1-11-1-1111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ1211111111111-1-11-1-1111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ1311111111111-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-11-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-111-1-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111111-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111111-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222-2-22222-2-2-222000000002222-2-2-2-2000000002222-2-2-2-2-2-20000000000002222000022-2-2-2-200000000000000000000
χ182222222-2-22222-2-2-222000000002222-2-2-2-2000000002222-2-2-2-2-2-2000000000000-2-2-2-20000-2-2222200000000000000000000
χ192222222-2-222-2-2-22222000000002222-2-2-2-200000000-2-2-2-2-2-2222200000000000022220000-2-2-2-22200000000000000000000
χ202222222-2-222-2-2-22222000000002222-2-2-2-200000000-2-2-2-2-2-22222000000000000-2-2-2-200002222-2-200000000000000000000
χ2122222−1+52−1−5222−1+52−1−5222222−1+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+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+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000222200000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000
χ2222222−1+52−1−5222−1+52−1−5222222−1+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+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+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-2-2-2-2000000000000001−521+521−521+521−521+521−521+520000
χ2322222−1+52−1−5222−1+52−1−5222222−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200002-22-200000000000000−1+52−1−521−521+52−1+52−1−521−521+520000
χ2422222−1+52−1−5222−1+52−1−5222222−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+520000-22-22000000000000001−521+52−1+52−1−521−521+52−1+52−1−520000
χ2522222−1+52−1−5222−1+52−1−52-2-22-2-2−1+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52000022-2-200000000000000−1+52−1−52−1+52−1−521−521+521−521+520000
χ2622222−1+52−1−5222−1+52−1−52-2-22-2-2−1+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+520000-2-222000000000000001−521+521−521+52−1+52−1−52−1+52−1−520000
χ2722222−1+52−1−5222−1+52−1−52-2-22-2-2−1+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200002-2-2200000000000000−1+52−1−521−521+521−521+52−1+52−1−520000
χ2822222−1+52−1−5222−1+52−1−52-2-22-2-2−1+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-222-2000000000000001−521+52−1+52−1−52−1+52−1−521−521+520000
χ2922222−1−52−1+5222−1−52−1+5222222−1−52−1+5222222222−1−52−1+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+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000222200000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000
χ3022222−1−52−1+5222−1−52−1+5222222−1−52−1+5222222222−1−52−1+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+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-2-2-2-2000000000000001+521−521+521−521+521−521+521−520000
χ3122222−1−52−1+5222−1−52−1+5222222−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200002-22-200000000000000−1−52−1+521+521−52−1−52−1+521+521−520000
χ3222222−1−52−1+5222−1−52−1+5222222−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−520000-22-22000000000000001+521−52−1−52−1+521+521−52−1−52−1+520000
χ3322222−1−52−1+5222−1−52−1+52-2-22-2-2−1−52−1+522222-2-2-2-2−1−52−1+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+521+521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52000022-2-200000000000000−1−52−1+52−1−52−1+521+521−521+521−520000
χ3422222−1−52−1+5222−1−52−1+52-2-22-2-2−1−52−1+522222-2-2-2-2−1−52−1+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+521+521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−520000-2-222000000000000001+521−521+521−52−1−52−1+52−1−52−1+520000
χ3522222−1−52−1+5222−1−52−1+52-2-22-2-2−1−52−1+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200002-2-2200000000000000−1−52−1+521+521−521+521−52−1−52−1+520000
χ3622222−1−52−1+5222−1−52−1+52-2-22-2-2−1−52−1+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-222-2000000000000001+521−52−1−52−1+52−1−52−1+521+521−520000
χ37222-2-22200220002i−2i2222−2−2i2i2−i2−i2-2-2-2-2000022−2−222−2−20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i222-2-2000000002i−2i22−2−2i2i2−i2−i2000000000000
χ38222-2-22200220002i−2i2222−2−2i2i2−i2−i2-2-2-2-2000022−2−222−2−20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2-2-22200000000−2i2i−2−222−i2−i2i2i2000000000000
χ39222-2-22200220002i−2i22−2−222−i2−i2i2i2-2-2-2-20000−2−222−2−2220000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i222-2-2000000002i−2i−2−222−i2−i2i2i2000000000000
χ40222-2-22200220002i−2i22−2−222−i2−i2i2i2-2-2-2-20000−2−222−2−2220000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i2-2-22200000000−2i2i22−2−2i2i2−i2−i2000000000000
χ41222-2-2220022000−2i2i2222−2−2−i2−i2i2i2-2-2-2-2000022−2−222−2−2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i222-2-200000000−2i2i22−2−2−i2−i2i2i2000000000000
χ42222-2-2220022000−2i2i2222−2−2−i2−i2i2i2-2-2-2-2000022−2−222−2−2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i2-2-222000000002i−2i−2−222i2i2−i2−i2000000000000
χ43222-2-2220022000−2i2i22−2−222i2i2−i2−i2-2-2-2-20000−2−222−2−222000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i222-2-200000000−2i2i−2−222i2i2−i2−i2000000000000
χ44222-2-2220022000−2i2i22−2−222i2i2−i2−i2-2-2-2-20000−2−222−2−222000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i2-2-222000000002i−2i22−2−2−i2−i2i2i2000000000000
χ4522-22-222222200-200-2-22-22-2000022-2-22222222222220000-2-20000-2-2-2-2000000002-22-20000002-2002-22-20000000000000000
χ4622-22-222222200-200-2-22-22-2000022-2-22222222222220000-2-20000-2-2-2-200000000-22-22000000-2200-22-220000000000000000
χ4722-22-222222200-200-2-2-22-22000022-2-22222-2-2-2-2-2-2-2-20000-2-200002222000000002-22-20000002-200-22-220000000000000000
χ4822-22-222222200-200-2-2-22-22000022-2-22222-2-2-2-2-2-2-2-20000-2-20000222200000000-22-22000000-22002-22-20000000000000000
χ4922-22-222-2-22200200-2-200002i−2i2i−2i22-2-2-2-2-2-200000000000022000000002i−2i2i−2i2i−2i2i−2i2-22-2000000-220000002i−2i2i−2i000000000000
χ5022-22-222-2-22200200-2-200002i−2i2i−2i22-2-2-2-2-2-200000000000022000000002i−2i2i−2i2i−2i2i−2i-22-220000002-2000000−2i2i−2i2i000000000000
χ5122-22-222-2-22200200-2-20000−2i2i−2i2i22-2-2-2-2-2-20000000000002200000000−2i2i−2i2i−2i2i−2i2i2-22-2000000-22000000−2i2i−2i2i000000000000
χ5222-22-222-2-22200200-2-20000−2i2i−2i2i22-2-2-2-2-2-20000000000002200000000−2i2i−2i2i−2i2i−2i2i-22-220000002-20000002i−2i2i−2i000000000000
χ5322-2-222200222-2000-2-22−2−222−2−22-2-222000022−2−222−2−222-2-2000000−22−222−2−222−2−222-2-2200002-200002−2−222−2−22000000000000
χ5422-2-222200222-2000-2-22−2−222−2−22-2-222000022−2−222−2−222-2-2000000−22−222−2−222−2−22-222-20000-220000−222−2−222−2000000000000
χ5522-2-222200222-2000-2-2−222−2−222−2-2-2220000−2−222−2−22222-2-20000002−22−2−222−2−222−22-2-2200002-20000−222−2−222−2000000000000
χ5622-2-222200222-2000-2-2−222−2−222−2-2-2220000−2−222−2−22222-2-20000002−22−2−222−2−222−2-222-20000-2200002−2−222−2−22000000000000
χ5722-2-22220022-22000-2-22−2−22−222−2-2-222000022−2−222−2−2-2-222000000−22−22−222−2−222−22-2-220000-2200002−2−22−222−2000000000000
χ5822-2-22220022-22000-2-22−2−22−222−2-2-222000022−2−222−2−2-2-222000000−22−22−222−2−222−2-222-200002-20000−222−22−2−22000000000000
χ5922-2-22220022-22000-2-2−222−22−2−22-2-2220000−2−222−2−222-2-2220000002−22−22−2−222−2−222-2-220000-220000−222−22−2−22000000000000
χ6022-2-22220022-22000-2-2−222−22−2−22-2-2220000−2−222−2−222-2-2220000002−22−22−2−222−2−22-222-200002-200002−2−22−222−2000000000000
χ6144444−1+5−1−5-4-4−1+5−1−544-4-4-4−1+5−1−500000000−1+5−1−5−1+5−1−51−51−51+51+500000000−1+5−1−5−1+5−1−51−51+51−51−51+51+50000000000000000000000000000000000000000000000
χ6244444−1+5−1−5-4-4−1+5−1−5-4-4-444−1+5−1−500000000−1+5−1−5−1+5−1−51−51−51+51+5000000001−51+51−51+51−51+5−1+5−1+5−1−5−1−50000000000000000000000000000000000000000000000
χ6344444−1−5−1+5-4-4−1−5−1+544-4-4-4−1−5−1+500000000−1−5−1+5−1−5−1+51+51+51−51−500000000−1−5−1+5−1−5−1+51+51−51+51+51−51−50000000000000000000000000000000000000000000000
χ6444444−1−5−1+5-4-4−1−5−1+5-4-4-444−1−5−1+500000000−1−5−1+5−1−5−1+51+51+51−51−5000000001+51−51+51−51+51−5−1−5−1−5−1+5−1+50000000000000000000000000000000000000000000000
χ65444-4-4−1+5−1−500−1+5−1−50004i−4i−1+5−1−52222−22−222i22i2−2i2−2i21−51+51−51+50000−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78000000−2ζ44−2ζ762ζ44+2ζ76−2ζ12−2ζ282ζ12+2ζ28−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78ζ14+ζ26+ζ46+ζ74ζ14+ζ26+ζ46+ζ74−ζ14−ζ26−ζ46−ζ74−ζ14−ζ26−ζ46−ζ74ζ42+ζ58+ζ62+ζ78ζ42+ζ58+ζ62+ζ78−ζ42−ζ58−ζ62−ζ78−ζ42−ζ58−ζ62−ζ780000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.