Finite Group Databasebeta

← Group #13026178

Character table — Group #13026178

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112224444444444888888888888888888888888888888888820202020202040404040408080808080808080
order12244222444510101024441010101010101010101020202020202020202020202020202020202020202244442244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11-11-11-11-1
χ6111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-11-11
χ7111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111i−i−iii−i−ii
χ8111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111−iii−i−iii−i
χ9111111-1-11-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-11111-1-1-1-1
χ10111111-1-11-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-11111
χ11111111-1-11-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111ii−i−i−i−iii
χ12111111-1-11-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111−i−iiiii−i−i
χ13111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1111-11-1-11-11
χ14111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-11-111-11-1
χ15111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1i−i−ii−iii−i
χ16111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1−iii−ii−i−ii
χ1722222-222-2-2-222220000-2-22222000022-2-2-2-2-2-20000000000002-2002-22-200000000000
χ1822222-222-2-2-222220000-2-22222000022-2-2-2-2-2-2000000000000-2200-22-2200000000000
χ1922222-2-2-2-22222220000-2-2-2-2-2-2000022-2-222220000000000002-2002-2-2200000000000
χ2022222-2-2-2-22222220000-2-2-2-2-2-2000022-2-22222000000000000-2200-222-200000000000
χ21222-2-2200-2002222002-22200000000-2-2-2-2000000002222-2-2-2-22-200-220002-200000000
χ22222-2-2200-2002222002-22200000000-2-2-2-2000000002222-2-2-2-2-22002-2000-2200000000
χ23222-2-2200-200222200-222200000000-2-2-2-200000000-2-2-2-222222-200-22000-2200000000
χ24222-2-2200-200222200-222200000000-2-2-2-200000000-2-2-2-22222-22002-20002-200000000
χ25222-2-2-20020022222-200-2-200002222-2-2220000-2-2-2-20000000022-2-2-2-20020000000000
χ26222-2-2-20020022222-200-2-200002222-2-2220000-2-2-2-200000000-2-2222200-20000000000
χ27222-2-2-2002002222-2200-2-20000-2-2-2-2-2-22200002222000000002222-2-200-20000000000
χ28222-2-2-2002002222-2200-2-20000-2-2-2-2-2-2220000222200000000-2-2-2-2220020000000000
χ2944444444444-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000
χ3044444444444-1-1-1-1-4-4-4-4-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111110000000000000000000
χ31444444-4-44-4-4-1-1-1-144-4-4-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111110000000000000000000
χ32444444-4-44-4-4-1-1-1-1-4-444-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000000
χ3344444-444-4-4-4-1-1-1-1000011-1-1-1-155−5−5-1-111111155−5−555−5−555−5−50000000000000000000
χ3444444-444-4-4-4-1-1-1-1000011-1-1-1-1−5−555-1-1111111−5−555−5−555−5−5550000000000000000000
χ3544444-4-4-4-444-1-1-1-1000011111155−5−5-1-111-1-1-1-155−5−5−5−555−5−5550000000000000000000
χ3644444-4-4-4-444-1-1-1-10000111111−5−555-1-111-1-1-1-1−5−55555−5−555−5−50000000000000000000
χ37444-4-4400-400-1-1-1-1004-4-1-155−5−555−5−5111155−5−5−5−555-1-1-1-111110000000000000000000
χ38444-4-4400-400-1-1-1-1004-4-1-1−5−555−5−5551111−5−55555−5−5-1-1-1-111110000000000000000000
χ39444-4-4400-400-1-1-1-100-44-1-155−5−5−5−555111155−5−555−5−51111-1-1-1-10000000000000000000
χ40444-4-4400-400-1-1-1-100-44-1-1−5−55555−5−51111−5−555−5−5551111-1-1-1-10000000000000000000
χ41444-4-4-400400-1-1-1-14-4001155−5−5-1-1-1-111-1-1−5−555111155−5−5−5−5550000000000000000000
χ42444-4-4-400400-1-1-1-14-40011−5−555-1-1-1-111-1-155−5−51111−5−55555−5−50000000000000000000
χ43444-4-4-400400-1-1-1-1-44001155−5−5111111-1-1−5−555-1-1-1-1−5−55555−5−50000000000000000000
χ44444-4-4-400400-1-1-1-1-440011−5−555111111-1-155−5−5-1-1-1-155−5−5−5−5550000000000000000000
χ4544-44-400004-44-4-44000000000000004-4004-44-40000000000000000000000000000000
χ4644-44-400004-4-111-100005−55−55−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18-115−5-11-11−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000
χ4744-44-400004-4-111-100005−55−55−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18-115−5-11-11ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000
χ4844-44-400004-4-111-10000−55−55−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18-11−55-11-11−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000
χ4944-44-400004-4-111-10000−55−55−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18-11−55-11-11ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000
χ5044-44-40000-444-4-44000000000000004-400-44-440000000000000000000000000000000
χ5144-44-40000-44-111-100005−5−55−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18-115−51-11-1−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000
χ5244-44-40000-44-111-100005−5−55−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18-115−51-11-1ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000
χ5344-44-40000-44-111-10000−555−55−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18-11−551-11-1−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000
χ5444-44-40000-44-111-10000−555−55−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18-11−551-11-1ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000
χ5544-4-4404-40004-4-440000004-4-440000-440000000000000000000000000000000000000
χ5644-4-4404-4000-111-100005−5-111-1−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ181-1−555−5−55ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000
χ5744-4-4404-4000-111-100005−5-111-1ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ181-1−555−5−55−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000
χ5844-4-4404-4000-111-10000−55-111-1−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ181-15−5−555−5ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000
χ5944-4-4404-4000-111-10000−55-111-1ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ181-15−5−555−5−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000
χ6044-4-440-440004-4-44000000-444-40000-440000000000000000000000000000000000000
χ6144-4-440-44000-111-100005−51-1-11−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ181-1−55−555−5ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000
χ6244-4-440-44000-111-100005−51-1-11ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ181-1−55−555−5−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000
χ6344-4-440-44000-111-10000−551-1-11−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ181-15−55−5−55ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000
χ6444-4-440-44000-111-10000−551-1-11ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ181-15−55−5−55−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000
χ658-8000000000800-80000000000000000000000000000000000004i−4i000000000000000
χ668-8000000000800-8000000000000000000000000000000000000−4i4i000000000000000
χ6716-16000000000-445−45400000000000000000000000000000000000000000000000000000
χ6816-16000000000-4−4545400000000000000000000000000000000000000000000000000000

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