Finite Group Databasebeta

← Group #13013852

Character table — Group #13013852

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222444444445588888888888101010161616161616161616161616202020204040404040404040404040404080808080
order1224424588102020228888810101020202024440404040404040404040404024888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ41111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−ii−ii−i
χ61111111111111-1-111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−ii−ii
χ71111111111111-1-11-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii−ii
χ81111111111111-1-11-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−ii−i
χ911111-1-11-1-1111111ii−i−i1-1-11-1-111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−iii−i−iii−i−i11-1-1
χ1011111-1-11-1-1111111ii−i−i1-1-11-1-111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i−i−iii−i−iii-1-111
χ1111111-1-11-1-1111111−i−iii1-1-11-1-111111-1-1−i−i−i−iiiii-1-1-1-11−i−iiiii−i−iii−i−i-1-111
χ1211111-1-11-1-1111111−i−iii1-1-11-1-111111-1-1−i−i−i−iiiii-1-1-1-11−i−iii−i−iii−i−iii11-1-1
χ1311111-1-11-1-1111-1-11ii−i−i1-1-11-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii11-1-1-1-111−iii−i
χ1411111-1-11-1-1111-1-11ii−i−i1-1-11-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii-1-11111-1-1i−i−ii
χ1511111-1-11-1-1111-1-11−i−iii1-1-11-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i11-1-1-1-111i−i−ii
χ1611111-1-11-1-1111-1-11−i−iii1-1-11-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i-1-11111-1-1−iii−i
χ1722222222-2-222222-20000222222222-2-2-2-20000000022-2-2-20000000000000000
χ1822222222-2-2222-2-2-20000222222-2-2-2-2-2-2-200000000-2-22220000000000000000
χ1922222-2-222222222-200002-2-22-2-2222-2-22200000000-2-222-20000000000000000
χ2022222-2-2222222-2-2-200002-2-22-2-2-2-2-2-2-2220000000022-2-220000000000000000
χ21222-2-22-22002-2-22200000222-2-2-22-2-20000000000002-20000000i2−i2i2−i2i2−i2i2−i20000
χ22222-2-22-22002-2-22200000222-2-2-22-2-20000000000002-20000000−i2i2−i2i2−i2i2−i2i20000
χ23222-2-22-22002-2-2-2-200000222-2-2-2-222000000000000-2200000002−22−2−22−220000
χ24222-2-22-22002-2-2-2-200000222-2-2-2-222000000000000-220000000−22−222−22−20000
χ25222-2-2-222002-2-222000002-2-2-2222-2-2000000000000-2200000002−2−222−2−220000
χ26222-2-2-222002-2-222000002-2-2-2222-2-2000000000000-220000000−222−2−222−20000
χ27222-2-2-222002-2-2-2-2000002-2-2-222-2220000000000002-20000000i2−i2−i2i2−i2i2i2−i20000
χ28222-2-2-222002-2-2-2-2000002-2-2-222-2220000000000002-20000000−i2i2i2−i2i2−i2−i2i20000
χ2922-22-20022i−2i2222201+i−1−i1−i−1+i-200-200-22-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i01+i−1−i1−i−1+i000000000000
χ3022-22-20022i−2i222220−1−i1+i−1+i1−i-200-200-22-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i0−1−i1+i−1+i1−i000000000000
χ3122-22-20022i−2i222-2-201+i−1−i1−i−1+i-200-2002-22002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i0−1−i1+i−1+i1−i000000000000
χ3222-22-20022i−2i222-2-20−1−i1+i−1+i1−i-200-2002-22002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i01+i−1−i1−i−1+i000000000000
χ3322-22-2002−2i2i2222201−i−1+i1+i−1−i-200-200-22-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i01−i−1+i1+i−1−i000000000000
χ3422-22-2002−2i2i222220−1+i1−i−1−i1+i-200-200-22-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i0−1+i1−i−1−i1+i000000000000
χ3522-22-2002−2i2i222-2-201−i−1+i1+i−1−i-200-2002-2200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i0−1+i1−i−1−i1+i000000000000
χ3622-22-2002−2i2i222-2-20−1+i1−i−1−i1+i-200-2002-2200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i01−i−1+i1+i−1−i000000000000
χ374444444-144-1-1-10044444-1-1-1-1-1-1000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ384444444-144-1-1-1004-4-4-4-4-1-1-1-1-1-1000-1-1-1-111111111000000000000000000000
χ394444444-1-4-4-1-1-100-40000-1-1-1-1-1-100011115−55−55−55−5000000000000000000000
χ404444444-1-4-4-1-1-100-40000-1-1-1-1-1-10001111−55−55−55−55000000000000000000000
χ4144444-4-4-144-1-1-100-40000-111-11100011-1-1i5−i5i5−i5−i5i5−i5i5000000000000000000000
χ4244444-4-4-144-1-1-100-40000-111-11100011-1-1−i5i5−i5i5i5−i5i5−i5000000000000000000000
χ4344444-4-4-1-4-4-1-1-10044i4i−4i−4i-111-111000-1-111−i−i−i−iiiii000000000000000000000
χ4444444-4-4-1-4-4-1-1-1004−4i−4i4i4i-111-111000-1-111iiii−i−i−i−i000000000000000000000
χ4544-44-400-14i−4i-1-1-10002+2i−2−2i2−2i−2+2i15−515−5000i5−i5−ii−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38000000000000000000000
χ4644-44-400-14i−4i-1-1-10002+2i−2−2i2−2i−2+2i1−551−55000−i5i5−ii−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28000000000000000000000
χ4744-44-400-14i−4i-1-1-1000−2−2i2+2i−2+2i2−2i15−515−5000i5−i5−iiζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38000000000000000000000
χ4844-44-400-14i−4i-1-1-1000−2−2i2+2i−2+2i2−2i1−551−55000−i5i5−iiζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28000000000000000000000
χ4944-44-400-1−4i4i-1-1-10002−2i−2+2i2+2i−2−2i15−515−5000−i5i5i−iζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38000000000000000000000
χ5044-44-400-1−4i4i-1-1-10002−2i−2+2i2+2i−2−2i1−551−55000i5−i5i−i−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28000000000000000000000
χ5144-44-400-1−4i4i-1-1-1000−2+2i2−2i−2−2i2+2i15−515−5000−i5i5i−i−ζ6+ζ12−ζ14+ζ28ζ4−ζ22+ζ36−ζ38ζ6−ζ12+ζ14−ζ28−ζ4+ζ22−ζ36+ζ38ζ6+ζ12+ζ14+ζ28ζ4+ζ22+ζ36+ζ38−ζ6−ζ12−ζ14−ζ28−ζ4−ζ22−ζ36−ζ38000000000000000000000
χ5244-44-400-1−4i4i-1-1-1000−2+2i2−2i−2−2i2+2i1−551−55000i5−i5i−iζ4−ζ22+ζ36−ζ38−ζ6+ζ12−ζ14+ζ28−ζ4+ζ22−ζ36+ζ38ζ6−ζ12+ζ14−ζ28ζ4+ζ22+ζ36+ζ38ζ6+ζ12+ζ14+ζ28−ζ4−ζ22−ζ36−ζ38−ζ6−ζ12−ζ14−ζ28000000000000000000000
χ5344-4-44004004-4-44400000-400400-4-44000000000000000000000000000000000
χ5444-4-44004004-4-4-4-400000-40040044-4000000000000000000000000000000000
χ55888-8-88-8-200-2220000000-2-2-2222000000000000000000000000000000000000
χ56888-8-8-88-200-2220000000-2222-2-2000000000000000000000000000000000000
χ5788-8-8800-200-2220000000225−25-2−2525000000000000000000000000000000000000
χ5888-8-8800-200-22200000002−2525-225−25000000000000000000000000000000000000
χ598-800000800-8008-800000000000000000000000000000000000000000000000
χ608-800000800-800-8800000000000000000000000000000000000000000000000
χ6116-1600000-40044i5−4i50000000000000000000000000000000000000000000000000
χ6216-1600000-4004−4i54i50000000000000000000000000000000000000000000000000

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