Finite Group Databasebeta

← Group #13013893

Character table — Group #13013893

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222444444445588888888888101010161616161616161616161616202020204040404040404040404040404080808080
order122445888810202044410161616162040404040224202040408080808080808080888841616161616161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ411111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ71111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−ii−ii
χ81111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiii−ii−i
χ9111111-1-1-1-11111111ii−i−i1-1-1-1-111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−iii−i−iii−i−i11-1-1
χ10111111-1-1-1-11111111ii−i−i1-1-1-1-111111-1-1iiii−i−i−i−i-1-1-1-11ii−i−i−i−iii−i−iii-1-111
χ11111111-1-1-1-11111111−i−iii1-1-1-1-111111-1-1−i−i−i−iiiii-1-1-1-11−i−iiiii−i−iii−i−i-1-111
χ12111111-1-1-1-11111111−i−iii1-1-1-1-111111-1-1−i−i−i−iiiii-1-1-1-11−i−iii−i−iii−i−iii11-1-1
χ13111111-1-1-1-1111-1-111ii−i−i1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii11-1-1-1-111−iii−i
χ14111111-1-1-1-1111-1-111ii−i−i1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1−i−iii-1-11111-1-1i−i−ii
χ15111111-1-1-1-1111-1-111−i−iii1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i11-1-1-1-111i−i−ii
χ16111111-1-1-1-1111-1-111−i−iii1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1ii−i−i-1-11111-1-1−iii−i
χ1722222222-2-222222-2200002-2-2-2-2222-2-22200000000-2-222-20000000000000000
χ1822222222-2-2222-2-2-2200002-2-2-2-2-2-2-2-2-2220000000022-2-220000000000000000
χ19222222-2-22222222-22000022222222-2-2-2-20000000022-2-2-20000000000000000
χ20222222-2-222222-2-2-22000022222-2-2-2-2-2-2-200000000-2-22220000000000000000
χ2122-22-22002i−2i2-2-2220-2000022i2i−2i−2i2-2-20000000000002i−2i00000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ2222-22-22002i−2i2-2-2220-2000022i2i−2i−2i2-2-20000000000002i−2i0000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ2322-22-22002i−2i2-2-2-2-20-2000022i2i−2i−2i-222000000000000−2i2i00000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ2422-22-22002i−2i2-2-2-2-20-2000022i2i−2i−2i-222000000000000−2i2i0000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ2522-22-2200−2i2i2-2-2220-200002−2i−2i2i2i2-2-2000000000000−2i2i00000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ2622-22-2200−2i2i2-2-2220-200002−2i−2i2i2i2-2-2000000000000−2i2i0000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ2722-22-2200−2i2i2-2-2-2-20-200002−2i−2i2i2i-2220000000000002i−2i00000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ2822-22-2200−2i2i2-2-2-2-20-200002−2i−2i2i2i-2220000000000002i−2i0000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ2922-2-2222i−2i00222220-21+i−1−i1−i−1+i-20000-22-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i01+i−1−i1−i−1+i000000000000
χ3022-2-2222i−2i00222220-2−1−i1+i−1+i1−i-20000-22-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i0−1−i1+i−1+i1−i000000000000
χ3122-2-2222i−2i00222-2-20-21+i−1−i1−i−1+i-200002-22002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i0−1−i1+i−1+i1−i000000000000
χ3222-2-2222i−2i00222-2-20-2−1−i1+i−1+i1−i-200002-22002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i01+i−1−i1−i−1+i000000000000
χ3322-2-222−2i2i00222220-21−i−1+i1+i−1−i-20000-22-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i01−i−1+i1+i−1−i000000000000
χ3422-2-222−2i2i00222220-2−1+i1−i−1−i1+i-20000-22-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i0−1+i1−i−1−i1+i000000000000
χ3522-2-222−2i2i00222-2-20-21−i−1+i1+i−1−i-200002-2200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i0−1+i1−i−1−i1+i000000000000
χ3622-2-222−2i2i00222-2-20-2−1+i1−i−1−i1+i-200002-2200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i01−i−1+i1+i−1−i000000000000
χ3744444-14444-1-1-1004-14444-1-1-1-1-1000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ3844444-14444-1-1-1004-1-4-4-4-4-1-1-1-1-1000-1-1-1-111111111000000000000000000000
χ3944444-144-4-4-1-1-100-4-10000-1111100011-1-1i5−i5i5−i5i5−i5i5−i5000000000000000000000
χ4044444-144-4-4-1-1-100-4-10000-1111100011-1-1−i5i5−i5i5−i5i5−i5i5000000000000000000000
χ4144444-1-4-444-1-1-100-4-10000-1-1-1-1-100011115−55−5−55−55000000000000000000000
χ4244444-1-4-444-1-1-100-4-10000-1-1-1-1-10001111−55−555−55−5000000000000000000000
χ4344444-1-4-4-4-4-1-1-1004-14i4i−4i−4i-11111000-1-111−i−i−i−iiiii000000000000000000000
χ4444444-1-4-4-4-4-1-1-1004-1−4i−4i4i4i-11111000-1-111iiii−i−i−i−i000000000000000000000
χ45444-4-4400004-4-444040000-40000-4-44000000000000000000000000000000000
χ46444-4-4400004-4-4-4-4040000-4000044-4000000000000000000000000000000000
χ4744-4-44-14i−4i00-1-1-100012+2i−2−2i2−2i−2+2i15−55−5000i5−i5−ii−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14000000000000000000000
χ4844-4-44-14i−4i00-1-1-100012+2i−2−2i2−2i−2+2i1−55−55000−i5i5−ii−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19000000000000000000000
χ4944-4-44-14i−4i00-1-1-10001−2−2i2+2i−2+2i2−2i15−55−5000i5−i5−iiζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14000000000000000000000
χ5044-4-44-14i−4i00-1-1-10001−2−2i2+2i−2+2i2−2i1−55−55000−i5i5−iiζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19000000000000000000000
χ5144-4-44-1−4i4i00-1-1-100012−2i−2+2i2+2i−2−2i15−55−5000−i5i5i−iζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14000000000000000000000
χ5244-4-44-1−4i4i00-1-1-100012−2i−2+2i2+2i−2−2i1−55−55000i5−i5i−i−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19000000000000000000000
χ5344-4-44-1−4i4i00-1-1-10001−2+2i2−2i−2−2i2+2i15−55−5000−i5i5i−i−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14000000000000000000000
χ5444-4-44-1−4i4i00-1-1-10001−2+2i2−2i−2−2i2+2i1−55−55000i5−i5i−iζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19000000000000000000000
χ55888-8-8-20000-222000-2000022i5−2i5−2i52i5000000000000000000000000000000000000
χ56888-8-8-20000-222000-200002−2i52i52i5−2i5000000000000000000000000000000000000
χ5788-88-8-2008i−8i-22200020000-2−2i−2i2i2i000000000000000000000000000000000000
χ5888-88-8-200−8i8i-22200020000-22i2i−2i−2i000000000000000000000000000000000000
χ598-800080000-8008i−8i00000000000000000000000000000000000000000000000
χ608-800080000-800−8i8i00000000000000000000000000000000000000000000000
χ6116-16000-4000044i5−4i50000000000000000000000000000000000000000000000000
χ6216-16000-400004−4i54i50000000000000000000000000000000000000000000000000

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