Finite Group Databasebeta

← Group #13013725

Character table — Group #13013725

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020202020204040404040808080808080
order12222244445101010410102020202022228820202020404040404040404044444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111111-1-1iiii−i−i−i−i-1-1-1ii−i−i-1-1ii−i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1−i−i−i−iiiii-1-1-1−i−iii-1-1−i−iii
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1ii−i−i11−i−iii
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−iii11ii−i−i
χ911111111-1-11111-111-1-1-1-11111i−i11-1-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1i−ii−ii−i
χ1011111111-1-11111-111-1-1-1-11111i−i11-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-11111i−i−ii−ii
χ1111111111-1-11111-111-1-1-1-11111−ii11-1-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1−ii−ii−ii
χ1211111111-1-11111-111-1-1-1-11111−ii11-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-11111−iii−ii−i
χ1311111111-1-11111-111-1-1-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111−i−iii−ii-111-1
χ1411111111-1-11111-111-1-1-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii111ii−i−i−ii1-1-11
χ1511111111-1-11111-111-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i111−i−iiii−i1-1-11
χ1611111111-1-11111-111-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111ii−i−ii−i-111-1
χ17222222-2-2222222-2222222222200-2-2-2-200000000-2-200000000-2-220000000000
χ18222222-2-2222222-2222222-2-2-2-200-2-2-2-200000000220000000022-20000000000
χ19222222-2-2-2-22222222-2-2-2-2222200-2-22200000000-2-20000000022-20000000000
χ20222222-2-2-2-22222222-2-2-2-2-2-2-2-200-2-222000000002200000000-2-220000000000
χ212-22-22-2002-22-22-202-2-2-2220000000000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i01+i−1−i1−i−1+i000000
χ222-22-22-2002-22-22-202-2-2-2220000000000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i0−1−i1+i−1+i1−i000000
χ232-22-22-2002-22-22-202-2-2-222000000000000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i01−i−1+i1+i−1−i000000
χ242-22-22-2002-22-22-202-2-2-222000000000000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i0−1+i1−i−1−i1+i000000
χ252-22-22-200-222-22-202-222-2-20000000000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i0−1−i1+i−1+i1−i000000
χ262-22-22-200-222-22-202-222-2-20000000000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i01+i−1−i1−i−1+i000000
χ272-22-22-200-222-22-202-222-2-2000000000000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i0−1+i1−i−1−i1+i000000
χ282-22-22-200-222-22-202-222-2-2000000000000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i01−i−1+i1+i−1−i000000
χ294444444444-1-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ304444444444-1-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ3144444444-4-4-1-1-1-1-4-1-1111100004i−4i-1-111−i−i−i−iiiii00000000000000000000000
χ3244444444-4-4-1-1-1-1-4-1-111110000−4i4i-1-111iiii−i−i−i−i00000000000000000000000
χ33444444-4-444-1-1-1-1-4-1-1-1-1-1-1000000111155−5−555−5−500000000000000000000000
χ34444444-4-444-1-1-1-1-4-1-1-1-1-1-10000001111−5−555−5−55500000000000000000000000
χ35444444-4-4-4-4-1-1-1-14-1-1111100000011-1-1i5i5−i5−i5−i5−i5i5i500000000000000000000000
χ36444444-4-4-4-4-1-1-1-14-1-1111100000011-1-1−i5−i5i5i5i5i5−i5−i500000000000000000000000
χ374444-4-4000044440-4-400004-44-40000000000000000000000000000000000000
χ384444-4-4000044440-4-40000-44-440000000000000000000000000000000000000
χ3944-4-400000044-4-40000000040-400000000000000002-22-22-22-20000000000000
χ4044-4-400000044-4-40000000040-40000000000000000-22-22-22-220000000000000
χ4144-4-400000044-4-400000000-40400000000000000002i−2i2i−2i−2i2i−2i2i0000000000000
χ4244-4-400000044-4-400000000-4040000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000
χ434-44-4-444i−4i004-44-40-4400000000004i−4i000000000000000000000000000000000
χ444-44-4-444i−4i00-11-1101-15−55−5000000−iii5−i5ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ1900000000000000000000000
χ454-44-4-444i−4i00-11-1101-15−55−5000000−iii5−i5−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ1900000000000000000000000
χ464-44-4-444i−4i00-11-1101-1−55−55000000−ii−i5i5−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ1400000000000000000000000
χ474-44-4-444i−4i00-11-1101-1−55−55000000−ii−i5i5ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ1400000000000000000000000
χ484-44-4-44−4i4i004-44-40-440000000000−4i4i000000000000000000000000000000000
χ494-44-4-44−4i4i00-11-1101-15−55−5000000i−i−i5i5ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ1900000000000000000000000
χ504-44-4-44−4i4i00-11-1101-15−55−5000000i−i−i5i5−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ1900000000000000000000000
χ514-44-4-44−4i4i00-11-1101-1−55−55000000i−ii5−i5−ζ2+ζ11+ζ18−ζ19ζ2−ζ11−ζ18+ζ19ζ3−ζ6−ζ7+ζ14−ζ3+ζ6+ζ7−ζ14ζ2+ζ11−ζ18−ζ19−ζ2−ζ11+ζ18+ζ19−ζ3−ζ6+ζ7+ζ14ζ3+ζ6−ζ7−ζ1400000000000000000000000
χ524-44-4-44−4i4i00-11-1101-1−55−55000000i−ii5−i5ζ2−ζ11−ζ18+ζ19−ζ2+ζ11+ζ18−ζ19−ζ3+ζ6+ζ7−ζ14ζ3−ζ6−ζ7+ζ14−ζ2−ζ11+ζ18+ζ19ζ2+ζ11−ζ18−ζ19ζ3+ζ6−ζ7−ζ14−ζ3−ζ6+ζ7+ζ1400000000000000000000000
χ534-4-440000004-4-44000000040-4000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000
χ544-4-440000004-4-44000000040-400000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000
χ554-4-440000004-4-440000000-404000000000000000002-2-222-2-220000000000000
χ564-4-440000004-4-440000000-40400000000000000000-222-2-222-20000000000000
χ578888-8-80000-2-2-2-202225−25−252500000000000000000000000000000000000000000
χ588888-8-80000-2-2-2-2022−252525−2500000000000000000000000000000000000000000
χ598-88-88-8008-8-22-220-2222-2-200000000000000000000000000000000000000000
χ608-88-88-800-88-22-220-22-2-22200000000000000000000000000000000000000000
χ611616-16-16000000-4-444000000000000000000000000000000000000000000000000
χ6216-16-1616000000-444-4000000000000000000000000000000000000000000000000

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