Finite Group Databasebeta

← Group #13021042

Character table — Group #13021042

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222444444510101010101010202020202020202020202020222244444420202020202020204444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-1
χ1111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-11-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-11
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ172222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000022-2-2000000000000000000
χ182222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000-2-222000000000000000000
χ1922222222-2-222-2-222222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000-2-222000000000000000000
χ2022222222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000022-2-2000000000000000000
χ2122-2-22-2-22002-200222-22-2-2-2000022-2-2000000002i2i−2i−2i00000000002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ2222-2-22-2-22002-200222-22-2-2-2000022-2-2000000002i2i−2i−2i00000000002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ2322-2-22-2-22002-200222-22-2-2-2000022-2-200000000−2i−2i2i2i0000000000−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ2422-2-22-2-22002-200222-22-2-2-2000022-2-200000000−2i−2i2i2i0000000000−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ2522-2-22-2-2200-2200222-22-2-2-20000-2-222000000002i2i−2i−2i0000000000−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ2622-2-22-2-2200-2200222-22-2-2-20000-2-222000000002i2i−2i−2i0000000000−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ2722-2-22-2-2200-2200222-22-2-2-20000-2-22200000000−2i−2i2i2i00000000002i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ2822-2-22-2-2200-2200222-22-2-2-20000-2-22200000000−2i−2i2i2i00000000002i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ292-2-22-2-22200002-222-2-2-2-2220000000022-2-222-2-22-22-20000000000000000000000002i−2i002i−2i00
χ302-2-22-2-22200002-222-2-2-2-2220000000022-2-222-2-22-22-2000000000000000000000000−2i2i00−2i2i00
χ312-2-22-2-22200002-222-2-2-2-2220000000022-2-2-2-222-22-220000000000000000000000002-200-2200
χ322-2-22-2-22200002-222-2-2-2-2220000000022-2-2-2-222-22-22000000000000000000000000-22002-200
χ332-2-22-2-2220000-2222-2-2-2-22200000000-2-22222-2-2-22-2200000000000000000000002i−2i002i−2i0000
χ342-2-22-2-2220000-2222-2-2-2-22200000000-2-22222-2-2-22-220000000000000000000000−2i2i00−2i2i0000
χ352-2-22-2-2220000-2222-2-2-2-22200000000-2-222-2-2222-22-200000000000000000000002-200-220000
χ362-2-22-2-2220000-2222-2-2-2-22200000000-2-222-2-2222-22-20000000000000000000000-22002-20000
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000000055−5−555−5−50000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000−5−555−5−5550000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111000000000055−5−5−5−5550000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000−5−55555−5−50000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000004-4-1-1-1-111110000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-100000000-441111-1-1-1-10000000000000000000000
χ45444-4-4-44-44i−4i00004-444-4-4-444i4i−4i−4i000000000000000000000000000000000000000000000000
χ46444-4-4-44-44i−4i0000-11-1-1111-1−i−iiii5−i5i5−i55−55−50000000000−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000000
χ47444-4-4-44-44i−4i0000-11-1-1111-1−i−iiii5−i5i5−i55−55−50000000000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000000
χ48444-4-4-44-44i−4i0000-11-1-1111-1−i−iii−i5i5−i5i5−55−550000000000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000000
χ49444-4-4-44-44i−4i0000-11-1-1111-1−i−iii−i5i5−i5i5−55−550000000000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000000
χ50444-4-4-44-4−4i4i00004-444-4-4-44−4i−4i4i4i000000000000000000000000000000000000000000000000
χ51444-4-4-44-4−4i4i0000-11-1-1111-1ii−i−ii5−i5i5−i5−55−550000000000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000000
χ52444-4-4-44-4−4i4i0000-11-1-1111-1ii−i−ii5−i5i5−i5−55−550000000000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000000
χ53444-4-4-44-4−4i4i0000-11-1-1111-1ii−i−i−i5i5−i5i55−55−50000000000−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000000
χ54444-4-4-44-4−4i4i0000-11-1-1111-1ii−i−i−i5i5−i5i55−55−50000000000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000000
χ5544-44-44-4-40000004-44-4-444-40000000000004-44-4000000000000000000000000000000000000
χ5644-44-44-4-40000004-44-4-444-4000000000000-44-44000000000000000000000000000000000000
χ574-4444-4-4-40000004-4-444-44-40000000000004-4-44000000000000000000000000000000000000
χ584-4444-4-4-40000004-4-444-44-4000000000000-444-4000000000000000000000000000000000000
χ594-44-4-44-4400000044-44-44-4-400000000000000004i−4i−4i4i00000000000000000000000000000000
χ604-44-4-44-4400000044-44-44-4-40000000000000000−4i4i4i−4i00000000000000000000000000000000
χ614-4-4-4444-40000004-4-4-444-44000000000000000000000000000000004-4000000000000000000
χ624-4-4-4444-40000004-4-4-444-4400000000000000000000000000000000-44000000000000000000
χ6388-88-88-8-8000000-22-222-2-2200002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ6488-88-88-8-8000000-22-222-2-220000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ6588-8-88-8-88008-800-2-2-22-22220000-2-22200000000000000000000000000000000000000000000
χ6688-8-88-8-8800-8800-2-2-22-2222000022-2-200000000000000000000000000000000000000000000
χ678-8888-8-8-8000000-222-2-22-222i5−2i52i5−2i5000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000-222-2-22-22−2i52i5−2i52i5000000000000000000000000000000000000000000000000
χ698-88-8-88-88000000-2-22-22-22225−25−2525000000000000000000000000000000000000000000000000
χ708-88-8-88-88000000-2-22-22-222−252525−25000000000000000000000000000000000000000000000000
χ718-8-88-8-88800008-8-2-22222-2-200000000-2-2220000000000000000000000000000000000000000
χ728-8-88-8-8880000-88-2-22222-2-20000000022-2-20000000000000000000000000000000000000000
χ738-8-8-8888-8000000-2222-2-22-20000000025−25−25250000000000000000000000000000000000000000
χ748-8-8-8888-8000000-2222-2-22-200000000−252525−250000000000000000000000000000000000000000

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