Finite Group Databasebeta

← Group #13022806

Character table — Group #13022806

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12222244444444510101020202020444444881010202020202020202020202222442020202040404040444444444488888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1ii−i−i-1-1ii−i−iii−i−iii−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1−i−iii-1-1−i−iii−i−iii−i−iii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i11−i−iiiii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii11ii−i−i−i−iiiii−i−i
χ91111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1
χ101111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ121111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ131111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i11ii−i−i−i−iii−i−iii
χ141111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iii11−i−iiiii−i−iii−i−i
χ151111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−i-1-1−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii-1-1ii−i−iii−i−i−i−iii
χ17222222-2-2-2-200002222-2-2-2-22222000022-2-200000000-2-2-2-22200000000000000000000000000002-22-2
χ18222222-2-2-2-200002222-2-2-2-22222000022-2-200000000-2-2-2-2220000000000000000000000000000-22-22
χ19222222-2-2-2-200002222-2-2-2-2-2-2-2-2000022-2-2000000002222-2-200000000000000000000000000002i−2i−2i2i
χ20222222-2-2-2-200002222-2-2-2-2-2-2-2-2000022-2-2000000002222-2-20000000000000000000000000000−2i2i2i−2i
χ212222-2-222-2-200002222-2-2-2-222222-200-2-222000000002-2-22-2-222-2-2000000002-2000000000000000000
χ222222-2-222-2-200002222-2-2-2-22222-2200-2-222000000002-2-22-2-2-2-22200000000-22000000000000000000
χ232222-2-222-2-200002222-2-2-2-2-2-2-2-22-200-2-22200000000-222-22222-2-200000000-22000000000000000000
χ242222-2-222-2-200002222-2-2-2-2-2-2-2-2-2200-2-22200000000-222-222-2-222000000002-2000000000000000000
χ252222-2-2-2-22200002222222222220000-2-2-2-200000000-222-2-2-20000000000000000000000002-22-20000
χ262222-2-2-2-22200002222222222220000-2-2-2-200000000-222-2-2-2000000000000000000000000-22-220000
χ272222-2-2-2-222000022222222-2-2-2-20000-2-2-2-2000000002-2-22220000000000000000000000002i−2i−2i2i0000
χ282222-2-2-2-222000022222222-2-2-2-20000-2-2-2-2000000002-2-2222000000000000000000000000−2i2i2i−2i0000
χ2922-2-22-22-22-2000022-2-222-2-222-2-200002-22-20000000022-2-22-2000000000000000000002-22-200000000
χ3022-2-22-22-22-2000022-2-222-2-222-2-200002-22-20000000022-2-22-200000000000000000000-22-2200000000
χ3122-2-22-22-22-2000022-2-222-2-2-2-22200002-22-200000000-2-222-22000000000000000000002i−2i−2i2i00000000
χ3222-2-22-22-22-2000022-2-222-2-2-2-22200002-22-200000000-2-222-2200000000000000000000−2i2i2i−2i00000000
χ3322-2-22-2-22-222i2i−2i−2i22-2-2-2-22222-2-200002-2-222i2i2i2i−2i−2i−2i−2i-2-2222-2000000002i2i−2i−2i00000000000000000000
χ3422-2-22-2-22-222i2i−2i−2i22-2-2-2-222-2-22200002-2-222i2i2i2i−2i−2i−2i−2i22-2-2-2200000000−2i−2i2i2i00000000000000000000
χ3522-2-22-2-22-22−2i−2i2i2i22-2-2-2-22222-2-200002-2-22−2i−2i−2i−2i2i2i2i2i-2-2222-200000000−2i−2i2i2i00000000000000000000
χ3622-2-22-2-22-22−2i−2i2i2i22-2-2-2-222-2-22200002-2-22−2i−2i−2i−2i2i2i2i2i22-2-2-22000000002i2i−2i−2i00000000000000000000
χ3722-2-2-222-2-22000022-2-2-2-22222-2-20000-222-2000000002-22-2-22000000000000002i−2i2i−2i00000000000000
χ3822-2-2-222-2-22000022-2-2-2-22222-2-20000-222-2000000002-22-2-2200000000000000−2i2i−2i2i00000000000000
χ3922-2-2-222-2-22000022-2-2-2-222-2-2220000-222-200000000-22-222-2000000000000002-2-2200000000000000
χ4022-2-2-222-2-22000022-2-2-2-222-2-2220000-222-200000000-22-222-200000000000000-222-200000000000000
χ4122-2-2-22-222-2000022-2-222-2-222-2-2002i−2i-22-2200000000-22-22-2200002i2i−2i−2i00000000002i−2i000000000000
χ4222-2-2-22-222-2000022-2-222-2-222-2-200−2i2i-22-2200000000-22-22-220000−2i−2i2i2i0000000000−2i2i000000000000
χ4322-2-2-22-222-2000022-2-222-2-2-2-222002i−2i-22-22000000002-22-22-200002i2i−2i−2i0000000000−2i2i000000000000
χ4422-2-2-22-222-2000022-2-222-2-2-2-22200−2i2i-22-22000000002-22-22-20000−2i−2i2i2i00000000002i−2i000000000000
χ4544444444444444-1-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ494444-4-444-4-40000-1-1-1-1111100004-40011-1-1i5i5−i5−i5i5i5−i5−i5000000-1-111i5−i5i5−i5000000000000000000000000
χ504444-4-444-4-40000-1-1-1-1111100004-40011-1-1−i5−i5i5i5−i5−i5i5i5000000-1-111−i5i5−i5i5000000000000000000000000
χ514444-4-444-4-40000-1-1-1-111110000-440011-1-1i5i5−i5−i5i5i5−i5−i500000011-1-1−i5i5−i5i5000000000000000000000000
χ524444-4-444-4-40000-1-1-1-111110000-440011-1-1−i5−i5i5i5−i5−i5i5i500000011-1-1i5−i5i5−i5000000000000000000000000
χ5344-4-44-4-44-444i4i−4i−4i-1-11111-1-100000000-111-1−i−i−i−iiiii000000i5−i5i5−i55−5−55000000000000000000000000
χ5444-4-44-4-44-444i4i−4i−4i-1-11111-1-100000000-111-1−i−i−i−iiiii000000−i5i5−i5i5−555−5000000000000000000000000
χ5544-4-44-4-44-44−4i−4i4i4i-1-11111-1-100000000-111-1iiii−i−i−i−i000000i5−i5i5−i5−555−5000000000000000000000000
χ5644-4-44-4-44-44−4i−4i4i4i-1-11111-1-100000000-111-1iiii−i−i−i−i000000−i5i5−i5i55−5−55000000000000000000000000
χ5744-4-4-44-444-40000-1-111-1-1110000004i−4i1-11-155−5−5−5−555000000−i5i5i5−i5−i−iii000000000000000000000000
χ5844-4-4-44-444-40000-1-111-1-1110000004i−4i1-11-1−5−55555−5−5000000i5−i5−i5i5−i−iii000000000000000000000000
χ5944-4-4-44-444-40000-1-111-1-111000000−4i4i1-11-155−5−5−5−555000000i5−i5−i5i5ii−i−i000000000000000000000000
χ6044-4-4-44-444-40000-1-111-1-111000000−4i4i1-11-1−5−55555−5−5000000−i5i5i5−i5ii−i−i000000000000000000000000
χ614-44-40000002-22-24-44-400004i−4i4i−4i000000002-22-22-22-2000000000000002i−2i2i−2i00000000000000000000
χ624-44-40000002-22-24-44-40000−4i4i−4i4i000000002-22-22-22-200000000000000−2i2i−2i2i00000000000000000000
χ634-44-4000000-22-224-44-400004i−4i4i−4i00000000-22-22-22-2200000000000000−2i2i−2i2i00000000000000000000
χ644-44-4000000-22-224-44-40000−4i4i−4i4i00000000-22-22-22-22000000000000002i−2i2i−2i00000000000000000000
χ654-4-440000002i−2i−2i2i4-4-4400004i−4i−4i4i000000002i−2i2i−2i−2i2i−2i2i00000000000000-222-200000000000000000000
χ664-4-440000002i−2i−2i2i4-4-440000−4i4i4i−4i000000002i−2i2i−2i−2i2i−2i2i000000000000002-2-2200000000000000000000
χ674-4-44000000−2i2i2i−2i4-4-4400004i−4i−4i4i00000000−2i2i−2i2i2i−2i2i−2i000000000000002-2-2200000000000000000000
χ684-4-44000000−2i2i2i−2i4-4-440000−4i4i4i−4i00000000−2i2i−2i2i2i−2i2i−2i00000000000000-222-200000000000000000000
χ69888888-8-8-8-80000-2-2-2-2222200000000-2-2220000000000000000000000000000000000000000000000
χ708888-8-8-8-8880000-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000000000
χ7188-8-88-88-88-80000-2-222-2-22200000000-22-220000000000000000000000000000000000000000000000
χ7288-8-8-888-8-880000-2-22222-2-2000000002-2-220000000000000000000000000000000000000000000000
χ738-88-80000004-44-4-22-222i5−2i52i5−2i5000000000000−1+i51−i5−1−i51+i5−1+i51−i5−1−i51+i500000000000000000000000000000000000000
χ748-88-80000004-44-4-22-22−2i52i5−2i52i5000000000000−1−i51+i5−1+i51−i5−1−i51+i5−1+i51−i500000000000000000000000000000000000000
χ758-88-8000000-44-44-22-222i5−2i52i5−2i50000000000001−i5−1+i51+i5−1−i51−i5−1+i51+i5−1−i500000000000000000000000000000000000000
χ768-88-8000000-44-44-22-22−2i52i5−2i52i50000000000001+i5−1−i51−i5−1+i51+i5−1−i51−i5−1+i500000000000000000000000000000000000000
χ778-8-880000004i−4i−4i4i-222-22i5−2i5−2i52i5000000000000ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ1900000000000000000000000000000000000000
χ788-8-880000004i−4i−4i4i-222-2−2i52i52i5−2i5000000000000−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ1900000000000000000000000000000000000000
χ798-8-88000000−4i4i4i−4i-222-22i5−2i5−2i52i5000000000000−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ1900000000000000000000000000000000000000
χ808-8-88000000−4i4i4i−4i-222-2−2i52i52i5−2i5000000000000ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ1900000000000000000000000000000000000000

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