Finite Group Databasebeta

← Group #10604456

Character table — Group #10604456

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1111222244444444444445555888888888888101010102020202020202020202020202040404040
order12224444444445101010202020204444202020202020202020202020224422444444444448888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-1
χ6111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111
χ7111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111iiii−i−i−i−i−i−iii
χ8111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111−i−i−i−iiiiiii−i−i
χ9111111-1-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-1-111-1-111-1-11-11-1
χ10111111-1-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-1-1-1-111-1-111-11-11
χ11111111-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111ii−i−i−i−iiii−i−ii
χ12111111-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111−i−iiiii−i−i−iii−i
χ13111111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-1-11-11
χ14111111-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111-1-111-1-1111-11-1
χ15111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1−i−iiiii−i−ii−i−ii
χ172222-2-222-20000222222222222-2-2-2-200000000-2-22200-200000000000000
χ182222-2-222-2000022222222-2-2-2-2-2-2-2-20000000022-2-200200000000000000
χ192222-2-2-2-2200002222-2-2-2-22222-2-22200000000-2-2-2-200200000000000000
χ202222-2-2-2-2200002222-2-2-2-2-2-2-2-2-2-22200000000222200-200000000000000
χ2122-2-2002i−2i000002-22-22i2i−2i−2i2i−2i2i−2i000000000000002-2000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ2222-2-2002i−2i000002-22-22i2i−2i−2i2i−2i2i−2i000000000000002-200000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ2322-2-2002i−2i000002-22-22i2i−2i−2i−2i2i−2i2i00000000000000-22000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ2422-2-2002i−2i000002-22-22i2i−2i−2i−2i2i−2i2i00000000000000-2200000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ2522-2-200−2i2i000002-22-2−2i−2i2i2i2i−2i2i−2i00000000000000-22000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ2622-2-200−2i2i000002-22-2−2i−2i2i2i2i−2i2i−2i00000000000000-2200000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ2722-2-200−2i2i000002-22-2−2i−2i2i2i−2i2i−2i2i000000000000002-2000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ2822-2-200−2i2i000002-22-2−2i−2i2i2i−2i2i−2i2i000000000000002-200000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ292-22-22-2000002i−2i2-2-22000022-2-22-20000002i2i−2i−2i-22000002i−2i000000000000
χ302-22-22-2000002i−2i2-2-220000-2-2222-20000002i2i−2i−2i2-200000−2i2i000000000000
χ312-22-22-200000−2i2i2-2-22000022-2-22-2000000−2i−2i2i2i-2200000−2i2i000000000000
χ322-22-22-200000−2i2i2-2-220000-2-2222-2000000−2i−2i2i2i2-2000002i−2i000000000000
χ332-22-2-220002-2002-2-22000022-2-2-220022-2-200002-2002-2000000000000000
χ342-22-2-220002-2002-2-220000-2-222-220022-2-20000-2200-22000000000000000
χ352-22-2-22000-22002-2-22000022-2-2-2200-2-22200002-200-22000000000000000
χ362-22-2-22000-22002-2-220000-2-222-2200-2-2220000-22002-2000000000000000
χ374444444444444-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ38444444444-4-4-4-4-1-1-1-1-1-1-1-10000-1-1-1-111111111000000000000000000000
χ39444444-4-4-444-4-4-1-1-1-111110000-1-111-1-1-1-11111000000000000000000000
χ40444444-4-4-4-4-444-1-1-1-111110000-1-1111111-1-1-1-1000000000000000000000
χ414444-4-444-40000-1-1-1-1-1-1-1-1000011115−55−55−55−5000000000000000000000
χ424444-4-444-40000-1-1-1-1-1-1-1-100001111−55−55−55−55000000000000000000000
χ434444-4-4-4-440000-1-1-1-11111000011-1-15−55−5−55−55000000000000000000000
χ444444-4-4-4-440000-1-1-1-11111000011-1-1−55−555−55−5000000000000000000000
χ454-44-44-4000004i−4i-111-1i5−i5i5−i50000-11i5−i55−5−55−i−iii000000000000000000000
χ464-44-44-4000004i−4i-111-1−i5i5−i5i50000-11−i5i5−555−5−i−iii000000000000000000000
χ474-44-44-400000−4i4i-111-1i5−i5i5−i50000-11i5−i5−555−5ii−i−i000000000000000000000
χ484-44-44-400000−4i4i-111-1−i5i5−i5i50000-11−i5i55−5−55ii−i−i000000000000000000000
χ494-44-4-440004-400-111-1i5−i5i5−i500001-1−i5i5-1-111i5−i5−i5i5000000000000000000000
χ504-44-4-440004-400-111-1−i5i5−i5i500001-1i5−i5-1-111−i5i5i5−i5000000000000000000000
χ514-44-4-44000-4400-111-1i5−i5i5−i500001-1−i5i511-1-1−i5i5i5−i5000000000000000000000
χ524-44-4-44000-4400-111-1−i5i5−i5i500001-1i5−i511-1-1i5−i5−i5i5000000000000000000000
χ534-4-4400000000044-4-400004i−4i−4i4i000000000000000000000000000000000
χ544-4-4400000000044-4-40000−4i4i4i−4i000000000000000000000000000000000
χ5588-8-8008i−8i00000-22-22−2i−2i2i2i0000000000000000000000000000000000000
χ5688-8-800−8i8i00000-22-222i2i−2i−2i0000000000000000000000000000000000000
χ578-8-88000000000-2-22225−25−25250000000000000000000000000000000000000
χ588-8-88000000000-2-222−252525−250000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).