Finite Group Databasebeta

← Group #10604374

Character table — Group #10604374

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1111222244444444444445555888888888888101010102020202020202020202020202040404040
order12224444244445101010202020202222101020202020202020202020444424444888888884444
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
χ5111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ6111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-111-111-1-111-1-111-1-11-11-1
χ10111111-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-111-111-1-1-1-111-1-111-11-11
χ11111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-111ii−i−i−i−iiii−i−ii
χ12111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-111−i−iiiii−i−i−iii−i
χ13111111-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-11111-1-111-1-1-11-11
χ14111111-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-111-1-111-1-1111-11-1
χ15111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ172222-2-222-20000222222222222-2-2-2-20000000022-2-2-20000000000000000
χ182222-2-222-2000022222222-2-2-2-2-2-2-2-200000000-2-22220000000000000000
χ192222-2-2-2-2200002222-2-2-2-2222222-2-200000000-2-2-2-220000000000000000
χ202222-2-2-2-2200002222-2-2-2-2-2-2-2-222-2-2000000002222-20000000000000000
χ2122-2-2002i−2i0000022-2-22i2i−2i−2i2-22-20000000000002i−2i0000000i2−i22−2i2−i22−20000
χ2222-2-2002i−2i0000022-2-22i2i−2i−2i2-22-20000000000002i−2i0000000−i2i2−22−i2i2−220000
χ2322-2-2002i−2i0000022-2-22i2i−2i−2i-22-22000000000000−2i2i00000002−2−i2i2−22i2−i20000
χ2422-2-2002i−2i0000022-2-22i2i−2i−2i-22-22000000000000−2i2i0000000−22i2−i22−2−i2i20000
χ2522-2-200−2i2i0000022-2-2−2i−2i2i2i2-22-2000000000000−2i2i0000000i2−i2−22i2−i2−220000
χ2622-2-200−2i2i0000022-2-2−2i−2i2i2i2-22-2000000000000−2i2i0000000−i2i22−2−i2i22−20000
χ2722-2-200−2i2i0000022-2-2−2i−2i2i2i-22-220000000000002i−2i00000002−2i2−i2−22−i2i20000
χ2822-2-200−2i2i0000022-2-2−2i−2i2i2i-22-220000000000002i−2i0000000−22−i2i22−2i2−i20000
χ292-22-22-2000002i−2i2-22-200002-2-22002-200002i2i−2i−2i002-20002i−2i000000000000
χ302-22-22-2000002i−2i2-22-20000-222-2002-200002i2i−2i−2i00-22000−2i2i000000000000
χ312-22-22-200000−2i2i2-22-200002-2-22002-20000−2i−2i2i2i002-2000−2i2i000000000000
χ322-22-22-200000−2i2i2-22-20000-222-2002-20000−2i−2i2i2i00-220002i−2i000000000000
χ332-22-2-220002i−2i002-22-200002-2-2200-222i2i−2i−2i000000-2202i−2i00000000000000
χ342-22-2-220002i−2i002-22-20000-222-200-222i2i−2i−2i0000002-20−2i2i00000000000000
χ352-22-2-22000−2i2i002-22-200002-2-2200-22−2i−2i2i2i000000-220−2i2i00000000000000
χ362-22-2-22000−2i2i002-22-20000-222-200-22−2i−2i2i2i0000002-202i−2i00000000000000
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
χ39444444-4-4-444-4-4-1-1-1-11111000011-1-1-1-1-1-11111000000000000000000000
χ40444444-4-4-4-4-444-1-1-1-11111000011-1-11111-1-1-1-1000000000000000000000
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
χ434444-4-4-4-440000-1-1-1-111110000-1-1115−55−5−55−55000000000000000000000
χ444444-4-4-4-440000-1-1-1-111110000-1-111−55−555−55−5000000000000000000000
χ454-44-44-4000004i−4i-11-115−55−500005−5-11i5−i5−i5i5−i−iii000000000000000000000
χ464-44-44-4000004i−4i-11-11−55−550000−55-11−i5i5i5−i5−i−iii000000000000000000000
χ474-44-44-400000−4i4i-11-115−55−500005−5-11−i5i5i5−i5ii−i−i000000000000000000000
χ484-44-44-400000−4i4i-11-11−55−550000−55-11i5−i5−i5i5ii−i−i000000000000000000000
χ494-44-4-440004i−4i00-11-115−55−50000−551-1−i−iiii5−i5−i5i5000000000000000000000
χ504-44-4-440004i−4i00-11-11−55−5500005−51-1−i−iii−i5i5i5−i5000000000000000000000
χ514-44-4-44000−4i4i00-11-115−55−50000−551-1ii−i−i−i5i5i5−i5000000000000000000000
χ524-44-4-44000−4i4i00-11-11−55−5500005−51-1ii−i−ii5−i5−i5i5000000000000000000000
χ534-4-440000000004-4-44000044-4-4000000000000000000000000000000000
χ544-4-440000000004-4-440000-4-444000000000000000000000000000000000
χ5588-8-8008i−8i00000-2-222−2i−2i2i2i0000000000000000000000000000000000000
χ5688-8-800−8i8i00000-2-2222i2i−2i−2i0000000000000000000000000000000000000
χ578-8-88000000000-222-22i5−2i5−2i52i50000000000000000000000000000000000000
χ588-8-88000000000-222-2−2i52i52i5−2i50000000000000000000000000000000000000

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