Finite Group Databasebeta

← Group #10598792

Character table — Group #10598792

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112244444444448888888888888820202020202020204040404040404040
order12442424510101020202020881010202040404040404040402244888888888888
χ11111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-1-11-11-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i1-11-1ii−i−i1-1i−i1-1i−i
χ1011-1-11-11-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i1-11-1ii−i−i-11−ii-11−ii
χ1111-1-11-11-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i-11-11−i−iiii−i-11−ii1-1
χ1211-1-11-11-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i-11-11−i−iii−ii1-1i−i-11
χ1311-1-11-11-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii1-11-1−i−iii1-1−ii1-1−ii
χ1411-1-11-11-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii1-11-1−i−iii-11i−i-11i−i
χ1511-1-11-11-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii-11-11ii−i−ii−i1-1−ii-11
χ1611-1-11-11-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii-11-11ii−i−i−ii-11i−i1-1
χ17222222-2-22222222200-2-2-2-2000000002-2-22000000000000
χ18222222-2-22222222200-2-2-2-200000000-222-2000000000000
χ1922-2-22-2-222222-2-2-2-200-2-2220000000022-2-2000000000000
χ2022-2-22-2-222222-2-2-2-200-2-22200000000-2-222000000000000
χ2144444444-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2244444444-1-1-1-1-1-1-1-1-4-4-1-1-1-1111111110000000000000000
χ23444444-4-4-1-1-1-1-1-1-1-100111155−5−555−5−50000000000000000
χ24444444-4-4-1-1-1-1-1-1-1-1001111−5−555−5−5550000000000000000
χ254444-4-4004-4-4444-4-4000000000000000000000000000000
χ264444-4-400-111-1-1-111005−55−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000
χ274444-4-400-111-1-1-111005−55−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000
χ284444-4-400-111-1-1-11100−55−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000
χ294444-4-400-111-1-1-11100−55−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000
χ3044-4-44-44-4-1-1-1-111114i−4i-1-111−i−i−i−iiiii0000000000000000
χ3144-4-44-44-4-1-1-1-11111−4i4i-1-111iiii−i−i−i−i0000000000000000
χ3244-4-44-4-44-1-1-1-111110011-1-1i5i5−i5−i5−i5−i5i5i50000000000000000
χ3344-4-44-4-44-1-1-1-111110011-1-1−i5−i5i5i5i5i5−i5−i50000000000000000
χ3444-4-4-44004-4-44-4-444000000000000000000000000000000
χ3544-4-4-4400-111-111-1-1005−5−55−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000
χ3644-4-4-4400-111-111-1-1005−5−55ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000
χ3744-4-4-4400-111-111-1-100−555−5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000
χ3844-4-4-4400-111-111-1-100−555−5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000
χ394-44i−4i0000400-44i−4i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ404-44i−4i0000400-44i−4i000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ414-4−4i4i0000400-4−4i4i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ424-4−4i4i0000400-4−4i4i000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ438-88i−8i0000-225−252−2i2i2i5−2i5000000000000000000000000000000
χ448-88i−8i0000-2−25252−2i2i−2i52i5000000000000000000000000000000
χ458-8−8i8i0000-225−2522i−2i−2i52i5000000000000000000000000000000
χ468-8−8i8i0000-2−252522i−2i2i5−2i5000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.