Finite Group Databasebeta

← Group #13018326

Character table — Group #13018326

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222244444444444444444444888888888888888888888888888810101010202020202020404040408080808080808080
order12224488882458810101020202020404040404040404024881010101010102020202020204040404040404040404040402244248888448844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-11-11-11-1
χ10111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11-11-11-11
χ11111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111i−i−iii−i−ii
χ12111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−iii−i−iii−i
χ13111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-11-1-11-11
χ14111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-11-111-11-1
χ15111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1−iii−ii−i−ii
χ172222222222-2-22-2-22222222222222220000-2-20000-2-20000-2-2-2-20000000022-2-2-2222-2-2000000000000
χ182222222222-2-22-2-22222222222222220000-2-20000-2-20000-2-2-2-200000000-2-2222-2-2-222000000000000
χ19222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-20000-2-2000022220000000022-2-2-22-2-222000000000000
χ20222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-20000-2-20000222200000000-2-2222-222-2-2000000000000
χ212222-2-200002-2200222-2-2-2-200000000002i−2i220000-2-2000000002i2i2i2i−2i−2i−2i−2i22-2-22-20000002i−2i00000000
χ222222-2-200002-2200222-2-2-2-200000000002i−2i220000-2-2000000002i2i2i2i−2i−2i−2i−2i-2-222-22000000−2i2i00000000
χ232222-2-200002-2200222-2-2-2-20000000000−2i2i220000-2-200000000−2i−2i−2i−2i2i2i2i2i22-2-22-2000000−2i2i00000000
χ242222-2-200002-2200222-2-2-2-20000000000−2i2i220000-2-200000000−2i−2i−2i−2i2i2i2i2i-2-222-220000002i−2i00000000
χ252222-2-20000-22200222-2-2-2-2000000002-200-2-2222222-2-2-2-20000000000002222-2-200002-20000000000
χ262222-2-20000-22200222-2-2-2-2000000002-200-2-2222222-2-2-2-2000000000000-2-2-2-2220000-220000000000
χ272222-2-20000-22200222-2-2-2-200000000-2200-2-2-2-2-2-22222220000000000002222-2-20000-220000000000
χ282222-2-20000-22200222-2-2-2-200000000-2200-2-2-2-2-2-2222222000000000000-2-2-2-22200002-20000000000
χ29444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ30444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-11111-1-11111-1-1-1-1111111110000000000000000000000
χ314444444444-4-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001155−5−51155−5−5111155−5−555−5−50000000000000000000000
χ324444444444-4-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011−5−55511−5−5551111−5−555−5−5550000000000000000000000
χ33444444-4-4-4-444-1-4-4-1-1-1-1-1-1-11111111144-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000
χ34444444-4-4-4-444-1-4-4-1-1-1-1-1-1-111111111-4-444-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000000000
χ35444444-4-4-4-4-4-4-144-1-1-1-1-1-1-11111111100001155−5−51155−5−5-1-1-1-1−5−555−5−5550000000000000000000000
χ36444444-4-4-4-4-4-4-144-1-1-1-1-1-1-111111111000011−5−55511−5−555-1-1-1-155−5−555−5−50000000000000000000000
χ374444-4-400004-4-100-1-1-11111i5i5i5i5−i5−i5−i5−i5004i−4i-1-155−5−511−5−555i5i5−i5−i5−i−i−i−iiiii0000000000000000000000
χ384444-4-400004-4-100-1-1-11111i5i5i5i5−i5−i5−i5−i500−4i4i-1-1−5−5551155−5−5i5i5−i5−i5iiii−i−i−i−i0000000000000000000000
χ394444-4-400004-4-100-1-1-11111−i5−i5−i5−i5i5i5i5i5004i−4i-1-1−5−5551155−5−5−i5−i5i5i5−i−i−i−iiiii0000000000000000000000
χ404444-4-400004-4-100-1-1-11111−i5−i5−i5−i5i5i5i5i500−4i4i-1-155−5−511−5−555−i5−i5i5i5iiii−i−i−i−i0000000000000000000000
χ414444-4-40000-44-100-1-1-11111i5i5i5i5−i5−i5−i5−i54-40011-1-1-1-1-1-11111−i5−i5i5i5i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ424444-4-40000-44-100-1-1-11111i5i5i5i5−i5−i5−i5−i5-4400111111-1-1-1-1-1-1−i5−i5i5i5−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ434444-4-40000-44-100-1-1-11111−i5−i5−i5−i5i5i5i5i54-40011-1-1-1-1-1-11111i5i5−i5−i5−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ444444-4-40000-44-100-1-1-11111−i5−i5−i5−i5i5i5i5i5-4400111111-1-1-1-1-1-1i5i5−i5−i5i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ4544-4-4002i22i2−2i2−2i2004004-4-400002i22i2−2i2−2i22i22i2−2i2−2i20000000000000000000000000000004i−4i000022−22000000000000
χ4644-4-4002i22i2−2i2−2i2004004-4-400002i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000000000000000−4i4i0000−2222000000000000
χ4744-4-400−2i2−2i22i22i2004004-4-40000−2i2−2i22i22i2−2i2−2i22i22i20000000000000000000000000000004i−4i0000−2222000000000000
χ4844-4-400−2i2−2i22i22i2004004-4-40000−2i2−2i22i22i2−2i2−2i22i22i2000000000000000000000000000000−4i4i000022−22000000000000
χ494-44-4002i2−2i22i2−2i200400-44-400002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000004-400002i2−2i200000000000000
χ504-44-4002i2−2i22i2−2i200400-44-400002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000-440000−2i22i200000000000000
χ514-44-400−2i22i2−2i22i200400-44-40000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000004-40000−2i22i200000000000000
χ524-44-400−2i22i2−2i22i200400-44-40000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000-4400002i2−2i200000000000000
χ534-4-444-400000044i−4i-4-4444-4-40000000000000000000000004i−4i4i−4i000000000000000000000000000000
χ544-4-444-40000004−4i4i-4-4444-4-4000000000000000000000000−4i4i−4i4i000000000000000000000000000000
χ554-4-444-4000000-14i−4i11-1-1-111i5−i5−i5i5−i5i5i5−i500005−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ii−iiζ6−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−ζ380000000000000000000000
χ564-4-444-4000000-14i−4i11-1-1-111i5−i5−i5i5−i5i5i5−i500005−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ii−ii−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+ζ380000000000000000000000
χ574-4-444-4000000-14i−4i11-1-1-111−i5i5i5−i5i5−i5−i5i50000−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ii−ii−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+ζ380000000000000000000000
χ584-4-444-4000000-14i−4i11-1-1-111−i5i5i5−i5i5−i5−i5i50000−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ii−iiζ6−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−ζ380000000000000000000000
χ594-4-444-4000000-1−4i4i11-1-1-111i5−i5−i5i5−i5i5i5−i50000−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−55−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36i−ii−iζ6−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−ζ380000000000000000000000
χ604-4-444-4000000-1−4i4i11-1-1-111i5−i5−i5i5−i5i5i5−i50000−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−55ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36i−ii−i−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+ζ380000000000000000000000
χ614-4-444-4000000-1−4i4i11-1-1-111−i5i5i5−i5i5−i5−i5i500005−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36i−ii−i−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+ζ380000000000000000000000
χ624-4-444-4000000-1−4i4i11-1-1-111−i5i5i5−i5i5−i5−i5i500005−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36i−ii−iζ6−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−ζ380000000000000000000000
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χ724-4-44-44-444-400-10011-111-1-11-1-111-1-110000−55ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ365−5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ365−5−55ζ4−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−ζ360000000000000000000000
χ7388-8-8004i24i2−4i2−4i200-200-2222i5−2i52i5−2i52ζ7+2ζ21+2ζ23+2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000000000000000000000
χ7488-8-8004i24i2−4i2−4i200-200-222−2i52i5−2i52i52ζ13+2ζ31+2ζ37+2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000000000000000000000
χ7588-8-800−4i2−4i24i24i200-200-2222i5−2i52i5−2i5−2ζ7−2ζ21−2ζ23−2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000000000000000000000
χ7688-8-800−4i2−4i24i24i200-200-222−2i52i5−2i52i5−2ζ13−2ζ31−2ζ37−2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000000000000000000000
χ778-88-8004i2−4i24i2−4i200-2002-222i5−2i5−2i52i52ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ2900000000000000000000000000000000000000000000000000
χ788-88-8004i2−4i24i2−4i200-2002-22−2i52i52i5−2i52ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ3900000000000000000000000000000000000000000000000000
χ798-88-800−4i24i2−4i24i200-2002-222i5−2i5−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ2900000000000000000000000000000000000000000000000000
χ808-88-800−4i24i2−4i24i200-2002-22−2i52i52i5−2i5−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ3900000000000000000000000000000000000000000000000000

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