Finite Group Databasebeta

← Group #13015104

Character table — Group #13015104

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111114444444444444488888888888810101010101010101616161616161616161620202020404040404040404040404040404040408080
order12222222444444510101010101010202020202020202020202020444444444420202020202020204444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-11
χ101111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-11
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111-1
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11-1
χ131111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii1-1
χ141111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i1-1
χ151111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-11
χ161111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-11
χ1722222222-2-222-2-222222222-2-2-2-2-2-2-2-2222222-2-222-2-2000000000022-2-2000000000000000000
χ1822222222-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-222-2-2220000000000-2-222000000000000000000
χ1922222222-2-2-2-22222222222-2-2-2-22222-2-2-2-222-2-222-2-20000000000-2-222000000000000000000
χ2022222222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000022-2-2000000000000000000
χ21222-2-2-22-22-200002-2-2-222-2222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ22222-2-2-22-22-200002-2-2-222-2222-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ23222-2-2-22-22-200002-2-2-222-2222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ24222-2-2-22-22-200002-2-2-222-2222-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ25222-2-2-22-2-2200002-2-2-222-22-2-222000000002i−2i−2i2i2i−2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ26222-2-2-22-2-2200002-2-2-222-22-2-222000000002i−2i−2i2i2i−2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ27222-2-2-22-2-2200002-2-2-222-22-2-22200000000−2i2i2i−2i−2i2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ28222-2-2-22-2-2200002-2-2-222-22-2-22200000000−2i2i2i−2i−2i2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ292-2-22-2-22200002-2222-22-2-2-2000022-2-200002i−2i00−2i2i000000000000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ302-2-22-2-22200002-2222-22-2-2-2000022-2-200002i−2i00−2i2i000000000000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ312-2-22-2-22200002-2222-22-2-2-2000022-2-20000−2i2i002i−2i00000000000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ322-2-22-2-22200002-2222-22-2-2-2000022-2-20000−2i2i002i−2i00000000000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ332-2-22-2-2220000-22222-22-2-2-20000-2-22200002i−2i00−2i2i00000000000000−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00
χ342-2-22-2-2220000-22222-22-2-2-20000-2-22200002i−2i00−2i2i00000000000000−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00
χ352-2-22-2-2220000-22222-22-2-2-20000-2-2220000−2i2i002i−2i000000000000002i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00
χ362-2-22-2-2220000-22222-22-2-2-20000-2-2220000−2i2i002i−2i000000000000002i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00
χ3744444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-10000000000000000000000
χ3844444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-4111111110000000000000000000000
χ394444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-111111111000000004-41111-1-1-1-10000000000000000000000
χ404444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-44-1-1-1-111110000000000000000000000
χ4144444444-4-444-4-4-1-1-1-1-1-1-1-111111111-1-1-1-1000000000055−5−555−5−50000000000000000000000
χ4244444444-4-444-4-4-1-1-1-1-1-1-1-111111111-1-1-1-10000000000−5−555−5−5550000000000000000000000
χ4344444444-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-11111000000000055−5−5−5−5550000000000000000000000
χ4444444444-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-111110000000000−5−55555−5−50000000000000000000000
χ4544-444-4-4-400000044-44-44-4-40000000000000000000000000000004-400000000000000000000
χ4644-444-4-4-400000044-44-44-4-4000000000000000000000000000000-4400000000000000000000
χ4744-4-4-44-44004i−4i004-44-4-444-4000000004i4i−4i−4i0000000000000000000000000000000000000000
χ4844-4-4-44-44004i−4i00-11-111-1-115−55−5i5−i5i5−i5−i−iii0000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ4944-4-4-44-44004i−4i00-11-111-1-115−55−5i5−i5i5−i5−i−iii0000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ5044-4-4-44-44004i−4i00-11-111-1-11−55−55−i5i5−i5i5−i−iii0000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ5144-4-4-44-44004i−4i00-11-111-1-11−55−55−i5i5−i5i5−i−iii0000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ5244-4-4-44-4400−4i4i004-44-4-444-400000000−4i−4i4i4i0000000000000000000000000000000000000000
χ5344-4-4-44-4400−4i4i00-11-111-1-115−55−5−i5i5−i5i5ii−i−i0000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000
χ5444-4-4-44-4400−4i4i00-11-111-1-115−55−5−i5i5−i5i5ii−i−i0000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000
χ5544-4-4-44-4400−4i4i00-11-111-1-11−55−55i5−i5i5−i5ii−i−i0000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000
χ5644-4-4-44-4400−4i4i00-11-111-1-11−55−55i5−i5i5−i5ii−i−i0000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000
χ574-444-44-4-400000044-4-4-4-444000000000000004i−4i00−4i4i00000000000000000000000000000000
χ584-444-44-4-400000044-4-4-4-44400000000000000−4i4i004i−4i00000000000000000000000000000000
χ594-44-44-4-440000004-444-4-4-44000000000000004400-4-400000000000000000000000000000000
χ604-44-44-4-440000004-444-4-4-4400000000000000-4-4004400000000000000000000000000000000
χ614-4-4-4444-40000004-4-444-44-40000000000004400-4-40000000000000000000000000000000000
χ624-4-4-4444-40000004-4-444-44-4000000000000-4-400440000000000000000000000000000000000
χ63888-8-8-88-88-80000-2222-2-22-2-2-222000000000000000000000000000000000000000000000000
χ64888-8-8-88-8-880000-2222-2-22-222-2-2000000000000000000000000000000000000000000000000
χ6588-888-8-8-8000000-2-22-22-22225−25−2525000000000000000000000000000000000000000000000000
χ6688-888-8-8-8000000-2-22-22-222−252525−25000000000000000000000000000000000000000000000000
χ678-888-88-8-8000000-2-22222-2-20000000025−2525−250000000000000000000000000000000000000000
χ688-888-88-8-8000000-2-22222-2-200000000−2525−25250000000000000000000000000000000000000000
χ698-88-88-8-88000000-22-2-2222-200002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ708-88-88-8-88000000-22-2-2222-20000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ718-8-88-8-88800008-8-2-2-22-22220000-2-22200000000000000000000000000000000000000000000
χ728-8-88-8-8880000-88-2-2-22-2222000022-2-200000000000000000000000000000000000000000000
χ738-8-8-8888-8000000-222-2-22-22000000002i5−2i5−2i52i50000000000000000000000000000000000000000
χ748-8-8-8888-8000000-222-2-22-2200000000−2i52i52i5−2i50000000000000000000000000000000000000000

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