Finite Group Databasebeta

← Group #13020022

Character table — Group #13020022

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888888888881010101016202020202020323232324040404040404040404040404040808080
order12224444510101022882020202020204040404040404040444422488881010101044444488888888488
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111-1-1-1-11-1-1ii−i−i1111-1-1ii−i−i-1-1iii−i−i−i-1i−i
χ4111111111111111111111111111111-1-1-1-11-1-1−i−iii1111-1-1−i−iii-1-1−i−i−iiii-1−ii
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111-111111111-1-111-1-1-1-1-1-1111111-1-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11-1-1-1-1−i−iii11iii−i−i−i1−ii
χ811111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11-1-1-1-1ii−i−i11−i−i−iiii1i−i
χ9111111111111-1-111111111111111111111-1111111-1-1-1-1-1-11111111-1-11-1-1-1-1-1
χ10111111111111-1-111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-111
χ11111111111111-1-11111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1-111ii−i−i-1-1i−i−i−iii1−ii
χ12111111111111-1-11111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1-111−i−iii-1-1−iiii−i−i1i−i
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11-1-11-1-1111
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111-1-11111-1-1-111-1111-1-1
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1ii−i−i-1-11111−i−iii11i−i−i−iii-1i−i
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1−i−iii-1-11111ii−i−i11−iiii−i−i-1−ii
χ17222222-2-22222000022-2-2-2-20000000022220-2-22222000000000000-200-200000
χ18222222-2-22222000022-2-2-2-20000000022220-2-2-2-2-2-2000000000000200200000
χ19222222-2-22222000022-2-2-2-200000000-2-2-2-20222i2i−2i−2i000000000000−2i002i00000
χ20222222-2-22222000022-2-2-2-200000000-2-2-2-2022−2i−2i2i2i0000000000002i00−2i00000
χ212222-2-22-222220000-2-222-2-20000000022-2-20-22000000000000000002i−2i02i−2i000
χ222222-2-22-222220000-2-222-2-20000000022-2-20-2200000000000000000−2i2i0−2i2i000
χ232222-2-22-222220000-2-222-2-200000000-2-22202-2000000000000000002-20-22000
χ242222-2-22-222220000-2-222-2-200000000-2-22202-200000000000000000-2202-2000
χ252222-2-2-2222222-200-2-2-2-2220000000022-2-202-200002-2002-2000000000000000
χ262222-2-2-2222222-200-2-2-2-22200000000-2-2220-2200002-200-22000000000000000
χ272222-2-2-222222-2200-2-2-2-2220000000022-2-202-20000-2200-22000000000000000
χ282222-2-2-222222-2200-2-2-2-22200000000-2-2220-220000-22002-2000000000000000
χ2922-2-22-20022-2-2002−22-200002222−2−2−2−22i−2i2i−2i000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000001+i−1−i1−i−1+ii2−i2000000000
χ3022-2-22-20022-2-2002−22-200002222−2−2−2−22i−2i2i−2i0002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−1−i1+i−1+i1−ii2−i2000000000
χ3122-2-22-20022-2-2002−22-200002222−2−2−2−2−2i2i−2i2i000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−1+i1−i−1−i1+i−i2i2000000000
χ3222-2-22-20022-2-2002−22-200002222−2−2−2−2−2i2i−2i2i0002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000001−i−1+i1+i−1−i−i2i2000000000
χ3322-2-22-20022-2-200−222-20000−2−2−2−222222i−2i2i−2i000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−1−i1+i−1+i1−i−i2i2000000000
χ3422-2-22-20022-2-200−222-20000−2−2−2−222222i−2i2i−2i0002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000001+i−1−i1−i−1+i−i2i2000000000
χ3522-2-22-20022-2-200−222-20000−2−2−2−22222−2i2i−2i2i000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000001−i−1+i1+i−1−ii2−i2000000000
χ3622-2-22-20022-2-200−222-20000−2−2−2−22222−2i2i−2i2i0002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−1+i1−i−1−i1+ii2−i2000000000
χ3744444444-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-100004000000-1-1-1-100000000000000000
χ3844444444-1-1-1-144-4-4-1-1-1-1-1-1111111110000-4000000-1-11100000000000000000
χ3944444444-1-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4000000111100000000000000000
χ4044444444-1-1-1-1-4-4-4-4-1-1-1-1-1-1111111110000400000011-1-100000000000000000
χ414444-4-4-44-1-1-1-14-4001111-1-155−5−555−5−500000000000-115−500000000000000000
χ424444-4-4-44-1-1-1-14-4001111-1-1−5−555−5−55500000000000-11−5500000000000000000
χ434444-4-4-44-1-1-1-1-44001111-1-155−5−555−5−5000000000001-1−5500000000000000000
χ444444-4-4-44-1-1-1-1-44001111-1-1−5−555−5−555000000000001-15−500000000000000000
χ4544-4-4-440044-4-40000-440000000000004i−4i−4i4i0000000000000000000000000000
χ4644-4-4-440044-4-40000-44000000000000−4i4i4i−4i0000000000000000000000000000
χ47888888-8-8-2-2-2-20000-2-222220000000000000000000000000000000000000000
χ488888-8-88-8-2-2-2-2000022-2-2220000000000000000000000000000000000000000
χ4988-8-88-800-2-2220042−42-220000−2−2−2−2222200000000000000000000000000000000
χ5088-8-88-800-2-22200−4242-2200002222−2−2−2−200000000000000000000000000000000
χ5188-8-8-8800-2-22200002-200001010−10−10−10−10101000000000000000000000000000000000
χ5288-8-8-8800-2-22200002-20000−10−1010101010−10−1000000000000000000000000000000000
χ538-88-800008-88-800000000000000000000000000000000000000000000000000
χ548-88-80000-22-2200000025−2500−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ3900000000000000000000000000000000
χ558-88-80000-22-2200000025−2500ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ3900000000000000000000000000000000
χ568-88-80000-22-22000000−252500ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ3900000000000000000000000000000000
χ578-88-80000-22-22000000−252500−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ3900000000000000000000000000000000
χ588-8-8800008-8-8800000000000000000000000000000000000000000000000000
χ598-8-880000-222-20000000025−252ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000000
χ608-8-880000-222-20000000025−25−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000000
χ618-8-880000-222-200000000−2525−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000000
χ628-8-880000-222-200000000−25252ζ4−2ζ36−2ζ4+2ζ36−2ζ12+2ζ282ζ12−2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000000

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