Finite Group Databasebeta

← Group #13026913

Character table — Group #13026913

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1124444444558888881016161616161616161620202020202020202020202020323232404040404040408080808080
order12222444510442441020204810101010202020202444488888888204040224888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1
χ3111111111111-11-11111-111-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1
χ4111111111111-11-11111-111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-11111
χ51111111111-1-1111111-1111111111-1-1-1-1-1iiii−i−i−i−i111-1-1-1ii−i−i-1ii−i−i
χ61111111111-1-1111111-1111111111-1-1-1-1-1−i−i−i−iiiii111-1-1-1−i−iii-1−i−iii
χ71111111111-1-1-11-1111-1-111-1-1-1-111-1-1-1-1-1iiii−i−i−i−i1-1-1-111ii−i−i1−i−iii
χ81111111111-1-1-11-1111-1-111-1-1-1-111-1-1-1-1-1−i−i−i−iiiii1-1-1-111−i−iii1ii−i−i
χ911111-1-1111111-111111-1111111-1-11-1-11111-1-111-1-1-1-1-1-1111-11-1-11-11-1
χ1011111-1-1111111-111111-1111111-1-11-1-111-1-111-1-111-1-1-1-111-11-11-1-11-11
χ1111111-1-111111-1-1-11111111-1-1-1-1-1-11-1-11111-1-111-1-1-111-1-1-11-11-11-11-11
χ1211111-1-111111-1-1-11111111-1-1-1-1-1-11-1-111-1-111-1-111-111-1-1-1-11-1111-11-1
χ1311111-1-1111-1-11-11111-1-1111111-1-1-111-1-1ii−i−i−i−iii-1-1-11-1-1i−i−ii1i−i−ii
χ1411111-1-1111-1-11-11111-1-1111111-1-1-111-1-1−i−iiiii−i−i-1-1-11-1-1−iii−i1−iii−i
χ1511111-1-1111-1-1-1-1-1111-1111-1-1-1-1-1-1-111-1-1ii−i−i−i−iii-111111i−i−ii-1−iii−i
χ1611111-1-1111-1-1-1-1-1111-1111-1-1-1-1-1-1-111-1-1−i−iiiii−i−i-111111−iii−i-1i−i−ii
χ172222-200-222220002-2-2202-2000000-2002-2002200220000000-20-200000
χ182222-200-222220002-2-2202-2000000-2002-200-2-200-2-2000000020200000
χ192222-200-222-2-20002-2-2-202-2000000200-22002i2i00−2i−2i0000000−2i02i00000
χ202222-200-222-2-20002-2-2-202-2000000200-2200−2i−2i002i2i00000002i0−2i00000
χ21222-2200-222220002-2-220-22000000-200-2222002200000000-20-2000000
χ22222-2200-222220002-2-220-22000000-200-22-2-200-2-200000000202000000
χ23222-2200-222-2-20002-2-2-20-220000002002-22i2i00−2i−2i00000000−2i02i000000
χ24222-2200-222-2-20002-2-2-20-220000002002-2−2i−2i002i2i000000002i0−2i000000
χ25222-2-222222220-2022220-2-2000022222-2-200000000-200-200000000000
χ26222-2-222222-2-20-20222-20-2-2000022-2-2-22200000000-200200000000000
χ27222-2-2-2-22222202022220-2-20000-2-22-2-2-2-200000000200200000000000
χ28222-2-2-2-2222-2-2020222-20-2-20000-2-2-2222200000000200-200000000000
χ2944444444-1-100444-1-1-104-1-1-1-1-1-1-1-10000000000000-1-1-1000000000000
χ3044444444-1-100-44-4-1-1-10-4-1-11111-1-10000000000000-111000000000000
χ3144444-4-44-1-1004-44-1-1-10-4-1-1-1-1-1-1110000000000000111000000000000
χ3244444-4-44-1-100-4-4-4-1-1-104-1-111111100000000000001-1-1000000000000
χ33444-4-4444-1-1000-40-1-1-100115−55−5-1-1000000000000015−5000000000000
χ34444-4-4444-1-1000-40-1-1-10011−55−55-1-100000000000001−55000000000000
χ35444-4-4-4-44-1-100040-1-1-100115−55−5110000000000000-1−55000000000000
χ36444-4-4-4-44-1-100040-1-1-10011−55−55110000000000000-15−5000000000000
χ3744-400000444420-2-400-400022-2-20000000000000000000-22000000000
χ3844-4000004444-202-400-4000-2-22200000000000000000002-2000000000
χ3944-40000044-4-420-2-400400022-2-200000000000000000002-2000000000
χ4044-40000044-4-4-202-4004000-2-2220000000000000000000-22000000000
χ414-40002i−2i04-44i−4i000000000000002i−2i02-200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ424-40002i−2i04-44i−4i000000000000002i−2i02-2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ434-40002i−2i04-4−4i4i000000000000002i−2i0-2200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ444-40002i−2i04-4−4i4i000000000000002i−2i0-22002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ454-4000−2i2i04-44i−4i00000000000000−2i2i0-2200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ464-4000−2i2i04-44i−4i00000000000000−2i2i0-22002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ474-4000−2i2i04-4−4i4i00000000000000−2i2i02-200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ484-4000−2i2i04-4−4i4i00000000000000−2i2i02-2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ498888-800-8-2-200000-22200-220000000000000000000000000000000000
χ50888-8800-8-2-200000-222002-20000000000000000000000000000000000
χ5188-800000-2-20040-4225−250000−1+5−1−51−51+5000000000000000000000000000000
χ5288-800000-2-20040-42−25250000−1−5−1+51+51−5000000000000000000000000000000
χ5388-800000-2-200-404225−2500001−51+5−1+5−1−5000000000000000000000000000000
χ5488-800000-2-200-4042−252500001+51−5−1−5−1+5000000000000000000000000000000
χ5516-160008i−8i0-440000000000000000−2i2i0000000000000000000000000000
χ5616-16000−8i8i0-4400000000000000002i−2i0000000000000000000000000000

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