Finite Group Databasebeta

← Group #13017861

Character table — Group #13017861

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888881010101016161616161616161616161620202020202040404040404040404040404080808080
order12224424510101022444410102020202022441010101020202020202020202224444444444488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ51111111111111-1-1-11-1111111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111-1-1-11-1111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−i
χ81111111111111-1-1-11-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii
χ9111111111111-11-1-1-111111111111-1-111-1-1-1-1-1-111-1-11-1-1111-1-111111111-1-1-1-1
χ10111111111111-11-1-1-111111111111-1-111-1-1-1-1-1-111-1-11-1-1111-1-1-1-1-1-1-1-1-1-11111
χ11111111111111-11-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-1-111ii−i−iii−i−i−ii−ii
χ12111111111111-11-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-1-111−i−iii−i−iiii−ii−i
χ13111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-111-1-1
χ14111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-111
χ15111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-1ii−i−i−i−iiii−i−ii
χ16111111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-1−i−iiiii−i−i−iii−i
χ17222222-2-222222000-20-2-222-2-222-2-222000000-2-20022-2-2-220000000000000000
χ18222222-2-222222000-20-2-222-2-2-2-22222000000-2-200-2-2222-20000000000000000
χ19222222-2-22222-200020-2-222-2-222-2-2-2-20000002200-2-2-22220000000000000000
χ20222222-2-22222-200020-2-222-2-2-2-222-2-20000002200222-2-2-20000000000000000
χ212222-2-22-22222002-20022-2-2-2-222-2-2000022-2-2000000200-2002-2000000000000
χ222222-2-22-22222002-20022-2-2-2-2-2-222000022-2-2000000-200200-22000000000000
χ232222-2-22-2222200-220022-2-2-2-222-2-20000-2-222000000200-200-22000000000000
χ242222-2-22-2222200-220022-2-2-2-2-2-2220000-2-222000000-2002002-2000000000000
χ252222-2-2-22222202000-2-2-2-2-22222220022000000-2-200-200-22-200000000000000
χ262222-2-2-22222202000-2-2-2-2-222-2-2-2-20022000000-2-2002002-2200000000000000
χ272222-2-2-2222220-20002-2-2-2-222222200-2-20000002200-200-2-2200000000000000
χ282222-2-2-2222220-20002-2-2-2-222-2-2-2-200-2-2000000220020022-200000000000000
χ2944444444-1-1-1-1444444-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ3044444444-1-1-1-14-4-4-44-4-1-1-1-1-1-10000-1-1111111-1-1110000000000000000000000
χ3144444444-1-1-1-1-44-4-4-44-1-1-1-1-1-1000011-1-1111111-1-10000000000000000000000
χ3244444444-1-1-1-1-4-444-4-4-1-1-1-1-1-100001111-1-1-1-111110000000000000000000000
χ33444444-4-4-1-1-1-14000-4011-1-1110000-1-15−55−55−5115−50000000000000000000000
χ34444444-4-4-1-1-1-14000-4011-1-1110000-1-1−55−55−5511−550000000000000000000000
χ35444444-4-4-1-1-1-1-40004011-1-1110000115−5−55−55-1-15−50000000000000000000000
χ36444444-4-4-1-1-1-1-40004011-1-111000011−555−55−5-1-1−550000000000000000000000
χ374444-4-44-4-1-1-1-1004-400-1-1111100005−55−5-1-1115−5−550000000000000000000000
χ384444-4-44-4-1-1-1-1004-400-1-111110000−55−55-1-111−555−50000000000000000000000
χ394444-4-44-4-1-1-1-100-4400-1-1111100005−5−5511-1-15−55−50000000000000000000000
χ404444-4-44-4-1-1-1-100-4400-1-111110000−555−511-1-1−55−550000000000000000000000
χ414444-4-4-44-1-1-1-104000-41111-1-100005−5-1-15−5−55−55110000000000000000000000
χ424444-4-4-44-1-1-1-104000-41111-1-10000−55-1-1−555−55−5110000000000000000000000
χ434444-4-4-44-1-1-1-10-400041111-1-100005−511−555−5−55-1-10000000000000000000000
χ444444-4-4-44-1-1-1-10-400041111-1-10000−55115−5−555−5-1-10000000000000000000000
χ4544-4-4000044-4-40000000000004-40000000000000000000000002-22-200000000
χ4644-4-4000044-4-40000000000004-4000000000000000000000000-22-2200000000
χ4744-4-4000044-4-4000000000000-440000000000000000000000002i−2i−2i2i00000000
χ4844-4-4000044-4-4000000000000-44000000000000000000000000−2i2i2i−2i00000000
χ494-44-400004-44-4000000000000004i−4i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ504-44-400004-44-4000000000000004i−4i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ514-44-400004-44-400000000000000−4i4i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ524-44-400004-44-400000000000000−4i4i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ534-4-444-4004-4-44000000004-40000000000000000000004-400000000000000000
χ544-4-444-4004-4-44000000004-4000000000000000000000-4400000000000000000
χ554-4-44-44004-4-4400000000-440000000000000000004-400000000000000000000
χ564-4-44-44004-4-4400000000-44000000000000000000-4400000000000000000000
χ578-8-888-800-222-200000025−25-2225−2500000000000000000000000000000000000000
χ588-8-888-800-222-2000000−2525-22−252500000000000000000000000000000000000000
χ598-8-88-8800-222-200000025−252-2−252500000000000000000000000000000000000000
χ608-8-88-8800-222-2000000−25252-225−2500000000000000000000000000000000000000
χ611616-16-160000-4-44400000000000000000000000000000000000000000000000000
χ6216-1616-160000-44-4400000000000000000000000000000000000000000000000000

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