Finite Group Databasebeta

← Group #13019264

Character table — Group #13019264

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222444444455558888888101010101616161616161616161620202020202020202020202020202032324040404040404040404040404080
order12224444444510101044444882020202022442202020202040404040444888888888888101044444888888884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-11
χ311111111111111111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1
χ411111111111111111111-1-111111111-111111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1-1-1-1-1
χ5111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1ii−i−iiiii−i−i−i−i11-1ii−i−i-1-1iii−i−i−i-1
χ6111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1−i−iii−i−i−i−iiiii11-1−i−iii-1-1−i−i−iiii-1
χ7111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1ii−i−i−i−i−i−iiiii-1-1-1−i−iii11iii−i−i−i1
χ8111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1−i−iiiiiii−i−i−i−i-1-1-1ii−i−i11−i−i−iiii1
χ9111111111-1-111111111-11111111111-11-1-1-1-11111-1-11111111111111-1-1-1-1-1-1-1111-1-11-1-1-1
χ10111111111-1-111111111-11111111111-11-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1
χ11111111111-1-111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11111-1-11-1-11-1-11
χ12111111111-1-111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-1111
χ13111111111-1-11111-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1ii−i−iiiii−i−i−i−i-1-11−i−iii-1-1i−i−i−iii1
χ14111111111-1-11111-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1−i−iii−i−i−i−iiiii-1-11ii−i−i-1-1−iiii−i−i1
χ15111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1ii−i−i−i−i−i−iiiii111ii−i−i11i−i−i−iii-1
χ16111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1−i−iiiiiii−i−i−i−i111−i−iii11−iiii−i−i-1
χ17222222-2-2-2002222222200022-2-222-2-20-20000000000-2222200000000000000000-200-2000
χ18222222-2-2-2002222222200022-2-222-2-20-20000000000-2-2-2-2-2000000000000000002002000
χ19222222-2-2-2002222-2-2-2-200022-2-2-2-2220-2000000000022i2i−2i−2i00000000000000000−2i002i000
χ20222222-2-2-2002222-2-2-2-200022-2-2-2-2220-200000000002−2i−2i2i2i000000000000000002i00−2i000
χ212222-2-222-22222222222-200-2-222-2-2220-222-2-2000022-200000000000000-20000000000000
χ222222-2-222-2222222-2-2-2-2-200-2-22222-2-20-222-2-20000-2-220000000000000020000000000000
χ232222-2-222-2-2-222222222200-2-222-2-2220-2-2-2220000-2-2-20000000000000020000000000000
χ242222-2-222-2-2-22222-2-2-2-2200-2-22222-2-20-2-2-222000022200000000000000-20000000000000
χ252222-2-2-2-220022222222000-2-2-2-2-2-2-2-2020000000000200000000000000000000002-202-20
χ262222-2-2-2-220022222222000-2-2-2-2-2-2-2-202000000000020000000000000000000000-220-220
χ272222-2-2-2-22002222-2-2-2-2000-2-2-2-22222020000000000-200000000000000000000002i−2i0−2i2i0
χ282222-2-2-2-22002222-2-2-2-2000-2-2-2-22222020000000000-20000000000000000000000−2i2i02i−2i0
χ2922-2-200-2202i−2i2-22-22i−2i2i−2i000002-2002i−2i002i−2i0000002-2000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0001+i−1−i1−i−1+i000000000
χ3022-2-200-2202i−2i2-22-22i−2i2i−2i000002-2002i−2i002i−2i0000002-200000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−1−i1+i−1+i1−i000000000
χ3122-2-200-2202i−2i2-22-2−2i2i−2i2i000002-200−2i2i002i−2i000000-22000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000−1+i1−i−1−i1+i000000000
χ3222-2-200-2202i−2i2-22-2−2i2i−2i2i000002-200−2i2i002i−2i000000-2200000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0001−i−1+i1+i−1−i000000000
χ3322-2-200-220−2i2i2-22-22i−2i2i−2i000002-2002i−2i00−2i2i000000-22000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000−1−i1+i−1+i1−i000000000
χ3422-2-200-220−2i2i2-22-22i−2i2i−2i000002-2002i−2i00−2i2i000000-2200000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0001+i−1−i1−i−1+i000000000
χ3522-2-200-220−2i2i2-22-2−2i2i−2i2i000002-200−2i2i00−2i2i0000002-2000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0001−i−1+i1+i−1−i000000000
χ3622-2-200-220−2i2i2-22-2−2i2i−2i2i000002-200−2i2i00−2i2i0000002-200000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−1+i1−i−1−i1+i000000000
χ372-2-222-20000022-2-222-2-20i2−i22-200-2200000000i2i2−i2−i20002-22-2i2−i2i2−i2i2−i2i2−i20000000i2−i20000000
χ382-2-222-20000022-2-222-2-20i2−i22-200-2200000000i2i2−i2−i2000-22-22−i2i2−i2i2−i2i2−i2i20000000i2−i20000000
χ392-2-222-20000022-2-222-2-20−i2i22-200-2200000000−i2−i2i2i20002-22-2−i2i2−i2i2−i2i2−i2i20000000−i2i20000000
χ402-2-222-20000022-2-222-2-20−i2i22-200-2200000000−i2−i2i2i2000-22-22i2−i2i2−i2i2−i2i2−i20000000−i2i20000000
χ412-2-222-20000022-2-2-2-2220i2−i22-2002-200000000i2i2−i2−i20002i−2i−2i2i−22−222−22−20000000−i2i20000000
χ422-2-222-20000022-2-2-2-2220i2−i22-2002-200000000i2i2−i2−i2000−2i2i2i−2i2−22−2−22−220000000−i2i20000000
χ432-2-222-20000022-2-2-2-2220−i2i22-2002-200000000−i2−i2i2i20002i−2i−2i2i2−22−2−22−220000000i2−i20000000
χ442-2-222-20000022-2-2-2-2220−i2i22-2002-200000000−i2−i2i2i2000−2i2i2i−2i−22−222−22−20000000i2−i20000000
χ4544444444444-1-1-1-10000444-1-1-1-100004-1-1-1-1-1-1-1-1-1000000000000000-1-100000000000000
χ4644444444444-1-1-1-100004-4-4-1-1-1-10000-4-1-1-1-1-111110000000000000001100000000000000
χ47444444444-4-4-1-1-1-10000-444-1-1-1-10000-4-11111-1-1-1-10000000000000001100000000000000
χ48444444444-4-4-1-1-1-10000-4-4-4-1-1-1-100004-111111111000000000000000-1-100000000000000
χ494444-4-444-444-1-1-1-10000-40011-1-1000001-1-1115−55−50000000000000005−500000000000000
χ504444-4-444-444-1-1-1-10000-40011-1-1000001-1-111−55−55000000000000000−5500000000000000
χ514444-4-444-4-4-4-1-1-1-1000040011-1-100000111-1-15−55−5000000000000000−5500000000000000
χ524444-4-444-4-4-4-1-1-1-1000040011-1-100000111-1-1−55−550000000000000005−500000000000000
χ5344-4-4004-40004-44-44i−4i4i−4i00000-4400−4i4i00000000000000000000000000000000000000000
χ5444-4-4004-40004-44-4−4i4i−4i4i00000-44004i−4i00000000000000000000000000000000000000000
χ554-44-400000004-4-444i−4i−4i4i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000
χ564-44-400000004-4-444i−4i−4i4i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
χ574-44-400000004-4-44−4i4i4i−4i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000
χ584-44-400000004-4-44−4i4i4i−4i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000
χ594-4-44-440000044-4-444-4-4000-44004-40000000000000000000000000000000000000000000
χ604-4-44-440000044-4-4-4-444000-4400-440000000000000000000000000000000000000000000
χ61888888-8-8-800-2-2-2-20000000-2-222000002000000000000000000000000000000000000000
χ628888-8-8-8-8800-2-2-2-20000000222200000-2000000000000000000000000000000000000000
χ6388-8-8008-8000-22-220000000002-20000000025−2500000000000000000000000000000000000
χ6488-8-8008-8000-22-220000000002-200000000−252500000000000000000000000000000000000
χ6588-8-800-8808i−8i-22-22000000000-22000000−2i2i0000000000000000000000000000000000000
χ6688-8-800-880−8i8i-22-22000000000-220000002i−2i0000000000000000000000000000000000000
χ678-8-888-800000-2-222000004i2−4i2-22000000000000−i2−i2i2i20000000000000000000000000000000
χ688-8-888-800000-2-22200000−4i24i2-22000000000000i2i2−i2−i20000000000000000000000000000000
χ698-8-88-8800000-2-22200000002-2000000000000i10−i10−i10i100000000000000000000000000000000
χ708-8-88-8800000-2-22200000002-2000000000000−i10i10i10−i100000000000000000000000000000000
χ7116-1616-160000000-444-400000000000000000000000000000000000000000000000000000000

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