Finite Group Databasebeta

← Group #13019221

Character table — Group #13019221

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222444444455558888888101010101616161616161616161620202020202020202020202020202032324040404040404040404040404080
order12224444444510101044444882020202044444202020202040404040222444444448888202048888888888882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11
χ311111111111111111111-1-111111111-111111-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1
χ411111111111111111111-1-111111111-111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-11-1-1111111-1-1-1-1-1
χ5111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1iiii−i−i−i−iii−i−i11-1-1-1i−iii−i−iii−i−i-1
χ6111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1−i−i−i−iiiii−i−iii11-1-1-1−ii−i−iii−i−iii-1
χ7111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1iiii−i−i−i−i−i−iii-1-1-111−ii−i−iiiii−i−i1
χ8111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1−i−i−i−iiiiiii−i−i-1-1-111i−iii−i−i−i−iii1
χ9111111111-1-111111111-11111111111-1-1-11-1-11111-1-11111111111111-1-1-11111-1-1-1-1-1-1-1-1-1
χ10111111111-1-111111111-11111111111-1-1-11-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1
χ11111111111-1-111111111-1-1-1111111111-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-11111-1-1-1-11
χ12111111111-1-111111111-1-1-1111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111111
χ13111111111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1111111-1iiii−i−i−i−iii−i−i-1-11-1-1i−i−i−iii−i−iii1
χ14111111111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1111111-1−i−i−i−iiiii−i−iii-1-11-1-1−iiii−i−iii−i−i1
χ15111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111-1iiii−i−i−i−i−i−iii11111−iiii−i−i−i−iii-1
χ16111111111-1-11111-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111-1−i−i−i−iiiiiii−i−i11111i−i−i−iiiii−i−i-1
χ17222222-2-2-2002222222200022-2-2-2-222000-200000000-200000000222200000-2-2000000000
χ18222222-2-2-2002222222200022-2-2-2-222000-200000000-200000000-2-2-2-20000022000000000
χ19222222-2-2-2002222-2-2-2-200022-2-222-2-2000-2000000002000000002i2i−2i−2i00000−2i2i000000000
χ20222222-2-2-2002222-2-2-2-200022-2-222-2-2000-200000000200000000−2i−2i2i2i000002i−2i000000000
χ212222-2-222-22222222222-200-2-22222-2-20-2-2-222000022-200000000000000-20000000000000
χ222222-2-222-2222222-2-2-2-2-200-2-222-2-2220-2-2-2220000-2-220000000000000020000000000000
χ232222-2-222-2-2-222222222200-2-22222-2-2022-2-2-20000-2-2-20000000000000020000000000000
χ242222-2-222-2-2-22222-2-2-2-2200-2-222-2-222022-2-2-2000022200000000000000-20000000000000
χ252222-2-2-2-220022222222000-2-2-2-2-2-2-2-2000200000000200000000000000000002-22-200000
χ262222-2-2-2-220022222222000-2-2-2-2-2-2-2-200020000000020000000000000000000-22-2200000
χ272222-2-2-2-22002222-2-2-2-2000-2-2-2-22222000200000000-200000000000000000002i−2i−2i2i00000
χ282222-2-2-2-22002222-2-2-2-2000-2-2-2-22222000200000000-20000000000000000000−2i2i2i−2i00000
χ2922-2-2002-202i−2i2-22-22i−2i2i−2i00000-222i−2i0000002i−2i00002-201+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000001−i−1+i1+i−1−i0
χ3022-2-2002-202i−2i2-22-22i−2i2i−2i00000-222i−2i0000002i−2i00002-20−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000−1+i1−i−1−i1+i0
χ3122-2-2002-202i−2i2-22-2−2i2i−2i2i00000-22−2i2i0000002i−2i0000-2201−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000−1−i1+i−1+i1−i0
χ3222-2-2002-202i−2i2-22-2−2i2i−2i2i00000-22−2i2i0000002i−2i0000-220−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000001+i−1−i1−i−1+i0
χ3322-2-2002-20−2i2i2-22-22i−2i2i−2i00000-222i−2i000000−2i2i0000-2201+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000−1+i1−i−1−i1+i0
χ3422-2-2002-20−2i2i2-22-22i−2i2i−2i00000-222i−2i000000−2i2i0000-220−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000001−i−1+i1+i−1−i0
χ3522-2-2002-20−2i2i2-22-2−2i2i−2i2i00000-22−2i2i000000−2i2i00002-201−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000001+i−1−i1−i−1+i0
χ3622-2-2002-20−2i2i2-22-2−2i2i−2i2i00000-22−2i2i000000−2i2i00002-20−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000−1−i1+i−1+i1−i0
χ372-2-222-20000022-2-22i−2i−2i2i02−22-200002i−2i00000022−2−20001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000i2−i200000000000
χ382-2-222-20000022-2-22i−2i−2i2i02−22-200002i−2i00000022−2−2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000i2−i200000000000
χ392-2-222-20000022-2-22i−2i−2i2i0−222-200002i−2i000000−2−2220001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000−i2i200000000000
χ402-2-222-20000022-2-22i−2i−2i2i0−222-200002i−2i000000−2−222000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000−i2i200000000000
χ412-2-222-20000022-2-2−2i2i2i−2i02−22-20000−2i2i00000022−2−20001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000−i2i200000000000
χ422-2-222-20000022-2-2−2i2i2i−2i02−22-20000−2i2i00000022−2−2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000−i2i200000000000
χ432-2-222-20000022-2-2−2i2i2i−2i0−222-20000−2i2i000000−2−2220001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000i2−i200000000000
χ442-2-222-20000022-2-2−2i2i2i−2i0−222-20000−2i2i000000−2−222000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000i2−i200000000000
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
χ47444444444-4-4-1-1-1-10000-444-1-1-1-10000-411-111-1-1-1-10000000000000001100000000000000
χ48444444444-4-4-1-1-1-10000-4-4-4-1-1-1-10000411-1111111000000000000000-1-100000000000000
χ494444-4-444-444-1-1-1-10000-40011-1-100000111-1-15−55−50000000000000005−500000000000000
χ504444-4-444-444-1-1-1-10000-40011-1-100000111-1-1−55−55000000000000000−5500000000000000
χ514444-4-444-4-4-4-1-1-1-1000040011-1-100000-1-11115−55−5000000000000000−5500000000000000
χ524444-4-444-4-4-4-1-1-1-1000040011-1-100000-1-1111−55−550000000000000005−500000000000000
χ5344-4-400-440004-44-44i−4i4i−4i000004-4−4i4i0000000000000000000000000000000000000000000
χ5444-4-400-440004-44-4−4i4i−4i4i000004-44i−4i0000000000000000000000000000000000000000000
χ554-44-400000004-4-4444-4-40000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ564-44-400000004-4-4444-4-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ574-44-400000004-4-44-4-4440000000000000000000000002-2-222-2-2200000000000000000000
χ584-44-400000004-4-44-4-444000000000000000000000000-222-2-222-200000000000000000000
χ594-4-44-440000044-4-44i−4i−4i4i000-440000−4i4i00000000000000000000000000000000000000000
χ604-4-44-440000044-4-4−4i4i4i−4i000-4400004i−4i00000000000000000000000000000000000000000
χ61888888-8-8-800-2-2-2-20000000-2-222000000020000000000000000000000000000000000000
χ628888-8-8-8-8800-2-2-2-2000000022220000000-20000000000000000000000000000000000000
χ6388-8-8008-808i−8i-22-220000000002-200000000−2i2i00000000000000000000000000000000000
χ6488-8-8008-80−8i8i-22-220000000002-2000000002i−2i00000000000000000000000000000000000
χ6588-8-800-88000-22-22000000000-220000025−2500000000000000000000000000000000000000
χ6688-8-800-88000-22-22000000000-2200000−252500000000000000000000000000000000000000
χ678-8-888-800000-2-2220000042−42-22000000000000−2−2220000000000000000000000000000000
χ688-8-888-800000-2-22200000−4242-2200000000000022−2−20000000000000000000000000000000
χ698-8-88-8800000-2-22200000002-200000000000010−10−10100000000000000000000000000000000
χ708-8-88-8800000-2-22200000002-2000000000000−101010−100000000000000000000000000000000
χ7116-1616-160000000-444-400000000000000000000000000000000000000000000000000000000

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