Finite Group Databasebeta

← Group #13019993

Character table — Group #13019993

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888101010101010161616161616161616162020202020202020203232404040404040404040404040808080
order12222244510101044881010202044444442020202020404040404888888882020248888888888488
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1
χ311111111111111111111-1-1-1-1-1-11111111111-1iiii−i−i−i−i11-1-1-1-1ii−i−iii−i−i-1i−i
χ411111111111111111111-1-1-1-1-1-11111111111-1−i−i−i−iiiii11-1-1-1-1−i−iii−i−iii-1−ii
χ511111111111111-1-11111111111-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1
χ611111111111111-1-11111111111-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111
χ711111111111111-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-111−i−iiiii−i−i1−ii
χ811111111111111-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-111ii−i−i−i−iii1i−i
χ9111111111111-1-1111111111111-11-1-1-1-11111111-1-111-1-1-1-1-1-11111111-11-1-1-1-1
χ10111111111111-1-1111111111111-11-1-1-1-111111-1-111-1-111-1-1-1-111-1-1-1-1-11-11-111
χ11111111111111-1-1111111-1-1-1-1-1-1-11-1-1-1-11111-1ii−i−i−i−iii-1-111-1-1ii−i−ii−i−ii1−ii
χ12111111111111-1-1111111-1-1-1-1-1-1-11-1-1-1-11111-1−i−iiiii−i−i-1-111-1-1−i−iii−iii−i1i−i
χ13111111111111-1-1-1-11111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111
χ14111111111111-1-1-1-11111111111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-11-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1ii−i−i−i−iii-1-11111−i−iiii−i−ii-1i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1−i−iiiii−i−i-1-11111ii−i−i−iii−i-1−ii
χ17222222-2-22222000022-2-222-2-2220-200000000-2220022000000000000-20-20000
χ18222222-2-22222000022-2-222-2-2220-200000000-2-2-200-2-20000000000002020000
χ19222222-2-22222000022-2-2-2-222-2-20-20000000022i2i00−2i−2i000000000000−2i02i0000
χ20222222-2-22222000022-2-2-2-222-2-20-2000000002−2i−2i002i2i0000000000002i0−2i0000
χ212222-2-22-222220000-2-2-2-222-2-2-2-202000000002002i2i00−2i−2i00000000000−2i02i000
χ222222-2-22-222220000-2-2-2-222-2-2-2-20200000000200−2i−2i002i2i000000000002i0−2i000
χ232222-2-22-222220000-2-2-2-2-2-222220200000000-20022002200000000000-20-2000
χ242222-2-22-222220000-2-2-2-2-2-222220200000000-200-2-200-2-200000000000202000
χ252222-2-2-2222222-200-2-2222222-2-20-200000000-2000000002-22-20000000000000
χ262222-2-2-2222222-200-2-222-2-2-2-2220-2000000002000000002-2-220000000000000
χ272222-2-2-222222-2200-2-2222222-2-20-200000000-200000000-22-220000000000000
χ282222-2-2-222222-2200-2-222-2-2-2-2220-200000000200000000-222-20000000000000
χ292-2-222-20022-2-2002−22-2002i−2i002i−2i00000022−2−20−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000i2−i21+i−1−i1−i−1+i0000000
χ302-2-222-20022-2-2002−22-2002i−2i002i−2i00000022−2−202ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2−i2−1−i1+i−1+i1−i0000000
χ312-2-222-20022-2-2002−22-200−2i2i00−2i2i00000022−2−20−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−i2i2−1+i1−i−1−i1+i0000000
χ322-2-222-20022-2-2002−22-200−2i2i00−2i2i00000022−2−202ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−i2i21−i−1+i1+i−1−i0000000
χ332-2-222-20022-2-200−222-2002i−2i002i−2i000000−2−2220−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−i2i2−1−i1+i−1+i1−i0000000
χ342-2-222-20022-2-200−222-2002i−2i002i−2i000000−2−22202ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−i2i21+i−1−i1−i−1+i0000000
χ352-2-222-20022-2-200−222-200−2i2i00−2i2i000000−2−2220−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000i2−i21−i−1+i1+i−1−i0000000
χ362-2-222-20022-2-200−222-200−2i2i00−2i2i000000−2−22202ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000i2−i2−1+i1−i−1−i1+i0000000
χ3744444444-1-1-1-14444-1-1-1-10000004-1-1-1-1-1-1-1-1-1000000000-1-1000000000000000
χ3844444444-1-1-1-144-4-4-1-1-1-1000000-4-111111111000000000-1-1000000000000000
χ3944444444-1-1-1-1-4-444-1-1-1-1000000-4-11111-1-1-1-100000000011000000000000000
χ4044444444-1-1-1-1-4-4-4-4-1-1-1-10000004-1-1-1-1-1111100000000011000000000000000
χ414444-4-4-44-1-1-1-14-40011-1-10000000155−5−55−55−5000000000-11000000000000000
χ424444-4-4-44-1-1-1-14-40011-1-100000001−5−555−55−55000000000-11000000000000000
χ434444-4-4-44-1-1-1-1-440011-1-10000000155−5−5−55−550000000001-1000000000000000
χ444444-4-4-44-1-1-1-1-440011-1-100000001−5−5555−55−50000000001-1000000000000000
χ454-44-400004-4-4400000000004i−4i0000000000000002+2i−2−2i002−2i−2+2i00000000000000000
χ464-44-400004-4-4400000000004i−4i000000000000000−2−2i2+2i00−2+2i2−2i00000000000000000
χ474-44-400004-4-440000000000−4i4i0000000000000002−2i−2+2i002+2i−2−2i00000000000000000
χ484-44-400004-4-440000000000−4i4i000000000000000−2+2i2−2i00−2−2i2+2i00000000000000000
χ494-4-44-440044-4-40000-44004i−4i00−4i4i000000000000000000000000000000000000
χ504-4-44-440044-4-40000-4400−4i4i004i−4i000000000000000000000000000000000000
χ51888888-8-8-2-2-2-20000-2-222000000020000000000000000000000000000000000
χ528888-8-88-8-2-2-2-2000022220000000-20000000000000000000000000000000000
χ5388-8-800008-88-800000000000000000000000000000000000000000000000000
χ5488-8-80000-22-2200000025−25000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000000
χ5588-8-80000-22-2200000025−2500000000−2ζ6+2ζ142ζ6−2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000000
χ5688-8-80000-22-22000000−252500000000−2ζ22+2ζ382ζ22−2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000
χ5788-8-80000-22-22000000−2525000000002ζ22−2ζ38−2ζ22+2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000
χ588-8-888-800-2-2220042−42-2200000000000000−2−22200000000000000000000000000
χ598-8-888-800-2-22200−4242-220000000000000022−2−200000000000000000000000000
χ608-8-88-8800-2-22200002-20000000000000010−10−101000000000000000000000000000
χ618-8-88-8800-2-22200002-200000000000000−101010−1000000000000000000000000000
χ6216-1616-160000-444-400000000000000000000000000000000000000000000000000

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