Finite Group Databasebeta

← Group #13017792

Character table — Group #13017792

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122224444444445555888888888888888810101010161616161616161616202020202020202020202020204040404040404040404040408080
order12224444444445101010444444442020202020202020202020202244202020202020202020444448888888822244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−iii−i−ii−i
χ411111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii−i−iii−ii
χ511111111111-1-1111111111-1-1-111-1-1-1-111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111-1-1
χ611111111111-1-1111111111-1-1-111-1-1-1-111111111111-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111
χ711111111111-1-11111-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-11-1-111-1-1-1-111-1-1-1iiii−i−i−i−i-1111−i−iiiii−i−i−ii
χ811111111111-1-11111-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-11-1-111-1-1-1-111-1-1-1−i−i−i−iiiii-1111ii−i−i−i−iiii−i
χ9111111111-1-11111111111-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-111-1-1111111111-1-1-111111-1-1-1-1-1-1
χ10111111111-1-11111111111-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111
χ11111111111-1-1111111-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1iiii−i−i−i−i111-1ii−i−i−i−iii−ii
χ12111111111-1-1111111-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1−i−i−i−iiiii111-1−i−iiiii−i−ii−i
χ13111111111-1-1-1-111111111-111-111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-111
χ14111111111-1-1-1-111111111-111-111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-111-111111111-1-1
χ15111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-1iiii−i−i−i−i1-1-11−i−iii−i−iiii−i
χ16111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-111111111-1−i−i−i−iiiii1-1-11ii−i−iii−i−i−ii
χ17222222-2-2-2220022222222-2000-2-2000022222222-2-2-200-2-200000022-200000000-20000000000000
χ18222222-2-2-222002222-2-2-2-2-2000-2-20000222222-2-222-200-2-2000000-2-220000000020000000000000
χ19222222-2-2-2-2-200222222222000-2-20000-2-2-2-22222-2-2-20022000000-2-2-20000000020000000000000
χ20222222-2-2-2-2-2002222-2-2-2-22000-2-20000-2-2-2-222-2-222-2002200000022200000000-20000000000000
χ212222-2-222-2002222222222000-22222220000-2-2-2-222-2-2-20000002200-200000000000-20000000000
χ222222-2-222-200222222-2-2-2-2000-22222220000-2-222-2-2-2-2-2000000-2-20020000000000020000000000
χ232222-2-222-200-2-222222222000222-2-2-2-20000-2-2-2-222-222000000-2-200-20000000000020000000000
χ242222-2-222-200-2-22222-2-2-2-2000222-2-2-2-20000-2-222-2-2-2220000002200200000000000-20000000000
χ252222-2-2-2-2200002222222202-20-2-200000000-2-2-2-2-2-22000022-2-2000020000000002-200000000000
χ262222-2-2-2-220000222222220-220-2-200000000-2-2-2-2-2-220000-2-22200002000000000-2200000000000
χ272222-2-2-2-2200002222-2-2-2-202-20-2-200000000-2-222222000022-2-20000-2000000000-2200000000000
χ282222-2-2-2-2200002222-2-2-2-20-220-2-200000000-2-2222220000-2-2220000-20000000002-200000000000
χ2922-2-22-20002i−2i002-2-2222-2-200000000002i2i−2i−2i2-2-2200000000000002i−2i0i2i2−i2−i2i2i2−i2−i2000000002−22−200
χ3022-2-22-20002i−2i002-2-2222-2-200000000002i2i−2i−2i2-2-2200000000000002i−2i0−i2−i2i2i2−i2−i2i2i200000000−22−2200
χ3122-2-22-20002i−2i002-2-22-2-22200000000002i2i−2i−2i2-22-20000000000000−2i2i022−2−2−2−22200000000−i2i2i2−i200
χ3222-2-22-20002i−2i002-2-22-2-22200000000002i2i−2i−2i2-22-20000000000000−2i2i0−2−22222−2−200000000i2−i2−i2i200
χ3322-2-22-2000−2i2i002-2-2222-2-20000000000−2i−2i2i2i2-2-220000000000000−2i2i0i2i2−i2−i2i2i2−i2−i200000000−22−2200
χ3422-2-22-2000−2i2i002-2-2222-2-20000000000−2i−2i2i2i2-2-220000000000000−2i2i0−i2−i2i2i2−i2−i2i2i2000000002−22−200
χ3522-2-22-2000−2i2i002-2-22-2-2220000000000−2i−2i2i2i2-22-200000000000002i−2i022−2−2−2−22200000000i2−i2−i2i200
χ3622-2-22-2000−2i2i002-2-22-2-2220000000000−2i−2i2i2i2-22-200000000000002i−2i0−2−22222−2−200000000−i2i2i2−i200
χ372-2-22002-20002-222-2-22i−2i2i−2i00002-222-2-2000000002i−2i0000000002i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i00001+i−1−i1−i−1+i000000
χ382-2-22002-20002-222-2-22i−2i2i−2i00002-222-2-2000000002i−2i0000000002i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−1−i1+i−1+i1−i000000
χ392-2-22002-20002-222-2-2−2i2i−2i2i00002-222-2-200000000−2i2i000000000−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i00001−i−1+i1+i−1−i000000
χ402-2-22002-20002-222-2-2−2i2i−2i2i00002-222-2-200000000−2i2i000000000−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−1+i1−i−1−i1+i000000
χ412-2-22002-2000-2222-2-22i−2i2i−2i00002-2-2-222000000002i−2i000000000−2i2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−1−i1+i−1+i1−i000000
χ422-2-22002-2000-2222-2-22i−2i2i−2i00002-2-2-222000000002i−2i000000000−2i2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00001+i−1−i1−i−1+i000000
χ432-2-22002-2000-2222-2-2−2i2i−2i2i00002-2-2-22200000000−2i2i0000000002i−2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−1+i1−i−1−i1+i000000
χ442-2-22002-2000-2222-2-2−2i2i−2i2i00002-2-2-22200000000−2i2i0000000002i−2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00001−i−1+i1+i−1−i000000
χ454444444444444-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ4644444444444-4-4-1-1-1-100004-4-4-4-1-11111-1-1-1-1-1-10000-111-1-11111000000000000000000000000000
χ47444444444-4-444-1-1-1-10000-4-4-44-1-1-1-1-1-11111-1-10000-1-1-1111111000000000000000000000000000
χ48444444444-4-4-4-4-1-1-1-10000-444-4-1-111111111-1-10000-11111-1-1-1-1000000000000000000000000000
χ49444444-4-4-44400-1-1-1-10000-4000115−55−5-1-1-1-1-1-1000015−5115−55−5000000000000000000000000000
χ50444444-4-4-44400-1-1-1-10000-400011−55−55-1-1-1-1-1-100001−5511−55−55000000000000000000000000000
χ51444444-4-4-4-4-400-1-1-1-100004000115−55−51111-1-1000015−5-1-1−55−55000000000000000000000000000
χ52444444-4-4-4-4-400-1-1-1-10000400011−55−551111-1-100001−55-1-15−55−5000000000000000000000000000
χ534444-4-444-40044-1-1-1-10000000-4-1-1-1-1-1-15−55−51100001115−55−5−55000000000000000000000000000
χ544444-4-444-40044-1-1-1-10000000-4-1-1-1-1-1-1−55−55110000111−55−555−5000000000000000000000000000
χ554444-4-444-400-4-4-1-1-1-100000004-1-111115−55−51100001-1-15−5−555−5000000000000000000000000000
χ564444-4-444-400-4-4-1-1-1-100000004-1-11111−55−551100001-1-1−555−5−55000000000000000000000000000
χ574444-4-4-4-440000-1-1-1-1000004-40115−55−55−55−5110000-1−55−55-1-111000000000000000000000000000
χ584444-4-4-4-440000-1-1-1-1000004-4011−55−55−55−55110000-15−55−5-1-111000000000000000000000000000
χ594444-4-4-4-440000-1-1-1-100000-440115−55−5−55−55110000-1−555−511-1-1000000000000000000000000000
χ604444-4-4-4-440000-1-1-1-100000-44011−55−555−55−5110000-15−5−5511-1-1000000000000000000000000000
χ6144-4-4-4400000004-4-4444-4-400000000000000-444-400000000000000000000000000000000000000
χ6244-4-4-4400000004-4-44-4-44400000000000000-44-4400000000000000000000000000000000000000
χ634-44-40000000004-44-44i−4i−4i4i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ644-44-40000000004-44-44i−4i−4i4i00000000000000000000000000000000002ζ7+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+2ζ3700000000000000
χ654-44-40000000004-44-4−4i4i4i−4i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ664-44-40000000004-44-4−4i4i4i−4i00000000000000000000000000000000002ζ13+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+2ζ3900000000000000
χ674-4-4400-440000044-4-44i−4i4i−4i0000-44000000000000−4i4i000000000000000000000000000000000000
χ684-4-4400-440000044-4-4−4i4i−4i4i0000-440000000000004i−4i000000000000000000000000000000000000
χ6988-8-88-80008i−8i00-222-200000000000000−2i−2i2i2i-220000000000000000000000000000000000000000
χ7088-8-88-8000−8i8i00-222-2000000000000002i2i−2i−2i-220000000000000000000000000000000000000000
χ7188-8-8-880000000-222-2000000000000002i5−2i5−2i52i52-20000000000000000000000000000000000000000
χ7288-8-8-880000000-222-200000000000000−2i52i52i5−2i52-20000000000000000000000000000000000000000
χ738-8-88008-80008-8-2-22200000000-22-2-2220000000000000000000000000000000000000000000000
χ748-8-88008-8000-88-2-22200000000-2222-2-20000000000000000000000000000000000000000000000
χ758-8-8800-8800000-2-222000000002-225−25−25250000000000000000000000000000000000000000000000
χ768-8-8800-8800000-2-222000000002-2−252525−250000000000000000000000000000000000000000000000
χ7716-1616-16000000000-44-44000000000000000000000000000000000000000000000000000000000000

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