Finite Group Databasebeta

← Group #13021309

Character table — Group #13021309

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222244444444444888888888888101010101010101010101616161616161616161620202020202020202020202020202020202020808080808080
order12222244888845881010101010101020202020404040404040404022444488882210101010101010102444444448888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1iiii−i−i−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1−i−i−i−iiiii-1-1−i−i−i−iiiii-1-1−i−iii
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii11ii−i−i
χ911111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11-11-11-1
χ1011111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-11-11
χ1111111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11-11-11
χ1211111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-111-11-1
χ1311111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1iiii−i−i−i−i11−i−i−i−iiiii-11i−i−ii
χ1411111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1−i−i−i−iiiii11iiii−i−i−i−i-11−iii−i
χ1511111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1iiii−i−i−i−i11−i−i−i−iiiii1-1−iii−i
χ1611111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1−i−i−i−iiiii11iiii−i−i−i−i1-1i−i−ii
χ17222222-2-20000-22002222222-2-2-2-20000000022-2-2-2-200000000000000200000000002i2i−2i−2i2i2i−2i−2i000000
χ18222222-2-20000-22002222222-2-2-2-20000000022-2-2-2-20000000000000020000000000−2i−2i2i2i−2i−2i2i2i000000
χ19222222-2-20000-22002222222-2-2-2-200000000-2-2222200000000000000-2000000000022-2-2-2-222000000
χ20222222-2-20000-22002222222-2-2-2-200000000-2-2222200000000000000-20000000000-2-22222-2-2000000
χ212222-2-2222222-22-2-222-2-2-2-222-2-222222-2-2-2-22222-2-222220000000000-200000000-2-200000000000000
χ222222-2-2222222-22-2-222-2-2-2-222-2-222222-2-2-2-2-2-2-2-222-2-2-2-200000000002000000002200000000000000
χ232222-2-222-2-2-2-2-222222-2-2-2-222-2-22-2-2-2-222222222-2-2-2-2-2-20000000000-2000000002200000000000000
χ242222-2-222-2-2-2-2-222222-2-2-2-222-2-22-2-2-2-22222-2-2-2-22222220000000000200000000-2-200000000000000
χ252222-2-2-2-20000220022-2-2-2-22-222-20000000022-2-22200000000000000-222-2-222-2-20000000000000000
χ262222-2-2-2-20000220022-2-2-2-22-222-20000000022-2-22200000000000000-2-2-222-2-2220000000000000000
χ272222-2-2-2-20000220022-2-2-2-22-222-200000000-2-222-2-20000000000000022i2i−2i−2i−2i−2i2i2i0000000000000000
χ282222-2-2-2-20000220022-2-2-2-22-222-200000000-2-222-2-2000000000000002−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-22-20022−2−2022−22-222-2-2-2000022−2−222−2−2002i−2i2i−2ii2i2−i2−i2000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ3022-2-22-20022−2−2022−22-222-2-2-2000022−2−222−2−2002i−2i2i−2ii2i2−i2−i200000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ3122-2-22-20022−2−2022−22-222-2-2-2000022−2−222−2−200−2i2i−2i2i−i2−i2i2i2000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ3222-2-22-20022−2−2022−22-222-2-2-2000022−2−222−2−200−2i2i−2i2i−i2−i2i2i200000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ3322-2-22-200−2−22202−222-222-2-2-20000−2−222−2−222002i−2i2i−2i−i2−i2i2i2000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ3422-2-22-200−2−22202−222-222-2-2-20000−2−222−2−222002i−2i2i−2i−i2−i2i2i200000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ3522-2-22-200−2−22202−222-222-2-2-20000−2−222−2−22200−2i2i−2i2ii2i2−i2−i2000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ3622-2-22-200−2−22202−222-222-2-2-20000−2−222−2−22200−2i2i−2i2ii2i2−i2−i200000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ3722-2-2-220022−2−202−222-2-2-222-2000022−2−2−2−222002i−2i−2i2ii2i2−i2−i2000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−i2i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ3822-2-2-220022−2−202−222-2-2-222-2000022−2−2−2−222002i−2i−2i2ii2i2−i2−i200000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−i2i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ3922-2-2-220022−2−202−222-2-2-222-2000022−2−2−2−22200−2i2i2i−2i−i2−i2i2i2000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−ii2−i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ4022-2-2-220022−2−202−222-2-2-222-2000022−2−2−2−22200−2i2i2i−2i−i2−i2i2i200000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ4122-2-2-2200−2−222022−22-2-2-222-20000−2−22222−2−2002i−2i−2i2i−i2−i2i2i2000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+ii2−i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ4222-2-2-2200−2−222022−22-2-2-222-20000−2−22222−2−2002i−2i−2i2i−i2−i2i2i200000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−ii2−i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ4322-2-2-2200−2−222022−22-2-2-222-20000−2−22222−2−200−2i2i2i−2ii2i2−i2−i2000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ4422-2-2-2200−2−222022−22-2-2-222-20000−2−22222−2−200−2i2i2i−2ii2i2−i2−i200000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−i2i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ454444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000044-1-1-1-1-1-1-1-10000000000000000000000000
χ464444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-4-4111111110000000000000000000000000
χ4744444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-11111111100000000004-4-1-1-1-111110000000000000000000000000
χ4844444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000000-441111-1-1-1-10000000000000000000000000
χ494444-4-4444444-4-1-4-4-1-11111-1-111-1-1-1-1-1111100000000000055−5−555−5−50000000000000000000000000
χ504444-4-4444444-4-1-4-4-1-11111-1-111-1-1-1-1-11111000000000000−5−555−5−5550000000000000000000000000
χ514444-4-444-4-4-4-4-4-144-1-11111-1-111-11111-1-1-1-100000000000055−5−5−5−5550000000000000000000000000
χ524444-4-444-4-4-4-4-4-144-1-11111-1-111-11111-1-1-1-1000000000000−5−55555−5−50000000000000000000000000
χ534-44-4004-400000400-4-400004400-4000000000000004i−4i4i−4i00000000000000000000000000000000000
χ544-44-4004-400000400-4-400004400-400000000000000−4i4i−4i4i00000000000000000000000000000000000
χ554-44-400-444-44-40400-4-400004-40044-44-40000000000000000000000000000000000000000000000000
χ564-44-400-444-44-40-100115−55−5-115−5-1-11-115−55−5000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000000
χ574-44-400-444-44-40-100115−55−5-115−5-1-11-115−55−5000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000000
χ584-44-400-444-44-40-10011−55−55-11−55-1-11-11−55−55000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000000
χ594-44-400-444-44-40-10011−55−55-11−55-1-11-11−55−55000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000000
χ604-44-400-44-44-440400-4-400004-4004-44-440000000000000000000000000000000000000000000000000
χ614-44-400-44-44-440-100115−55−5-115−5-11-11-1−55−55000000000000−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000000
χ624-44-400-44-44-440-100115−55−5-115−5-11-11-1−55−55000000000000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000000
χ634-44-400-44-44-440-10011−55−55-11−55-11-11-15−55−5000000000000−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000000
χ644-44-400-44-44-440-10011−55−55-11−55-11-11-15−55−5000000000000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000000
χ654-4-44000022−22−22220400-440000-4000022−22−222200004-4000022−22−222200000000000000000000000000000000000
χ664-4-44000022−22−22220400-440000-4000022−22−22220000-440000−222222−2200000000000000000000000000000000000
χ674-4-440000−222222−220400-440000-40000−222222−2200004-40000−222222−2200000000000000000000000000000000000
χ684-4-440000−222222−220400-440000-40000−222222−220000-44000022−22−222200000000000000000000000000000000000
χ69888888-8-80000-8-200-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000
χ708888-8-8-8-800008-200-2-22222-22-2-2200000000000000000000000000000000000000000000000000000
χ7188-8-88-8004242−42−420-242−42-22-2-22220000−2−222−2−222000000000000000000000000000000000000000000000
χ7288-8-88-800−42−4242420-2−4242-22-2-2222000022−2−222−2−2000000000000000000000000000000000000000000000
χ7388-8-8-88004242−42−420-2−4242-2222-2-220000−2−22222−2−2000000000000000000000000000000000000000000000
χ7488-8-8-8800−42−4242420-242−42-2222-2-22000022−2−2−2−222000000000000000000000000000000000000000000000
χ758-88-8008-800000-2002225−2525−25-2-2−2525200000000000000000000000000000000000000000000000000000
χ768-88-8008-800000-20022−2525−2525-2-225−25200000000000000000000000000000000000000000000000000000
χ778-8-88000042−42−42420-2002-225−25−252520000−222−210−10−1010000000000000000000000000000000000000000000000
χ788-8-88000042−42−42420-2002-2−252525−2520000−222−2−101010−10000000000000000000000000000000000000000000000
χ798-8-880000−424242−420-2002-225−25−2525200002−2−22−101010−10000000000000000000000000000000000000000000000
χ808-8-880000−424242−420-2002-2−252525−25200002−2−2210−10−1010000000000000000000000000000000000000000000000

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