Finite Group Databasebeta

← Group #13013850

Character table — Group #13013850

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222444444445588888888888101010161616161616161616161616202020204040404040404040404040404080808080
order1224424588102020228101616161620404040402441020404080808080808080802488444444448161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ411111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111
χ51111111111111-1-111111111111-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1i−ii−i
χ61111111111111-1-111111111111-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−ii−ii
χ71111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-11111−ii−ii
χ81111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-11111i−ii−i
χ911111-1-11-1-11111111ii−i−i1-1-1-1-1111-1-111iiii−i−i−i−i-1-1-1-1ii−i−iii−i−i1ii−i−i11-1-1
χ1011111-1-11-1-11111111ii−i−i1-1-1-1-1111-1-111iiii−i−i−i−i-1-1-1-1−i−iii−i−iii1ii−i−i-1-111
χ1111111-1-11-1-11111111−i−iii1-1-1-1-1111-1-111−i−i−i−iiiii-1-1-1-1ii−i−iii−i−i1−i−iii-1-111
χ1211111-1-11-1-11111111−i−iii1-1-1-1-1111-1-111−i−i−i−iiiii-1-1-1-1−i−iii−i−iii1−i−iii11-1-1
χ1311111-1-11-1-1111-1-111ii−i−i1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i111111-1-1-1-111-1−i−iii−iii−i
χ1411111-1-11-1-1111-1-111ii−i−i1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111-1-11111-1-1-1−i−iiii−i−ii
χ1511111-1-11-1-1111-1-111−i−iii1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii111111-1-1-1-111-1ii−i−ii−i−ii
χ1611111-1-11-1-1111-1-111−i−iii1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111-1-11111-1-1-1ii−i−i−iii−i
χ1722222222-2-222222-2200002-2-2-2-222222-2-20000000022-2-200000000-200000000
χ1822222222-2-2222-2-2-2200002-2-2-2-2-2-2-222-2-200000000-2-22200000000200000000
χ1922222-2-222222222-22000022222222-2-2-2-200000000-2-22200000000-200000000
χ2022222-2-2222222-2-2-22000022222-2-2-2-2-2-2-20000000022-2-200000000200000000
χ21222-2-22-22002-2-222022−22−2-200002-2-22-20022−2−222−2−22-2000000000002−22−20000
χ22222-2-22-22002-2-22202−22−22-200002-2-22-200−2−222−2−2222-200000000000−22−220000
χ23222-2-22-22002-2-2-2-2022−22−2-20000-2222-20022−2−222−2−2-2200000000000−22−220000
χ24222-2-22-22002-2-2-2-202−22−22-20000-2222-200−2−222−2−222-22000000000002−22−20000
χ25222-2-2-222002-2-22202i2−i2−i2i2-200002-2-2-2200i2i2−i2−i2−i2−i2i2i2-2200000000000i2−i2−i2i20000
χ26222-2-2-222002-2-22202−i2i2i2−i2-200002-2-2-2200−i2−i2i2i2i2i2−i2−i2-2200000000000−i2i2i2−i20000
χ27222-2-2-222002-2-2-2-202i2−i2−i2i2-20000-222-2200i2i2−i2−i2−i2−i2i2i22-200000000000−i2i2i2−i20000
χ28222-2-2-222002-2-2-2-202−i2i2i2−i2-20000-222-2200−i2−i2i2i2i2i2−i2−i22-200000000000i2−i2−i2i20000
χ2922-22-20022i−2i2-2-2220-2000022i2i−2i−2i-22-2000000000000002i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000
χ3022-22-20022i−2i2-2-2220-2000022i2i−2i−2i-22-2000000000000002i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000
χ3122-22-20022i−2i2-2-2-2-20-2000022i2i−2i−2i2-2200000000000000−2i2i1−i−1+i−1−i1+i−1+i1−i1+i−1−i000000000
χ3222-22-20022i−2i2-2-2-2-20-2000022i2i−2i−2i2-2200000000000000−2i2i−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000000
χ3322-22-2002−2i2i2-2-2220-200002−2i−2i2i2i-22-200000000000000−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000
χ3422-22-2002−2i2i2-2-2220-200002−2i−2i2i2i-22-200000000000000−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000
χ3522-22-2002−2i2i2-2-2-2-20-200002−2i−2i2i2i2-22000000000000002i−2i1+i−1−i−1+i1−i−1−i1+i1−i−1+i000000000
χ3622-22-2002−2i2i2-2-2-2-20-200002−2i−2i2i2i2-22000000000000002i−2i−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000000
χ374444444-144-1-1-1004-14444-1-1-1-1-1000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ384444444-144-1-1-1004-1-4-4-4-4-1-1-1-1-1000-1-1-1-111111111000000000000000000000
χ394444444-1-4-4-1-1-100-4-10000-11111000-1-111i5−i5i5−i5i5−i5i5−i5000000000000000000000
χ404444444-1-4-4-1-1-100-4-10000-11111000-1-111−i5i5−i5i5−i5i5−i5i5000000000000000000000
χ4144444-4-4-144-1-1-100-4-10000-1-1-1-1-100011115−55−5−55−55000000000000000000000
χ4244444-4-4-144-1-1-100-4-10000-1-1-1-1-10001111−55−555−55−5000000000000000000000
χ4344444-4-4-1-4-4-1-1-1004-14i4i−4i−4i-1111100011-1-1−i−i−i−iiiii000000000000000000000
χ4444444-4-4-1-4-4-1-1-1004-1−4i−4i4i4i-1111100011-1-1iiii−i−i−i−i000000000000000000000
χ45444-4-44-4-100-111000-122−2222−221i5−i5i5−i5000-11i5−i5−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000
χ46444-4-44-4-100-111000-122−2222−221−i5i5−i5i5000-11−i5i5ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000
χ47444-4-44-4-100-111000-1−2222−22221i5−i5i5−i5000-11i5−i5ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000
χ48444-4-44-4-100-111000-1−2222−22221−i5i5−i5i5000-11−i5i5−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000
χ49444-4-4-44-100-111000-12i2−2i2−2i22i21i5−i5i5−i50001-1−i5i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39000000000000000000000
χ50444-4-4-44-100-111000-12i2−2i2−2i22i21−i5i5−i5i50001-1i5−i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29000000000000000000000
χ51444-4-4-44-100-111000-1−2i22i22i2−2i21i5−i5i5−i50001-1−i5i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39000000000000000000000
χ52444-4-4-44-100-111000-1−2i22i22i2−2i21−i5i5−i5i50001-1i5−i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29000000000000000000000
χ5344-4-4400400444440-40000-40000-4-44000000000000000000000000000000000
χ5444-4-4400400444-4-40-40000-4000044-4000000000000000000000000000000000
χ5588-88-800-28i−8i-22200020000-2−2i−2i2i2i000000000000000000000000000000000000
χ5688-88-800-2−8i8i-22200020000-22i2i−2i−2i000000000000000000000000000000000000
χ5788-8-8800-200-2-2-200020000225−25−2525000000000000000000000000000000000000
χ5888-8-8800-200-2-2-2000200002−252525−25000000000000000000000000000000000000
χ598-800000800-8008-800000000000000000000000000000000000000000000000
χ608-800000800-800-8800000000000000000000000000000000000000000000000
χ6116-1600000-40044i5−4i50000000000000000000000000000000000000000000000000
χ6216-1600000-4004−4i54i50000000000000000000000000000000000000000000000000

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