Finite Group Databasebeta

← Group #13026576

Character table — Group #13026576

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222224444444444488888888888888888101010101616161616161616202020204040404040404040404040404080808080
order1224488245810101020202020444481010202040404040404040402244202020202020202024884444816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1
χ6111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1iiii−i−i−i−i−i−iii
χ8111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−i−i−iiiiiii−i−i
χ91111111-1-111111-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1-111-1-11-11-1
χ101111111-1-111111-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-111-1-111-11-11
χ111111111-1-111111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111ii−i−i−i−iiii−i−ii
χ121111111-1-111111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111−i−iiiii−i−i−iii−i
χ131111111-1-111111-1-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-111-1-1-11-11
χ141111111-1-111111-1-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-111-1-1111-11-1
χ151111111-1-111111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11ii−i−i−i−iii−iii−i
χ161111111-1-111111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11−i−iiiii−i−ii−i−ii
χ1722222-2-2222-222222220000-22222-2-2-2-2-2-2-2-222220000000022-2-20000-2000000000000
χ1822222-2-2222-222222220000-22222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22200002000000000000
χ1922222-2-2-2-22-2222-2-2-2-200002-2-222-2-2-2-22222222200000000-2-2-2-200002000000000000
χ2022222-2-2-2-22-2222-2-2-2-200002-2-222-2-2-2-22222-2-2-2-20000000022220000-2000000000000
χ21222-2-2002-220222-2-2-2-20000022-2-20000000022-2-200000000-2200000002−22−22−22−20000
χ22222-2-2002-220222-2-2-2-20000022-2-20000000022-2-200000000-220000000−22−22−22−220000
χ23222-2-2002-220222-2-2-2-20000022-2-200000000-2-222000000002-20000000i2−i2i2−i2−i2i2−i2i20000
χ24222-2-2002-220222-2-2-2-20000022-2-200000000-2-222000000002-20000000−i2i2−i2i2i2−i2i2−i20000
χ25222-2-200-2220222222200000-2-2-2-20000000022-2-2000000002-200000002−2−222−2−220000
χ26222-2-200-2220222222200000-2-2-2-20000000022-2-2000000002-20000000−222−2−222−20000
χ27222-2-200-2220222222200000-2-2-2-200000000-2-22200000000-220000000i2−i2−i2i2−i2i2i2−i20000
χ28222-2-200-2220222222200000-2-2-2-200000000-2-22200000000-220000000−i2i2i2−i2i2−i2−i2i20000
χ2922-2-2222002-22-2-20000002i−2i000-2222-2-200002-22-200002i2i−2i−2i002-2002i−2i0000000000000
χ3022-2-2222002-22-2-20000002i−2i000-2222-2-20000-22-2200002i2i−2i−2i00-2200−2i2i0000000000000
χ3122-2-2222002-22-2-2000000−2i2i000-2222-2-200002-22-20000−2i−2i2i2i002-200−2i2i0000000000000
χ3222-2-2222002-22-2-2000000−2i2i000-2222-2-20000-22-220000−2i−2i2i2i00-22002i−2i0000000000000
χ3322-2-22-2-200222-2-200002i−2i00000-22-2-22200002-22-22i2i−2i−2i000000-222i−2i000000000000000
χ3422-2-22-2-200222-2-200002i−2i00000-22-2-2220000-22-222i2i−2i−2i0000002-2−2i2i000000000000000
χ3522-2-22-2-200222-2-20000−2i2i00000-22-2-22200002-22-2−2i−2i2i2i000000-22−2i2i000000000000000
χ3622-2-22-2-200222-2-20000−2i2i00000-22-2-2220000-22-22−2i−2i2i2i0000002-22i−2i000000000000000
χ37444444444-14-1-1-1-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000000000000
χ38444444444-14-1-1-1-1-1-1-1-4-4-4-44-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000000000000
χ394444444-4-4-14-1-1-1111144-4-4-411-1-1-1-1-1-111110000-1-1-1-11111000000000000000000000
χ404444444-4-4-14-1-1-11111-4-444-411-1-1-1-1-1-1111100001111-1-1-1-1000000000000000000000
χ4144444-4-444-1-4-1-1-1-1-1-1-10000-4-1-1-1-11111111100005−55−55−55−5000000000000000000000
χ4244444-4-444-1-4-1-1-1-1-1-1-10000-4-1-1-1-1111111110000−55−55−55−55000000000000000000000
χ4344444-4-4-4-4-1-4-1-1-111110000411-1-11111-1-1-1-100005−55−5−55−55000000000000000000000
χ4444444-4-4-4-4-1-4-1-1-111110000411-1-11111-1-1-1-10000−55−555−55−5000000000000000000000
χ4544-44-40000404-4-4000000000004-4000000004-4-4400000000000000000000000000000
χ4644-44-40000404-4-4000000000004-400000000-444-400000000000000000000000000000
χ4744-4-444400-1-4-11155−5−5004i−4i05−51-1-1-11155−5−50000i5−i5−i5i5−i−iii000000000000000000000
χ4844-4-444400-1-4-11155−5−500−4i4i05−51-1-1-11155−5−50000−i5i5i5−i5ii−i−i000000000000000000000
χ4944-4-444400-1-4-111−5−555004i−4i0−551-1-1-111−5−5550000−i5i5i5−i5−i−iii000000000000000000000
χ5044-4-444400-1-4-111−5−55500−4i4i0−551-1-1-111−5−5550000i5−i5−i5i5ii−i−i000000000000000000000
χ5144-4-44-4-400-14-11155−5−54i−4i0005−51-111-1-1−5−5550000−i−iiii5−i5−i5i5000000000000000000000
χ5244-4-44-4-400-14-11155−5−5−4i4i0005−51-111-1-1−5−5550000ii−i−i−i5i5i5−i5000000000000000000000
χ5344-4-44-4-400-14-111−5−5554i−4i000−551-111-1-155−5−50000−i−iii−i5i5i5−i5000000000000000000000
χ5444-4-44-4-400-14-111−5−555−4i4i000−551-111-1-155−5−50000ii−i−ii5−i5−i5i5000000000000000000000
χ55888-8-8008-8-20-2-2-2222200000-2-22200000000000000000000000000000000000000000
χ56888-8-800-88-20-2-2-2-2-2-2-200000222200000000000000000000000000000000000000000
χ5788-88-80000-20-2222525−25−2500000−2525-2200000000000000000000000000000000000000000
χ5888-88-80000-20-222−25−2525250000025−25-2200000000000000000000000000000000000000000
χ598-80004i2−4i20080-80000000000000004i2−4i2000000000000000000000000000000000000000
χ608-80004i2−4i200-20225−25−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ38000000000−i2i2i10−i10ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39000000000000000000000000000000000
χ618-80004i2−4i200-20225−252ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38000000000−i2i2i10−i10−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39000000000000000000000000000000000
χ628-80004i2−4i200-202−25252ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38000000000−i2i2−i10i10ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39000000000000000000000000000000000
χ638-80004i2−4i200-202−2525−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38000000000−i2i2−i10i10−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39000000000000000000000000000000000
χ648-8000−4i24i20080-8000000000000000−4i24i2000000000000000000000000000000000000000
χ658-8000−4i24i200-20225−25−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ38000000000i2−i2−i10i10−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39000000000000000000000000000000000
χ668-8000−4i24i200-20225−252ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38000000000i2−i2−i10i10ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39000000000000000000000000000000000
χ678-8000−4i24i200-202−25252ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38000000000i2−i2i10−i10−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39000000000000000000000000000000000
χ688-8000−4i24i200-202−2525−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38000000000i2−i2i10−i10ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39000000000000000000000000000000000

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