Finite Group Databasebeta

← Group #13026437

Character table — Group #13026437

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444444444444488888888888888881010101016161616161616162020202020202020202040408080808080808080
order12442424444451010102020202088881010202020202020202020208888404040404040404022448888882488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−iii−i−i
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii−i−iii
χ711111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ911111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11-11-11-11-1
χ1011111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-11-11-11-11
χ1111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111i−ii−i−ii−ii
χ1211111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−ii−iii−ii−i
χ1311111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ1411111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ1511111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-111-1
χ1611111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-11-1-11
χ17222222-2-20000222222222-200-2-2-2-200000000222222-2-200002-22-20000-2-20000000000
χ18222222-2-20000222222222-200-2-2-2-200000000-2-2-2-222-2-20000-22-220000220000000000
χ19222222-2-2000022222222-2200-2-2-2-2000000002222-2-2220000-22-220000-2-20000000000
χ20222222-2-2000022222222-2200-2-2-2-200000000-2-2-2-2-2-22200002-22-20000220000000000
χ2122-2-22-22-200002222-2-2-2-2002i−2i22-2-200000000000000002i2i−2i−2i2-2-222i2i−2i−2i000000000000
χ2222-2-22-22-200002222-2-2-2-2002i−2i22-2-200000000000000002i2i−2i−2i-222-2−2i−2i2i2i000000000000
χ2322-2-22-22-200002222-2-2-2-200−2i2i22-2-20000000000000000−2i−2i2i2i2-2-22−2i−2i2i2i000000000000
χ2422-2-22-22-200002222-2-2-2-200−2i2i22-2-20000000000000000−2i−2i2i2i-222-22i2i−2i−2i000000000000
χ2522-2-22-2-2222-2-22222-2-2-2-20000-2-2222222-2-2-2-200000000000022-2-20000002-200000000
χ2622-2-22-2-2222-2-22222-2-2-2-20000-2-2222222-2-2-2-2000000000000-2-222000000-2200000000
χ2722-2-22-2-22-2-2222222-2-2-2-20000-2-222-2-2-2-2222200000000000022-2-2000000-2200000000
χ2822-2-22-2-22-2-2222222-2-2-2-20000-2-222-2-2-2-22222000000000000-2-2220000002-200000000
χ29444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000
χ30444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000
χ3144444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000
χ3244444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000
χ33444444-4-40000-1-1-1-1-1-1-1-14-400111155−5−555−5−50000-1-1115−55−500000000000000000000
χ34444444-4-40000-1-1-1-1-1-1-1-14-4001111−5−555−5−5550000-1-111−55−5500000000000000000000
χ35444444-4-40000-1-1-1-1-1-1-1-1-4400111155−5−555−5−5000011-1-1−55−5500000000000000000000
χ36444444-4-40000-1-1-1-1-1-1-1-1-44001111−5−555−5−555000011-1-15−55−500000000000000000000
χ374444-4-400000044-4-444-4-40000000000000000000000000000000000004i−4i0000000000
χ384444-4-400000044-4-444-4-4000000000000000000000000000000000000−4i4i0000000000
χ3944-4-44-44-40000-1-1-1-11111004i−4i-1-11155−5−5−5−5550000i5−i5i5−i5−i−iii00000000000000000000
χ4044-4-44-44-40000-1-1-1-11111004i−4i-1-111−5−55555−5−50000−i5i5−i5i5−i−iii00000000000000000000
χ4144-4-44-44-40000-1-1-1-1111100−4i4i-1-11155−5−5−5−5550000−i5i5−i5i5ii−i−i00000000000000000000
χ4244-4-44-44-40000-1-1-1-1111100−4i4i-1-111−5−55555−5−50000i5−i5i5−i5ii−i−i00000000000000000000
χ4344-4-44-4-4444-4-4-1-1-1-11111000011-1-1-1-1-1-111110000i5−i5−i5i5i5−i5−i5i500000000000000000000
χ4444-4-44-4-4444-4-4-1-1-1-11111000011-1-1-1-1-1-111110000−i5i5i5−i5−i5i5i5−i500000000000000000000
χ4544-4-44-4-44-4-444-1-1-1-11111000011-1-11111-1-1-1-10000i5−i5−i5i5−i5i5i5−i500000000000000000000
χ4644-4-44-4-44-4-444-1-1-1-11111000011-1-11111-1-1-1-10000−i5i5i5−i5i5−i5−i5i500000000000000000000
χ4744-4-4-4400000044-4-4-4-444000000000000000044-4-40000000000000000000000000000
χ4844-4-4-4400000044-4-4-4-4440000000000000000-4-4440000000000000000000000000000
χ494-44i−4i00002-22i−2i4-4004i−4i00000000002-22-22i−2i2i−2i2i2−2i222−22000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ504-44i−4i00002-22i−2i4-4004i−4i00000000002-22-22i−2i2i−2i−2i22i2−22220000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ514-44i−4i0000-22−2i2i4-4004i−4i0000000000-22-22−2i2i−2i2i2i2−2i222−220000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ524-44i−4i0000-22−2i2i4-4004i−4i0000000000-22-22−2i2i−2i2i−2i22i2−2222000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ534-4−4i4i00002-2−2i2i4-400−4i4i00000000002-22-2−2i2i−2i2i2i2−2i2−2222000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ544-4−4i4i00002-2−2i2i4-400−4i4i00000000002-22-2−2i2i−2i2i−2i22i222−220000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ554-4−4i4i0000-222i−2i4-400−4i4i0000000000-22-222i−2i2i−2i2i2−2i2−22220000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ564-4−4i4i0000-222i−2i4-400−4i4i0000000000-22-222i−2i2i−2i−2i22i222−22000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ578888-8-8000000-2-222-2-222000025−2525−250000000000000000000000000000000000000000
χ588888-8-8000000-2-222-2-2220000−2525−25250000000000000000000000000000000000000000
χ5988-8-8-88000000-2-22222-2-2000025−25−25250000000000000000000000000000000000000000
χ6088-8-8-88000000-2-22222-2-20000−252525−250000000000000000000000000000000000000000
χ618-88i−8i00004-44i−4i-2225−25−2i2i2i5−2i500000000−1+51−5−1−51+5−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ628-88i−8i00004-44i−4i-22−2525−2i2i−2i52i500000000−1−51+5−1+51−5−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000
χ638-88i−8i0000-44−4i4i-2225−25−2i2i2i5−2i5000000001−5−1+51+5−1−52ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ648-88i−8i0000-44−4i4i-22−2525−2i2i−2i52i5000000001+5−1−51−5−1+52ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ658-8−8i8i00004-4−4i4i-2225−252i−2i−2i52i500000000−1+51−5−1−51+52ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ668-8−8i8i00004-4−4i4i-22−25252i−2i2i5−2i500000000−1−51+5−1+51−52ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ678-8−8i8i0000-444i−4i-2225−252i−2i−2i52i5000000001−5−1+51+5−1−5−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000000
χ688-8−8i8i0000-444i−4i-22−25252i−2i2i5−2i5000000001+5−1−51−5−1+5−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000000

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