Finite Group Databasebeta

← Group #11793969

Character table — Group #11793969

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122444444444444448888888888181818182424242424242424242424242424242436364848484872727272
order122244336666668812121212121224242424242424242244244444668812122424242488121212128888
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-111-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ811111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1
χ9222222222222222222222222222222-2-2-2-20000000000000000-2-200000000
χ1022222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000
χ112222-2-22222222200-2-2-2-2-2-20000000022-2-2000000002i−2i002i2i−2i−2i0000000000
χ122222-2-22222222200-2-2-2-2-2-20000000022-2-200000000−2i2i00−2i−2i2i2i0000000000
χ132222-2-22222222200-2-2-2-2-2-200000000-2-222200-2002200-2-200000000000000
χ142222-2-22222222200-2-2-2-2-2-200000000-2-222-200200-2-2002200000000000000
χ152-2-222-222-2-2-22-2200-2-2222-2000000002-22-202i−2i0000000000000002i−2i000000
χ162-2-222-222-2-2-22-2200-2-2222-2000000002-22-20−2i2i000000000000000−2i2i000000
χ172-2-222-222-2-2-22-2200-2-2222-200000000-22-2200002-2000000000000002-20000
χ182-2-222-222-2-2-22-2200-2-2222-200000000-22-220000-2200000000000000-220000
χ192-2-22-2222-2-2-22-220022-2-2-22000000002-2-220000000000000000000000002-2
χ202-2-22-2222-2-2-22-220022-2-2-22000000002-2-22000000000000000000000000-22
χ212-2-22-2222-2-2-22-220022-2-2-2200000000-222-200000000000000000000002i−2i00
χ222-2-22-2222-2-2-22-220022-2-2-2200000000-222-20000000000000000000000−2i2i00
χ234444441-21-2-2-21144-2-2-2-211-2-2-2-211110000022022000000000000-1-1-1-10000
χ244444441-21-2-2-21144-2-2-2-211-2-2-2-2111100000-2-20-2-200000000000011110000
χ254444441-21-2-2-211-4-4-2-2-2-2112222-1-1-1-100000220-2-2000000000000-1-1110000
χ264444441-21-2-2-211-4-4-2-2-2-2112222-1-1-1-100000-2-202200000000000011-1-10000
χ27444444-21-2111-2-2441111-2-21111-2-2-2-20000200200-1-122-1-1-1-1-1-10000000000
χ28444444-21-2111-2-2441111-2-21111-2-2-2-20000-200-20011-2-21111110000000000
χ29444444-21-2111-2-2-4-41111-2-2-1-1-1-122220000200200-1-1-2-2-1-111110000000000
χ30444444-21-2111-2-2-4-41111-2-2-1-1-1-122220000-200-200112211-1-1-1-10000000000
χ314444-4-4-21-2111-2-200-1-1-1-1223i3i−3i−3i00000000200-200-1-12i−2i11−i−iii0000000000
χ324444-4-4-21-2111-2-200-1-1-1-1223i3i−3i−3i00000000-20020011−2i2i-1-1ii−i−i0000000000
χ334444-4-4-21-2111-2-200-1-1-1-122−3i−3i3i3i00000000200-200-1-1−2i2i11ii−i−i0000000000
χ344444-4-4-21-2111-2-200-1-1-1-122−3i−3i3i3i00000000-200200112i−2i-1-1−i−iii0000000000
χ3544-4-4004444-4-4-4-400000000000000000000000000000000000022−2200000000
χ3644-4-4004444-4-4-4-4000000000000000000000000000000000000−222200000000
χ374-44-40044-4-44-44-4−2i22i2000000−2i22i2−2i22i2−2i2−2i22i22i2000000000000000000000000000000
χ384-44-40044-4-44-44-42i2−2i20000002i2−2i22i2−2i22i22i2−2i2−2i2000000000000000000000000000000
χ394-44-400-212-11-1-22−2i22i23i−3i3i−3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2i2−i2−i20000000000−i3i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ404-44-400-212-11-1-22−2i22i23i−3i3i−3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2i2−i2−i20000000000i3−i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ414-44-400-212-11-1-22−2i22i2−3i3i−3i3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2i2−i2−i20000000000−i3i300−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ424-44-400-212-11-1-22−2i22i2−3i3i−3i3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2i2−i2−i20000000000i3−i3003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ434-44-400-212-11-1-222i2−2i23i−3i3i−3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2−i2i2i20000000000−i3i3003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ444-44-400-212-11-1-222i2−2i23i−3i3i−3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2−i2i2i20000000000i3−i300−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ454-44-400-212-11-1-222i2−2i2−3i3i−3i3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2−i2i2i20000000000−i3i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ464-44-400-212-11-1-222i2−2i2−3i3i−3i3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2−i2i2i20000000000i3−i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ474-4-444-41-2-122-2-110022-2-21-100003i−3i3i−3i000002i−2i02-2000000000000−ii-110000
χ484-4-444-41-2-122-2-110022-2-21-100003i−3i3i−3i00000−2i2i0-22000000000000i−i1-10000
χ494-4-444-41-2-122-2-110022-2-21-10000−3i3i−3i3i000002i−2i0-22000000000000−ii1-10000
χ504-4-444-41-2-122-2-110022-2-21-10000−3i3i−3i3i00000−2i2i02-2000000000000i−i-110000
χ518888-8-82-42-4-4-422004444-2-200000000000000000000000000000000000000
χ5288-8-8002-42-444-2-200000000000032−32−3232000000000000000000000000000000
χ5388-8-8002-42-444-2-2000000000000−323232−32000000000000000000000000000000
χ5488-8-800-42-42-2-244006i−6i−6i6i0000000000000000000000000000000000000000
χ5588-8-800-42-42-2-24400−6i6i6i−6i0000000000000000000000000000000000000000
χ568-88-8002-4-24-442-2−4i24i20000002i2−2i22i2−2i2−i2−i2i2i2000000000000000000000000000000
χ578-88-8002-4-24-442-24i2−4i2000000−2i22i2−2i22i2i2i2−i2−i2000000000000000000000000000000
χ588-8-888-8-424-2-224-400-2-222-4400000000000000000000000000000000000000
χ598-8-88-882-4-244-4-2200-4-444-2200000000000000000000000000000000000000
χ608-8-88-88-424-2-224-40022-2-24-400000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.