Finite Group Databasebeta

← Group #11792746

Character table — Group #11792746

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122444444444444448888888888181818182424242424242424242424242424242436364848484872727272
order1222443366666688121212121212242424242424242422442224446688121224242424886612128888
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111111-1-1111-1-111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-111-1-111
χ811111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1
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
χ132222-2-22222222200-2-2-2-2-2-200000000-2-22200200-22200-2-200000000000000
χ142222-2-22222222200-2-2-2-2-2-200000000-2-22200-2002-2-2002200000000000000
χ152-2-222-222-2-2-2-22200-2-2222-2000000002-22-20000000000000000000000002-2
χ162-2-222-222-2-2-2-22200-2-2222-2000000002-22-2000000000000000000000000-22
χ172-2-222-222-2-2-2-22200-2-2222-200000000-22-2200000000000000000000002-200
χ182-2-222-222-2-2-2-22200-2-2222-200000000-22-220000000000000000000000-2200
χ192-2-22-2222-2-2-2-2220022-2-2-22000000002-2-222-200000000000000002-2000000
χ202-2-22-2222-2-2-2-2220022-2-2-22000000002-2-22-220000000000000000-22000000
χ212-2-22-2222-2-2-2-2220022-2-2-2200000000-222-20002-20000000000000002-20000
χ222-2-22-2222-2-2-2-2220022-2-2-2200000000-222-2000-22000000000000000-220000
χ234444441-211-2-21-2441111-2-21111-2-2-2-20000002002-1-122-1-1-1-1-1-10000000000
χ244444441-211-2-21-2441111-2-21111-2-2-2-2000000-200-211-2-21111110000000000
χ254444441-211-2-21-2-4-41111-2-2-1-1-1-122220000002002-1-1-2-2-1-111110000000000
χ264444441-211-2-21-2-4-41111-2-2-1-1-1-12222000000-200-2112211-1-1-1-10000000000
χ27444444-21-2-211-2144-2-2-2-211-2-2-2-211110000220220000000000000-1-1-1-10000
χ28444444-21-2-211-2144-2-2-2-211-2-2-2-211110000-2-20-2-2000000000000011110000
χ29444444-21-2-211-21-4-4-2-2-2-2112222-1-1-1-10000220-2-20000000000000-1-1110000
χ30444444-21-2-211-21-4-4-2-2-2-2112222-1-1-1-10000-2-2022000000000000011-1-10000
χ314444-4-41-211-2-21-200-1-1-1-1223i3i−3i−3i0000000000200-2-1-12i−2i11−i−iii0000000000
χ324444-4-41-211-2-21-200-1-1-1-1223i3i−3i−3i0000000000-200211−2i2i-1-1ii−i−i0000000000
χ334444-4-41-211-2-21-200-1-1-1-122−3i−3i3i3i0000000000200-2-1-1−2i2i11ii−i−i0000000000
χ344444-4-41-211-2-21-200-1-1-1-122−3i−3i3i3i0000000000-2002112i−2i-1-1−i−iii0000000000
χ3544-4-4001-21-12-2-12−2i22i23i−3i3i−3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2i2i20000000000−i3i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ3644-4-4001-21-12-2-12−2i22i23i−3i3i−3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2i2i20000000000i3−i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ3744-4-4001-21-12-2-12−2i22i2−3i3i−3i3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i2−i2i2i20000000000−i3i300−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ3844-4-4001-21-12-2-12−2i22i2−3i3i−3i3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i2−i2i2i20000000000i3−i3003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ3944-4-4001-21-12-2-122i2−2i23i−3i3i−3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−i2−i20000000000−i3i3003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4044-4-4001-21-12-2-122i2−2i23i−3i3i−3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−i2−i20000000000i3−i300−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4144-4-4001-21-12-2-122i2−2i2−3i3i−3i3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−i2−i20000000000−i3i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4244-4-4001-21-12-2-122i2−2i2−3i3i−3i3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−i2−i20000000000i3−i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4344-4-400444-4-44-4-4−2i22i20000002i2−2i2−2i22i22i22i2−2i2−2i2000000000000000000000000000000
χ4444-4-400444-4-44-4-42i2−2i2000000−2i22i22i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ454-44-40044-444-4-4-4000000000000000000000000000000000000−2i22i200000000
χ464-44-40044-444-4-4-40000000000000000000000000000000000002i2−2i200000000
χ474-4-44-44-2122-1-1-2100-2-222-1100003-33-300002-202-20000000000000-11-110000
χ484-4-44-44-2122-1-1-2100-2-222-1100003-33-30000-220-2200000000000001-11-10000
χ494-4-44-44-2122-1-1-2100-2-222-110000-33-3300002-20-220000000000000-111-10000
χ504-4-44-44-2122-1-1-2100-2-222-110000-33-330000-2202-200000000000001-1-110000
χ518888-8-8-42-4-422-42004444-2-200000000000000000000000000000000000000
χ5288-8-800-42-44-224-2−4i24i2000000−2i22i22i2−2i2i2i2−i2−i2000000000000000000000000000000
χ5388-8-800-42-44-224-24i2−4i20000002i2−2i2−2i22i2−i2−i2i2i2000000000000000000000000000000
χ548-88-8002-4-22-44-24006i−6i−6i6i0000000000000000000000000000000000000000
χ558-88-8002-4-22-44-2400−6i6i6i−6i0000000000000000000000000000000000000000
χ568-88-800-424-42-24-2000000000000−3i23i23i2−3i2000000000000000000000000000000
χ578-88-800-424-42-24-20000000000003i2−3i2−3i23i2000000000000000000000000000000
χ588-8-888-82-4-2-2442-400-2-222-4400000000000000000000000000000000000000
χ598-8-888-8-4244-2-2-420044-4-42-200000000000000000000000000000000000000
χ608-8-88-882-4-2-2442-40022-2-24-400000000000000000000000000000000000000

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