Finite Group Databasebeta

← Group #11795320

Character table — Group #11795320

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122444444444444448888888888181818182424242424242424242424242424242436364848484872727272
order12224433666666881212121212122424242424242424224444444488121212122424242488121212128888
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111
χ811111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ9222222222222222222222222222222-2-2-2-20000000000000000-2-200000000
χ1022222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000
χ112222-2-22222222200-2-2-2-2-2-20000000022-2-20000002i−2i00002i2i−2i−2i0000000000
χ122222-2-22222222200-2-2-2-2-2-20000000022-2-2000000−2i2i0000−2i−2i2i2i0000000000
χ132222-2-22222222200-2-2-2-2-2-200000000-2-2222-200000022-2-200000000000000
χ142222-2-22222222200-2-2-2-2-2-200000000-2-222-22000000-2-22200000000000000
χ152-22-22-222-222-2-2-20022-2-22-2000000002-22-20000000000000000000000002-2
χ162-22-22-222-222-2-2-20022-2-22-2000000002-22-2000000000000000000000000-22
χ172-22-22-222-222-2-2-20022-2-22-200000000-22-2200000000000000000000002-200
χ182-22-22-222-222-2-2-20022-2-22-200000000-22-220000000000000000000000-2200
χ192-22-2-2222-222-2-2-200-2-222-22000000002-2-22002i−2i000000000000002i−2i000000
χ202-22-2-2222-222-2-2-200-2-222-22000000002-2-2200−2i2i00000000000000−2i2i000000
χ212-22-2-2222-222-2-2-200-2-222-2200000000-222-200002i−2i000000000000002i−2i0000
χ222-22-2-2222-222-2-2-200-2-222-2200000000-222-20000−2i2i00000000000000−2i2i0000
χ234444441-211-2-2-2144-2-2-2-211-2-2-2-211110000002222000000000000-1-1-1-10000
χ244444441-211-2-2-2144-2-2-2-211-2-2-2-21111000000-2-2-2-200000000000011110000
χ254444441-211-2-2-21-4-4-2-2-2-2112222-1-1-1-100000022-2-2000000000000-1-1110000
χ264444441-211-2-2-21-4-4-2-2-2-2112222-1-1-1-1000000-2-22200000000000011-1-10000
χ27444444-21-2-2111-2441111-2-21111-2-2-2-2000022000022-1-1-1-1-1-1-1-10000000000
χ28444444-21-2-2111-2441111-2-21111-2-2-2-20000-2-20000-2-2111111110000000000
χ29444444-21-2-2111-2-4-41111-2-2-1-1-1-122220000220000-2-2-1-1-1-111110000000000
χ30444444-21-2-2111-2-4-41111-2-2-1-1-1-122220000-2-20000221111-1-1-1-10000000000
χ314444-4-4-21-2-2111-200-1-1-1-1223i3i−3i−3i000000002-200002i−2i-1-111−i−iii0000000000
χ324444-4-4-21-2-2111-200-1-1-1-1223i3i−3i−3i00000000-220000−2i2i11-1-1ii−i−i0000000000
χ334444-4-4-21-2-2111-200-1-1-1-122−3i−3i3i3i000000002-20000−2i2i-1-111ii−i−i0000000000
χ344444-4-4-21-2-2111-200-1-1-1-122−3i−3i3i3i00000000-2200002i−2i11-1-1−i−iii0000000000
χ3544-4-400444-4-44-4-422−2200000022−2222−222222−22−22000000000000000000000000000000
χ3644-4-400444-4-44-4-4−2222000000−2222−2222−22−222222000000000000000000000000000000
χ3744-4-400-21-22-11-1222−223i−3i3i−3i00−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2−222000000000000−i3i33−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ3844-4-400-21-22-11-1222−223i−3i3i−3i00−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2−222000000000000i3−i3−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ3944-4-400-21-22-11-1222−22−3i3i−3i3i00ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2−222000000000000−i3i3−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ4044-4-400-21-22-11-1222−22−3i3i−3i3i00ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2−222000000000000i3−i33−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4144-4-400-21-22-11-12−22223i−3i3i−3i002ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2322−2−2000000000000−i3i33−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4244-4-400-21-22-11-12−22223i−3i3i−3i002ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2322−2−2000000000000i3−i3−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4344-4-400-21-22-11-12−2222−3i3i−3i3i00−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2322−2−2000000000000−i3i3−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ4444-4-400-21-22-11-12−2222−3i3i−3i3i00−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2322−2−2000000000000i3−i33−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ454-44-4-441-2-11-222-10022-2-2-1100003-33-30000002i−2i2i−2i000000000000−ii−ii0000
χ464-44-4-441-2-11-222-10022-2-2-1100003-33-3000000−2i2i−2i2i000000000000i−ii−i0000
χ474-44-4-441-2-11-222-10022-2-2-110000-33-330000002i−2i−2i2i000000000000−iii−i0000
χ484-44-4-441-2-11-222-10022-2-2-110000-33-33000000−2i2i2i−2i000000000000i−i−ii0000
χ494-4-440044-4-4-4-44400000000000000000000000000000000000022−2200000000
χ504-4-440044-4-4-4-444000000000000000000000000000000000000−222200000000
χ518888-8-82-422-4-4-42004444-2-200000000000000000000000000000000000000
χ5288-8-8002-42-24-44-242−42000000−2222−222222−2−2000000000000000000000000000000
χ5388-8-8002-42-24-44-2−424200000022−2222−22−2−222000000000000000000000000000000
χ548-88-88-82-4-22-444-200-4-4442-200000000000000000000000000000000000000
χ558-88-88-8-424-42-2-240022-2-2-4400000000000000000000000000000000000000
χ568-88-8-88-424-42-2-2400-2-2224-400000000000000000000000000000000000000
χ578-8-88002-4-2-244-4200000000000032−32−3232000000000000000000000000000000
χ588-8-88002-4-2-244-42000000000000−323232−32000000000000000000000000000000
χ598-8-8800-4244-2-22-4006i−6i−6i6i0000000000000000000000000000000000000000
χ608-8-8800-4244-2-22-400−6i6i6i−6i0000000000000000000000000000000000000000

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