Finite Group Databasebeta

← Group #11781978

Character table — Group #11781978

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122444444444444448888888888181824242424242424242424242436363648484848484872727272
order12224433666666881212121212122424242424242424444488121212122424242448844121212128888
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-11-111-1-111-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11-1-111-1-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-11-111-1-1-1-111
χ811111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1-11-1-11111-1-1
χ9222222222222222222222222222222-2-2000000000000-2-2-20000000000
χ1022222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2000000000000-2220000000000
χ112222-2-22222222200-2-2-2-2-2-200000000222-20022-2-20000-2000000000000
χ122222-2-22222222200-2-2-2-2-2-20000000022-2200-2-2220000-2000000000000
χ132222-2-22222222200-2-2-2-2-2-200000000-2-2002i−2i00002i2i−2i−2i2000000000000
χ142222-2-22222222200-2-2-2-2-2-200000000-2-200−2i2i0000−2i−2i2i2i2000000000000
χ1522-2-2-2222-222-2-2-20022-2-22-2000000000000000000000002-20000002−22−2
χ1622-2-2-2222-222-2-2-20022-2-22-2000000000000000000000002-2000000−22−22
χ1722-2-2-2222-222-2-2-20022-2-22-200000000000000000000000-220000002−2−22
χ1822-2-2-2222-222-2-2-20022-2-22-200000000000000000000000-22000000−222−2
χ194444441-211-2-2-2144-2-2-2-211-2-2-2-211110000000000000000022-1-1-1-10000
χ204444441-211-2-2-2144-2-2-2-211-2-2-2-2111100000000000000000-2-211110000
χ214444441-211-2-2-21-4-4-2-2-2-2112222-1-1-1-1000000000000000002-2-1-1110000
χ224444441-211-2-2-21-4-4-2-2-2-2112222-1-1-1-100000000000000000-2211-1-10000
χ23444444-21-2-2111-2441111-2-21111-2-2-2-2002222-1-1-1-1-1-1-1-10000000000000
χ24444444-21-2-2111-2441111-2-21111-2-2-2-200-2-2-2-2111111110000000000000
χ25444444-21-2-2111-2-4-41111-2-2-1-1-1-122220022-2-2-1-1-1-111110000000000000
χ26444444-21-2-2111-2-4-41111-2-2-1-1-1-1222200-2-2221111-1-1-1-10000000000000
χ274444-4-4-21-2-2111-200-1-1-1-1223i3i−3i−3i0000002-22i−2i-1-111−i−iii0000000000000
χ284444-4-4-21-2-2111-200-1-1-1-1223i3i−3i−3i000000-22−2i2i11-1-1ii−i−i0000000000000
χ294444-4-4-21-2-2111-200-1-1-1-122−3i−3i3i3i0000002-2−2i2i-1-111ii−i−i0000000000000
χ304444-4-4-21-2-2111-200-1-1-1-122−3i−3i3i3i000000-222i−2i11-1-1−i−iii0000000000000
χ3144-4-44-41-2-11-222-10022-2-2-11000033-3-300000000000000000003−33−30000
χ3244-4-44-41-2-11-222-10022-2-2-11000033-3-30000000000000000000−33−330000
χ3344-4-44-41-2-11-222-10022-2-2-110000-3-33300000000000000000003−3−330000
χ3444-4-44-41-2-11-222-10022-2-2-110000-3-3330000000000000000000−333−30000
χ3544-4-44-444-444-4-4-400-4-444-4400000000000000000000000000000000000
χ364-44-400444-4-44-4-422−2200000022−2222−2222−2222−22000000000000000000000000000
χ374-44-400444-4-44-4-4−2222000000−2222−2222−2222−2222000000000000000000000000000
χ384-44-400-21-22-11-1222−223i−3i3i−3i00−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−22−22000000−i3i33−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000
χ394-44-400-21-22-11-1222−223i−3i3i−3i00−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−22−22000000i3−i3−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000
χ404-44-400-21-22-11-1222−22−3i3i−3i3i00ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−22−22000000−i3i3−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000
χ414-44-400-21-22-11-1222−22−3i3i−3i3i00ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−22−22000000i3−i33−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000
χ424-44-400-21-22-11-12−22223i−3i3i−3i002ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232−22−2000000−i3i33−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000
χ434-44-400-21-22-11-12−22223i−3i3i−3i002ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232−22−2000000i3−i3−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000
χ444-44-400-21-22-11-12−2222−3i3i−3i3i00−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232−22−2000000−i3i3−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000
χ454-44-400-21-22-11-12−2222−3i3i−3i3i00−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232−22−2000000i3−i33−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000
χ464-4-440044-4-4-4-44400000000000000004-40000000000000000000000000
χ474-4-440044-4-4-4-4440000000000000000-440000000000000000000000000
χ488888-8-82-422-4-4-42004444-2-200000000000000000000000000000000000
χ4988-8-88-8-424-42-2-2400-2-2224-400000000000000000000000000000000000
χ5088-8-8-882-4-22-444-200-4-4442-200000000000000000000000000000000000
χ5188-8-8-88-424-42-2-240022-2-2-4400000000000000000000000000000000000
χ528-88-8002-42-24-44-242−42000000−2222−22222−22−2000000000000000000000000000
χ538-88-8002-42-24-44-2−424200000022−2222−22−22−22000000000000000000000000000
χ548-8-88002-4-2-244-4200000000000032−32−3232000000000000000000000000000
χ558-8-88002-4-2-244-42000000000000−323232−32000000000000000000000000000
χ568-8-8800-4244-2-22-4006i−6i−6i6i0000000000000000000000000000000000000
χ578-8-8800-4244-2-22-400−6i6i6i−6i0000000000000000000000000000000000000

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