Finite Group Databasebeta

← Group #72341890

Character table — Group #72341890

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112266668888121212121212121232323232323232323232323232323232484848484848484848484848484848484848
order12224422448888222244443666121212122424242424242424444444444444888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1
χ41111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ511-1-1-111-1-1111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1i−ii−ii−ii−iii−i−i1-1ii−i−i
χ611-1-1-111-1-1111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1−ii−ii−ii−ii−i−iii1-1−i−iii
χ711-1-1-111-1-11-1-11111-1-111-1-11-1-11-1-111-1-1-1-11111i−i−iii−i−iiii−i−i-11−i−iii
χ811-1-1-111-1-11-1-11111-1-111-1-11-1-11-1-111-1-1-1-11111−iii−i−iii−i−i−iii-11ii−i−i
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000220000
χ102222222222-2-2-2-222222222-1-1-1-1-1-1-1-111111111000000000000-2-20000
χ112222-2-222-2-200002-2-222-2-222222-2-2-2-200000000000000000000000000
χ122222-2-222-2-200002-2-222-2-22-1-1-1-1111133−3−333−3−3000000000000000000
χ132222-2-222-2-200002-2-222-2-22-1-1-1-11111−3−333−3−333000000000000000000
χ1422-2-22-22-22-200002-22-22-22-22-2-2222-2-200000000000000000000000000
χ1522-2-22-22-22-200002-22-22-22-2-111-1-1-11133−3−3−3−333000000000000000000
χ1622-2-22-22-22-200002-22-22-22-2-111-1-1-111−3−33333−3−3000000000000000000
χ1722-2-2-222-2-2222-2-222-2-222-2-2-111-111-1-1-1-1-1-111110000000000002-20000
χ1822-2-2-222-2-22-2-22222-2-222-2-2-111-111-1-11111-1-1-1-1000000000000-220000
χ1933333333333333-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1-1-1-1-1
χ2033333333333333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-11111-1-11111
χ213333333333-3-3-3-3-1-1-1-1-1-1-1-1000000000000000011-1-111-1-1-1-1-1-1111111
χ223333333333-3-3-3-3-1-1-1-1-1-1-1-10000000000000000-1-111-1-111111111-1-1-1-1
χ2333-3-3-333-3-3333-3-3-1-111-1-1110000000000000000i−ii−ii−ii−i−i−iii-11−i−iii
χ2433-3-3-333-3-3333-3-3-1-111-1-1110000000000000000−ii−ii−ii−iiii−i−i-11ii−i−i
χ2533-3-3-333-3-33-3-333-1-111-1-1110000000000000000i−i−iii−i−ii−i−iii1-1ii−i−i
χ2633-3-3-333-3-33-3-333-1-111-1-1110000000000000000−iii−i−iii−iii−i−i1-1−i−iii
χ27666666-2-2-2-200002-2-22-222-200000000000000002200-2-2000000000000
χ28666666-2-2-2-200002-2-22-222-20000000000000000-2-20022000000000000
χ29666666-2-2-2-20000-222-22-2-220000000000000000002200-2-20000000000
χ30666666-2-2-2-20000-222-22-2-22000000000000000000-2-200220000000000
χ316666-6-666-6-60000-222-2-222-20000000000000000000000000000000000
χ326666-6-6-2-22200002222-2-2-2-20000000000000000000000002-22-2000000
χ336666-6-6-2-22200002222-2-2-2-2000000000000000000000000-22-22000000
χ346666-6-6-2-2220000-2-2-2-222220000000000000000000000000000002-22-2
χ356666-6-6-2-2220000-2-2-2-22222000000000000000000000000000000-22-22
χ3666-6-66-66-66-60000-22-22-22-220000000000000000000000000000000000
χ3766-6-66-6-22-22000022-2-2-2-2220000000000000000000000002i−2i−2i2i000000
χ3866-6-66-6-22-22000022-2-2-2-222000000000000000000000000−2i2i2i−2i000000
χ3966-6-66-6-22-220000-2-22222-2-20000000000000000000000000000002i−2i−2i2i
χ4066-6-66-6-22-220000-2-22222-2-2000000000000000000000000000000−2i2i2i−2i
χ4166-6-6-66-222-200002-22-2-22-2200000000000000002i−2i00−2i2i000000000000
χ4266-6-6-66-222-200002-22-2-22-220000000000000000−2i2i002i−2i000000000000
χ4366-6-6-66-222-20000-22-222-22-20000000000000000002i−2i00−2i2i0000000000
χ4466-6-6-66-222-20000-22-222-22-2000000000000000000−2i2i002i−2i0000000000
χ458-88-8000000−2i22i2−2i22i20000000022-2-20000−i2i2−i2i2−i2i2−i2i2000000000000000000
χ468-88-8000000−2i22i2−2i22i200000000-1-1113−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000
χ478-88-8000000−2i22i2−2i22i200000000-1-111−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000
χ488-88-80000002i2−2i22i2−2i20000000022-2-20000i2−i2i2−i2i2−i2i2−i2000000000000000000
χ498-88-80000002i2−2i22i2−2i200000000-1-1113−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000
χ508-88-80000002i2−2i22i2−2i200000000-1-111−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000
χ518-8-88000000−2i22i22i2−2i2000000002-22-20000−i2i2−i2i2i2−i2i2−i2000000000000000000
χ528-8-88000000−2i22i22i2−2i200000000-11-113−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000
χ538-8-88000000−2i22i22i2−2i200000000-11-11−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000
χ548-8-880000002i2−2i2−2i22i2000000002-22-20000i2−i2i2−i2−i2i2−i2i2000000000000000000
χ558-8-880000002i2−2i2−2i22i200000000-11-113−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000
χ568-8-880000002i2−2i2−2i22i200000000-11-11−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000

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