Finite Group Databasebeta

← Group #72342089

Character table — Group #72342089

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112266668888121212121212121232323232323232323232323232323232484848484848484848484848484848484848
order12442422448888222244443666121212122424242424242424444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1
χ41111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511-1-1-111-11-111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1ii−i−ii−ii−i1-1i−ii−iii−i−i
χ611-1-1-111-11-111-1-111-1-111-1-11-1-11-1-1111111-1-1-1-1−i−iii−ii−ii1-1−ii−ii−i−iii
χ711-1-1-111-11-1-1-11111-1-111-1-11-1-11-1-111-1-1-1-11111ii−i−ii−i−ii-11i−i−ii−i−iii
χ811-1-1-111-11-1-1-11111-1-111-1-11-1-11-1-111-1-1-1-11111−i−iii−iii−i-11−iii−iii−i−i
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002200000000
χ102222222222-2-2-2-222222222-1-1-1-1-1-1-1-11111111100000000-2-200000000
χ112222-2-22-2-2200002-2-222-2-222-2-2222-2-200000000000000000000000000
χ122222-2-22-2-2200002-2-222-2-22-111-1-1-11133−3−333−3−3000000000000000000
χ132222-2-22-2-2200002-2-222-2-22-111-1-1-111−3−333−3−333000000000000000000
χ1422-2-22-222-2-200002-22-22-22-22222-2-2-2-200000000000000000000000000
χ1522-2-22-222-2-200002-22-22-22-2-1-1-1-1111133−3−3−3−333000000000000000000
χ1622-2-22-222-2-200002-22-22-22-2-1-1-1-11111−3−33333−3−3000000000000000000
χ1722-2-2-222-22-222-2-222-2-222-2-2-111-111-1-1-1-1-1-11111000000002-200000000
χ1822-2-2-222-22-2-2-22222-2-222-2-2-111-111-1-11111-1-1-1-100000000-2200000000
χ1933333333333333-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1-1-1-1-1-1-11111
χ2033333333333333-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111-1-11111-1-1-1-1
χ213333333333-3-3-3-3-1-1-1-1-1-1-1-100000000000000001111-1-11111-1-111-1-1-1-1
χ223333333333-3-3-3-3-1-1-1-1-1-1-1-10000000000000000-1-1-1-111-1-11111-1-11111
χ2333-3-3-333-33-333-3-3-1-111-1-1110000000000000000ii−i−i−ii−ii-11−ii−iiii−i−i
χ2433-3-3-333-33-333-3-3-1-111-1-1110000000000000000−i−iiii−ii−i-11i−ii−i−i−iii
χ2533-3-3-333-33-3-3-333-1-111-1-1110000000000000000ii−i−i−iii−i1-1−iii−i−i−iii
χ2633-3-3-333-33-3-3-333-1-111-1-1110000000000000000−i−iiii−i−ii1-1i−i−iiii−i−i
χ27666666-2-2-2-200002-22-2-22-220000000000000000000000220000-2-20000
χ28666666-2-2-2-200002-22-2-22-220000000000000000000000-2-20000220000
χ29666666-2-2-2-20000-22-222-22-200000000000000000000220000-2-2000000
χ30666666-2-2-2-20000-22-222-22-200000000000000000000-2-2000022000000
χ316666-6-66-6-660000-222-2-222-20000000000000000000000000000000000
χ326666-6-6-222-2000022-2-2-2-2220000000000000000000000000000002-22-2
χ336666-6-6-222-2000022-2-2-2-222000000000000000000000000000000-22-22
χ346666-6-6-222-20000-2-22222-2-200000000000000002-22-200000000000000
χ356666-6-6-222-20000-2-22222-2-20000000000000000-22-2200000000000000
χ3666-6-66-666-6-60000-22-22-22-220000000000000000000000000000000000
χ3766-6-66-6-2-22200002222-2-2-2-20000000000000000000000000000002i−2i−2i2i
χ3866-6-66-6-2-22200002222-2-2-2-2000000000000000000000000000000−2i2i2i−2i
χ3966-6-66-6-2-2220000-2-2-2-2222200000000000000002i−2i−2i2i00000000000000
χ4066-6-66-6-2-2220000-2-2-2-222220000000000000000−2i2i2i−2i00000000000000
χ4166-6-6-66-22-2200002-2-22-222-200000000000000000000002i−2i0000−2i2i0000
χ4266-6-6-66-22-2200002-2-22-222-20000000000000000000000−2i2i00002i−2i0000
χ4366-6-6-66-22-220000-222-22-2-22000000000000000000002i−2i0000−2i2i000000
χ4466-6-6-66-22-220000-222-22-2-2200000000000000000000−2i2i00002i−2i000000
χ458-88i−8i00000022−22−2i22i200000000200-22i−2i002−22−2−i2i2−i2i2000000000000000000
χ468-88i−8i00000022−22−2i22i200000000-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000
χ478-88i−8i00000022−22−2i22i200000000-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000
χ488-88i−8i000000−22222i2−2i200000000200-22i−2i00−22−22i2−i2i2−i2000000000000000000
χ498-88i−8i000000−22222i2−2i200000000-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000
χ508-88i−8i000000−22222i2−2i200000000-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000
χ518-8−8i8i00000022−222i2−2i200000000200-2−2i2i002−22−2i2−i2i2−i2000000000000000000
χ528-8−8i8i00000022−222i2−2i200000000-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000000000
χ538-8−8i8i00000022−222i2−2i200000000-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000000000
χ548-8−8i8i000000−2222−2i22i200000000200-2−2i2i00−22−22−i2i2−i2i2000000000000000000
χ558-8−8i8i000000−2222−2i22i200000000-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000000000
χ568-8−8i8i000000−2222−2i22i200000000-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000000000

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