Finite Group Databasebeta

← Group #72341906

Character table — Group #72341906

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122666612121212121212121616242424243232323248484848484848484848484848484848646464646464
order1244242244222244442444443612124444888888888888666121212
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-11-1-11-1-1
χ4111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-1
χ511-1-1-111-11-111-1-111-1-11-1ii−i−i11-1-1i−i1-1i−ii−iii−i−iii−i−i-1111-1-1
χ611-1-1-111-11-111-1-111-1-11-1−i−iii11-1-1−ii1-1−ii−ii−i−iii−i−iii-1111-1-1
χ711-1-1-111-11-111-1-111-1-1-11ii−i−i11-1-1i−i-11−ii−iiii−i−i−i−iii-1-1-1111
χ811-1-1-111-11-111-1-111-1-1-11−i−iii11-1-1−ii-11i−ii−i−i−iiiii−i−i-1-1-1111
χ9222222222222222222220000-1-1-1-10022000000000000-1-1-1-1-1-1
χ10222222222222222222-2-20000-1-1-1-100-2-2000000000000-111-111
χ112222-2-22-2-222-22-22-22-200000022220000000000000000-200-200
χ122222-2-22-2-222-22-22-22-2000000-1-1-1-100000000000000001−i3i31−i3i3
χ132222-2-22-2-222-22-22-22-2000000-1-1-1-100000000000000001i3−i31i3−i3
χ1422-2-22-222-2-22-2-222-2-2200000022-2-20000000000000000200-200
χ1522-2-22-222-2-22-2-222-2-22000000-1-1110000000000000000-1−i3i31i3−i3
χ1622-2-22-222-2-22-2-222-2-22000000-1-1110000000000000000-1i3−i31−i3i3
χ1722-2-2-222-22-222-2-222-2-22-20000-1-111002-20000000000001-1-1-111
χ1822-2-2-222-22-222-2-222-2-2-220000-1-11100-22000000000000111-1-1-1
χ193333333333-1-1-1-1-1-1-1-1331111000011-1-11111-1-1-1-1-1-1-1-1000000
χ203333333333-1-1-1-1-1-1-1-133-1-1-1-10000-1-1-1-1-1-1-1-111111111000000
χ213333333333-1-1-1-1-1-1-1-1-3-3111100001111-1-1-1-1-1-1-1-11111000000
χ223333333333-1-1-1-1-1-1-1-1-3-3-1-1-1-10000-1-11111111111-1-1-1-1000000
χ2333-3-3-333-33-3-1-111-1-1113-3ii−i−i0000i−i-11i−ii−i−i−iii−i−iii000000
χ2433-3-3-333-33-3-1-111-1-1113-3−i−iii0000−ii-11−ii−iiii−i−iii−i−i000000
χ2533-3-3-333-33-3-1-111-1-111-33ii−i−i0000i−i1-1−ii−ii−i−iiiii−i−i000000
χ2633-3-3-333-33-3-1-111-1-111-33−i−iii0000−ii1-1i−ii−iii−i−i−i−iii000000
χ27666666-2-2-2-22-2-22-222-20000000000000022-2-200000000000000
χ28666666-2-2-2-22-2-22-222-200000000000000-2-22200000000000000
χ29666666-2-2-2-2-222-22-2-220022220000-2-200000000000000000000
χ30666666-2-2-2-2-222-22-2-2200-2-2-2-200002200000000000000000000
χ316666-6-66-6-66-22-22-22-2200000000000000000000000000000000
χ326666-6-6-222-222-2-2-2-22200000000000000000000002-22-2000000
χ336666-6-6-222-222-2-2-2-2220000000000000000000000-22-22000000
χ346666-6-6-222-2-2-22222-2-20000000000000000002i−2i2i−2i0000000000
χ356666-6-6-222-2-2-22222-2-2000000000000000000−2i2i−2i2i0000000000
χ3666-6-66-666-6-6-222-2-222-200000000000000000000000000000000
χ3766-6-66-6-2-2222222-2-2-2-200000000000000000000002i−2i−2i2i000000
χ3866-6-66-6-2-2222222-2-2-2-20000000000000000000000−2i2i2i−2i000000
χ3966-6-66-6-2-222-2-2-2-222220000000000000000002-2-220000000000
χ4066-6-66-6-2-222-2-2-2-22222000000000000000000-222-20000000000
χ4166-6-6-66-22-222-22-2-22-22000000000000002i−2i−2i2i00000000000000
χ4266-6-6-66-22-222-22-2-22-2200000000000000−2i2i2i−2i00000000000000
χ4366-6-6-66-22-22-22-222-22-2002i2i−2i−2i0000−2i2i00000000000000000000
χ4466-6-6-66-22-22-22-222-22-200−2i−2i2i2i00002i−2i00000000000000000000
χ458-88i−8i00000000000000002+2i−2−2i2−2i−2+2i2-22i−2i0000000000000000000000
χ468-88i−8i0000000000000000−2−2i2+2i−2+2i2−2i2-22i−2i0000000000000000000000
χ478-8−8i8i00000000000000002−2i−2+2i2+2i−2−2i2-2−2i2i0000000000000000000000
χ488-8−8i8i0000000000000000−2+2i2−2i−2−2i2+2i2-2−2i2i0000000000000000000000
χ4916-1616i−16i00000000000000000000-22−2i2i0000000000000000000000
χ5016-16−16i16i00000000000000000000-222i−2i0000000000000000000000

Here i is the imaginary unit (i² = −1).