Finite Group Databasebeta

← Group #72239407

Character table — Group #72239407

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111133336666666612121212121212121212121212121212242424242424242424242424242424244848484848484848256256256256256256256256
order12442244222244444444444444444444222244444444444488888888336612121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ433333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ53333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ63333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-100000000
χ73333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-100000000
χ83333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000
χ93333-1-1-1-13-1-1-13-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i3-1-1-13-1-1-11111−1+2i−1+2i−1−2i−1−2i11−1+2i−1−2i11−1+2i−1−2i00000000
χ103333-1-1-1-13-1-1-13-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i-13-1-1-13-1-11111−1−2i−1−2i−1+2i−1+2i−1+2i−1−2i11−1+2i−1−2i1100000000
χ113333-1-1-1-13-1-1-13-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i-1-13-1-1-13-1−1+2i−1+2i−1−2i−1−2i111111−1−2i−1+2i−1−2i−1+2i1100000000
χ123333-1-1-1-13-1-1-13-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i-1-1-13-1-1-13−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i1111−1−2i−1+2i00000000
χ133333-1-1-1-13-1-1-13-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i3-1-1-13-1-1-11111−1−2i−1−2i−1+2i−1+2i11−1−2i−1+2i11−1−2i−1+2i00000000
χ143333-1-1-1-13-1-1-13-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i-13-1-1-13-1-11111−1+2i−1+2i−1−2i−1−2i−1−2i−1+2i11−1−2i−1+2i1100000000
χ153333-1-1-1-13-1-1-13-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i-1-13-1-1-13-1−1−2i−1−2i−1+2i−1+2i111111−1+2i−1−2i−1+2i−1−2i1100000000
χ163333-1-1-1-13-1-1-13-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i-1-1-13-1-1-13−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i1111−1+2i−1−2i00000000
χ173333-1-1-1-13-1-1-13-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i111111113-1-1-13-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1−2i−1+2i11−1+2i−1−2i1100000000
χ183333-1-1-1-13-1-1-13-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i11111111-13-1-1-13-1-1−1−2i−1−2i−1+2i−1+2i111111−1−2i−1+2i11−1+2i−1−2i00000000
χ193333-1-1-1-13-1-1-13-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i11111111-1-13-1-1-13-11111−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i1111−1−2i−1+2i00000000
χ203333-1-1-1-13-1-1-13-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i11111111-1-1-13-1-1-131111−1−2i−1−2i−1+2i−1+2i11−1+2i−1−2i−1−2i−1+2i1100000000
χ213333-1-1-1-13-1-1-13-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i111111113-1-1-13-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1+2i−1−2i11−1−2i−1+2i1100000000
χ223333-1-1-1-13-1-1-13-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i11111111-13-1-1-13-1-1−1+2i−1+2i−1−2i−1−2i111111−1+2i−1−2i11−1−2i−1+2i00000000
χ233333-1-1-1-13-1-1-13-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i11111111-1-13-1-1-13-11111−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i1111−1+2i−1−2i00000000
χ243333-1-1-1-13-1-1-13-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i11111111-1-1-13-1-1-131111−1+2i−1+2i−1−2i−1−2i11−1−2i−1+2i−1+2i−1−2i1100000000
χ2544-4-444-4-44444-4-4-4-400000000000000000000000000000000000000001111-1-1-1-1
χ2644-4-444-4-44444-4-4-4-40000000000000000000000000000000000000000−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ2744-4-444-4-44444-4-4-4-40000000000000000000000000000000000000000−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ284-44i−4i4-44i−4i000000002-22i−2i2-22i−2i2-22i−2i2-22i−2i00000000000000000000000011-1-1i−ii−i
χ294-44i−4i4-44i−4i000000002-22i−2i2-22i−2i2-22i−2i2-22i−2i000000000000000000000000−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7
χ304-44i−4i4-44i−4i000000002-22i−2i2-22i−2i2-22i−2i2-22i−2i000000000000000000000000−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11
χ314-4−4i4i4-4−4i4i000000002-2−2i2i2-2−2i2i2-2−2i2i2-2−2i2i00000000000000000000000011-1-1−ii−ii
χ324-4−4i4i4-4−4i4i000000002-2−2i2i2-2−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7
χ334-4−4i4i4-4−4i4i000000002-2−2i2i2-2−2i2i2-2−2i2i2-2−2i2i000000000000000000000000−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11
χ3466-6-666-6-6-2-2-2-2222222-2-222-2-222-2-222-2-22222-2-2-2-22-22-22-22-20000000000000000
χ3566-6-666-6-6-2-2-2-2222222-2-222-2-222-2-222-2-2-2-2-2-22222-22-22-22-220000000000000000
χ3666-6-666-6-6-2-2-2-22222-2-222-2-222-2-222-2-2222222-2-2-2-2-22-22-22-220000000000000000
χ3766-6-666-6-6-2-2-2-22222-2-222-2-222-2-222-2-222-2-2-2-222222-22-22-22-20000000000000000
χ3866-6-6-2-222-26-2-2222-62i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-22-2-22-222i−2i−2i2i2i−2i−2i2i0000000000000000
χ3966-6-6-2-222-26-2-2222-62i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-22-222-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4066-6-6-2-222-26-2-2222-6−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-22-2-22-22−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4166-6-6-2-222-26-2-2222-6−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-222-22-22i−2i−2i2i2i−2i−2i2i0000000000000000
χ4266-6-6-2-222-2-26-222-622i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i0000000000000000
χ4366-6-6-2-222-2-26-222-622i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4466-6-6-2-222-2-26-222-62−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4566-6-6-2-222-2-26-222-62−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000
χ4666-6-6-2-222-2-2-262-62222-2-222-2-2-2-222-2-22222-2-2-2-2222-22-2-22-220000000000000000
χ4766-6-6-2-222-2-2-262-62222-2-222-2-2-2-222-2-222-2-22222-2-2-22-222-22-20000000000000000
χ4866-6-6-2-222-2-2-262-622-2-222-2-22222-2-222-2-222-2-2-2-222-22-222-22-20000000000000000
χ4966-6-6-2-222-2-2-262-622-2-222-2-22222-2-222-2-2-2-22222-2-22-22-2-22-220000000000000000
χ501212121212121212-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5112121212-4-4-4-4-412-4-4-4-4-412000000000000000000000000000000000000000000000000
χ5212121212-4-4-4-4-4-412-4-4-412-4000000000000000000000000000000000000000000000000
χ5312121212-4-4-4-4-4-4-412-412-4-4000000000000000000000000000000000000000000000000
χ541212-12-12-4-44412-4-4-4-12444000000000000000000000000000000000000000000000000
χ5512-1212i−12i12-1212i−12i00000000-22−2i2i-22−2i2i-22−2i2i-22−2i2i00000000000000000000000000000000
χ5612-1212i−12i-44−4i4i000000002-22i−2i2-22i−2i−2+4i2−4i−4−2i4+2i−2−4i2+4i4−2i−4+2i00000000000000000000000000000000
χ5712-1212i−12i-44−4i4i000000002-22i−2i2-22i−2i−2−4i2+4i4−2i−4+2i−2+4i2−4i−4−2i4+2i00000000000000000000000000000000
χ5812-1212i−12i-44−4i4i00000000−2+4i2−4i−4−2i4+2i−2−4i2+4i4−2i−4+2i2-22i−2i2-22i−2i00000000000000000000000000000000
χ5912-1212i−12i-44−4i4i00000000−2−4i2+4i4−2i−4+2i−2+4i2−4i−4−2i4+2i2-22i−2i2-22i−2i00000000000000000000000000000000
χ6012-12−12i12i12-12−12i12i00000000-222i−2i-222i−2i-222i−2i-222i−2i00000000000000000000000000000000
χ6112-12−12i12i-444i−4i000000002-2−2i2i2-2−2i2i−2+4i2−4i4+2i−4−2i−2−4i2+4i−4+2i4−2i00000000000000000000000000000000
χ6212-12−12i12i-444i−4i000000002-2−2i2i2-2−2i2i−2−4i2+4i−4+2i4−2i−2+4i2−4i4+2i−4−2i00000000000000000000000000000000
χ6312-12−12i12i-444i−4i00000000−2+4i2−4i4+2i−4−2i−2−4i2+4i−4+2i4−2i2-2−2i2i2-2−2i2i00000000000000000000000000000000
χ6412-12−12i12i-444i−4i00000000−2−4i2+4i−4+2i4−2i−2+4i2−4i4+2i−4−2i2-2−2i2i2-2−2i2i00000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.