Finite Group Databasebeta

← Group #72260706

Character table — Group #72260706

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1133333333334444441212121212122424242424242424242424242424242464646464646464646464646464646464
order1222222222222244442244444444444444444444336666661212121212121212
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ411111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ511111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ611111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ7111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ8111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ9111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ10111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ11111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ12111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ132-22222-2-2-2-2-222-22i−2i2i−2i2-22i−2i2i−2i0000000000000000-1-11-11-111i−ii−ii−ii−i
χ142-22222-2-2-2-2-222-22i−2i2i−2i2-22i−2i2i−2i00000000000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ152-22222-2-2-2-2-222-22i−2i2i−2i2-22i−2i2i−2i00000000000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ162-22222-2-2-2-2-222-2−2i2i−2i2i2-2−2i2i−2i2i0000000000000000-1-11-11-111−ii−ii−ii−ii
χ172-22222-2-2-2-2-222-2−2i2i−2i2i2-2−2i2i−2i2i00000000000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ182-22222-2-2-2-2-222-2−2i2i−2i2i2-2−2i2i−2i2i00000000000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ192-22222-2-2-2-2-22-222i−2i−2i2i-222i−2i−2i2i0000000000000000-1-1-11-1111i−i−iii−i−ii
χ202-22222-2-2-2-2-22-222i−2i−2i2i-222i−2i−2i2i00000000000000001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ212-22222-2-2-2-2-22-222i−2i−2i2i-222i−2i−2i2i00000000000000001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ222-22222-2-2-2-2-22-22−2i2i2i−2i-22−2i2i2i−2i0000000000000000-1-1-11-1111−iii−i−iii−i
χ232-22222-2-2-2-2-22-22−2i2i2i−2i-22−2i2i2i−2i00000000000000001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ242-22222-2-2-2-2-22-22−2i2i2i−2i-22−2i2i2i−2i00000000000000001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ25333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2633333333333333-3-3-3-333-3-3-3-3-1-1-1-1-1-1-1-1111111110000000000000000
χ27333333333333-3-333-3-3-3-333-3-3-1-1-1-11111-1-1-1-111110000000000000000
χ28333333333333-3-3-3-333-3-3-3-333-1-1-1-111111111-1-1-1-10000000000000000
χ29666-2-2-26-2-2-2-2-20000660000-2-22i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ30666-2-2-26-2-2-2-2-20000660000-2-2−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ31666-2-2-26-2-2-2-2-20000-6-60000222i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ32666-2-2-26-2-2-2-2-20000-6-6000022−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ3366-26-2-2-26-2-2-2-200660000-2-2002i−2i2i−2i00002i2i−2i−2i00000000000000000000
χ3466-26-2-2-26-2-2-2-200660000-2-200−2i2i−2i2i0000−2i−2i2i2i00000000000000000000
χ3566-26-2-2-26-2-2-2-200-6-6000022002i−2i2i−2i0000−2i−2i2i2i00000000000000000000
χ3666-26-2-2-26-2-2-2-200-6-600002200−2i2i−2i2i00002i2i−2i−2i00000000000000000000
χ3766-2-2-2-2-2-26-2-26660000-2-200002-2-2222-2-2000000000000000000000000
χ3866-2-2-2-2-2-26-2-26660000-2-20000-222-2-2-222000000000000000000000000
χ3966-2-2-2-2-2-26-2-26-6-600002200002-2-22-2-222000000000000000000000000
χ4066-2-2-2-2-2-26-2-26-6-60000220000-222-222-2-2000000000000000000000000
χ416-66-2-2-2-62222-200006i−6i0000−2i2i00002-22-22i−2i2i−2i00000000000000000000
χ426-66-2-2-2-62222-200006i−6i0000−2i2i0000-22-22−2i2i−2i2i00000000000000000000
χ436-66-2-2-2-62222-20000−6i6i00002i−2i00002-22-2−2i2i−2i2i00000000000000000000
χ446-66-2-2-2-62222-20000−6i6i00002i−2i0000-22-222i−2i2i−2i00000000000000000000
χ456-6-26-2-22-6222-2006i−6i0000−2i2i0000002-2-2200002i−2i2i−2i0000000000000000
χ466-6-26-2-22-6222-2006i−6i0000−2i2i000000-222-20000−2i2i−2i2i0000000000000000
χ476-6-26-2-22-6222-200−6i6i00002i−2i0000002-2-220000−2i2i−2i2i0000000000000000
χ486-6-26-2-22-6222-200−6i6i00002i−2i000000-222-200002i−2i2i−2i0000000000000000
χ496-6-2-2-2-222-62266-60000-220000000000002-2-222-2-220000000000000000
χ506-6-2-2-2-222-62266-60000-22000000000000-222-2-222-20000000000000000
χ516-6-2-2-2-222-6226-6600002-20000000000002-2-22-222-20000000000000000
χ526-6-2-2-2-222-6226-6600002-2000000000000-222-22-2-220000000000000000
χ531212-4-412-4-4-4-412-4-400000000000000000000000000000000000000000000
χ541212-4-4-412-4-4-4-412-400000000000000000000000000000000000000000000
χ5512-12-4-412-4444-124-400000000000000000000000000000000000000000000
χ5612-12-4-4-4124444-12-400000000000000000000000000000000000000000000

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