Finite Group Databasebeta

← Group #72227804

Character table — Group #72227804

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111666666666666121212122424242424242424242424242424242464646464646464646464646464646464
order1222444422222244444422448888888888888888336666661212121212121212
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
χ42222-2-2-2-2222222-2-2-2-2-2-222-2-20000000000000000-1-1-1-1-1-1-1-111111111
χ52222-2-2-2-2222222-2-2-2-2-2-222-2-200000000000000001+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ62222-2-2-2-2222222-2-2-2-2-2-222-2-200000000000000001−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ7333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ83333333333-1-1-1-133-1-1-1-1-1-1-1-111111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i0000000000000000
χ93333333333-1-1-1-133-1-1-1-1-1-1-1-111111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i0000000000000000
χ103333333333-1-1-1-133-1-1-1-1-1-1-1-1−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i111111110000000000000000
χ113333333333-1-1-1-133-1-1-1-1-1-1-1-1−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i111111110000000000000000
χ1233333333-1-133-1-1-1-133-1-1-1-1-1-111−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i0000000000000000
χ1333333333-1-133-1-1-1-133-1-1-1-1-1-111−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i0000000000000000
χ1433333333-1-133-1-1-1-133-1-1-1-1-1-1−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11−1+2i−1−2i110000000000000000
χ1533333333-1-133-1-1-1-133-1-1-1-1-1-1−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11−1−2i−1+2i110000000000000000
χ1633333333-1-1-1-133-1-1-1-133-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-130000000000000000
χ1733333333-1-1-1-133-1-1-1-133-1-1-1-1-13-1-13-1-1-1-1-1-13-1-13-10000000000000000
χ1833333333-1-1-1-133-1-1-1-133-1-1-1-1-1-13-1-1-1-133-1-1-1-13-1-10000000000000000
χ1933333333-1-1-1-133-1-1-1-133-1-1-1-1-1-1-13-1-13-1-13-1-13-1-1-10000000000000000
χ2033333333-1-1-1-1-1-1-1-1-1-1-1-13-13-11−1+2i1−1−2i−1−2i1−1+2i1−1+2i1−1−2i11−1−2i1−1+2i0000000000000000
χ2133333333-1-1-1-1-1-1-1-1-1-1-1-13-13-11−1−2i1−1+2i−1+2i1−1−2i1−1−2i1−1+2i11−1+2i1−1−2i0000000000000000
χ2233333333-1-1-1-1-1-1-1-1-1-1-1-13-13-1−1+2i1−1−2i11−1−2i1−1+2i1−1+2i1−1−2i−1−2i1−1+2i10000000000000000
χ2333333333-1-1-1-1-1-1-1-1-1-1-1-13-13-1−1−2i1−1+2i11−1+2i1−1−2i1−1−2i1−1+2i−1+2i1−1−2i10000000000000000
χ2433333333-1-1-1-1-1-1-1-1-1-1-1-1-13-131−1+2i−1−2i1−1−2i11−1+2i1−1−2i−1+2i1−1+2i11−1−2i0000000000000000
χ2533333333-1-1-1-1-1-1-1-1-1-1-1-1-13-131−1−2i−1+2i1−1+2i11−1−2i1−1+2i−1−2i1−1−2i11−1+2i0000000000000000
χ2633333333-1-1-1-1-1-1-1-1-1-1-1-1-13-13−1+2i11−1−2i1−1−2i−1+2i1−1−2i11−1+2i1−1+2i−1−2i10000000000000000
χ2733333333-1-1-1-1-1-1-1-1-1-1-1-1-13-13−1−2i11−1+2i1−1+2i−1−2i1−1+2i11−1−2i1−1−2i−1+2i10000000000000000
χ2844-4-44i4i−4i−4i004-400004i−4i0000000000000000000000111-11-1-1-1ii−i−iii−i−i
χ2944-4-44i4i−4i−4i004-400004i−4i0000000000000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7
χ3044-4-44i4i−4i−4i004-400004i−4i0000000000000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11
χ3144-4-4−4i−4i4i4i004-40000−4i4i0000000000000000000000111-11-1-1-1−i−iii−i−iii
χ3244-4-4−4i−4i4i4i004-40000−4i4i0000000000000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7
χ3344-4-4−4i−4i4i4i004-40000−4i4i0000000000000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11
χ344-44-44i−4i4i−4i4-400004i−4i00000000000000000000000011-11-11-1-1i−ii−ii−ii−i
χ354-44-44i−4i4i−4i4-400004i−4i000000000000000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ364-44-44i−4i4i−4i4-400004i−4i000000000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ374-44-4−4i4i−4i4i4-40000−4i4i00000000000000000000000011-11-11-1-1−ii−ii−ii−ii
χ384-44-4−4i4i−4i4i4-40000−4i4i000000000000000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ394-44-4−4i4i−4i4i4-40000−4i4i000000000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ404-4-444-4-4400004-400004-40000000000000000000011-1-1-1-1111-1-111-1-11
χ414-4-444-4-4400004-400004-400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ424-4-444-4-4400004-400004-400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
χ434-4-44-444-400004-40000-440000000000000000000011-1-1-1-111-111-1-111-1
χ444-4-44-444-400004-40000-4400000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ454-4-44-444-400004-40000-4400000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ466666-6-6-6-666-2-2-2-2-6-62222-2-22200000000000000000000000000000000
χ476666-6-6-6-6-2-266-2-222-6-622-2-22200000000000000000000000000000000
χ486666-6-6-6-6-2-2-2-2662222-6-6-2-22200000000000000000000000000000000
χ496666-6-6-6-6-2-2-2-2-2-22222226-2-6200000000000000000000000000000000
χ506666-6-6-6-6-2-2-2-2-2-2222222-262-600000000000000000000000000000000
χ511212-12-1212i12i−12i−12i00-440000−4i4i00000000000000000000000000000000000000
χ521212-12-12−12i−12i12i12i00-4400004i−4i00000000000000000000000000000000000000
χ5312-1212-1212i−12i12i−12i-440000−4i4i0000000000000000000000000000000000000000
χ5412-1212-12−12i12i−12i12i-4400004i−4i0000000000000000000000000000000000000000
χ5512-12-121212-12-12120000-440000-44000000000000000000000000000000000000
χ5612-12-1212-121212-120000-4400004-4000000000000000000000000000000000000

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