Finite Group Databasebeta

← Group #11723663

Character table — Group #11723663

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222222222224444444444444444444444444444444444444444444444363636363636363636363636363636363636
order12233344666661212121233333666666666666666661212121212121212121212121212121212121212121212122444668812121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ511-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-11111111111-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-111-1-111-1-1
χ611-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-11111111111-1-1-1-1-1-1-1-1-1-11-1-1111-11-1-1-1-111-1-111
χ711-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111
χ811-1111-11-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-11111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-111-1-11111-1-1
χ9222222-2-222222-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000
χ1022222-122222-12-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12200-1-100-1-100000000
χ1122222-122222-12-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20011001100000000
χ1222222-1-2-2222-1211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-2-2-211111111-2-2111111110000−i3i300−i3i300000000
χ1322222-1-2-2222-1211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-2-2-211111111-2-2111111110000i3−i300i3−i300000000
χ142222-122222-12222-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-1
χ152222-122222-12222-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000-2-20000001111
χ162222-12-2-222-122-2-211-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-2-2-211-2-211111111-2-2111111000000000000003−33−3
χ172222-12-2-222-122-2-211-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-2-2-211-2-211111111-2-211111100000000000000−33−33
χ18222-12222-1-122-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-10000
χ19222-12222-1-122-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-200000011110000
χ20222-122-2-2-1-122-1-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-2111111-2-211111111-2-211110000000000−i3i3−i3i30000
χ21222-122-2-2-1-122-1-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-2111111-2-211111111-2-211110000000000i3−i3i3−i30000
χ2222-22222-2-2-222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22-2-2-2-2-2-2-2-2-2-22222222222000000000000000000
χ2322-222-12-2-2-22-12-1-1-2-22-1-1-1-1-21-2-2111111112-1-1-1-121-22-2-21111111122-1-1-1-1-1-1-1-10000−i3i300i3−i300000000
χ2422-222-12-2-2-22-12-1-1-2-22-1-1-1-1-21-2-2111111112-1-1-1-121-22-2-21111111122-1-1-1-1-1-1-1-10000i3−i300−i3i300000000
χ2522-222-1-22-2-22-1211222-1-1-1-1-21-2-2111111112-1-1-1-1-2-12-222-1-1-1-1-1-1-1-1-2-2111111112-200-1-1001100000000
χ2622-222-1-22-2-22-1211222-1-1-1-1-21-2-2111111112-1-1-1-1-2-12-222-1-1-1-1-1-1-1-1-2-211111111-22001100-1-100000000
χ2722-22-122-2-2-2-1222211-12-1-1-11-211-2-2111111-12-1-1-1-1-2-2211-2-2111111-1-122-1-1-1-1-1-1000000000000003−3−33
χ2822-22-122-2-2-2-1222211-12-1-1-11-211-2-2111111-12-1-1-1-1-2-2211-2-2111111-1-122-1-1-1-1-1-100000000000000−333−3
χ2922-22-12-22-2-2-122-2-2-1-1-12-1-1-11-211-2-2111111-12-1-1-1122-2-1-122-1-1-1-1-1-111-2-21111110000002-2000000-1-111
χ3022-22-12-22-2-2-122-2-2-1-1-12-1-1-11-211-2-2111111-12-1-1-1122-2-1-122-1-1-1-1-1-111-2-2111111000000-2200000011-1-1
χ3122-2-1222-21122-122-2-2-1-12-1-1-2-21111-2-21111-1-12-1-12-21-11111-2-21111-1-1-1-122-1-1-1-10000000000−i3i3i3−i30000
χ3222-2-1222-21122-122-2-2-1-12-1-1-2-21111-2-21111-1-12-1-12-21-11111-2-21111-1-1-1-122-1-1-1-10000000000i3−i3−i3i30000
χ3322-2-122-221122-1-2-222-1-12-1-1-2-21111-2-21111-1-12-1-1-22-11-1-1-1-122-1-1-1-11111-2-21111002-2000000-1-1110000
χ3422-2-122-221122-1-2-222-1-12-1-1-2-21111-2-21111-1-12-1-1-22-11-1-1-1-122-1-1-1-11111-2-2111100-2200000011-1-10000
χ354444-2-24444-2-24-2-2-2-2-2-2111-2-2-2-2-2-2111111-2-2111-2-244-2-2-2-2111111-2-2-2-2111111000000000000000000
χ364444-2-2-4-444-2-242222-2-2111-2-2-2-2-2-2111111-2-211122-4-42222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000
χ37444-24-244-2-24-2-2-2-244-21-2114-2-2-211-2-21111-21-2114-2-2-2-2-211-2-21111-2-211-2-21111000000000000000000
χ38444-24-2-4-4-2-24-2-222-4-4-21-2114-2-2-211-2-21111-21-211-422222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000
χ39444-2-2444-2-2-24-244-2-21-2-211-2411-2-2-2-211111-2-211-24-2-211-2-2-2-2111111-2-2-2-21111000000000000000000
χ40444-2-24-4-4-2-2-24-2-4-4221-2-211-2411-2-2-2-211111-2-2112-422-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000
χ41444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000
χ42444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000
χ43444-2-2-2-4-4-2-2-2-2-22222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000
χ44444-2-2-2-4-4-2-2-2-2-22222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000
χ4544-44-2-24-4-4-4-2-24-2-222-2-2111222222-1-1-1-1-1-1-2-2111-22-442222-1-1-1-1-1-1-2-2-2-2111111000000000000000000
χ4644-44-2-2-44-4-4-2-2422-2-2-2-2111222222-1-1-1-1-1-1-2-21112-24-4-2-2-2-21111112222-1-1-1-1-1-1000000000000000000
χ4744-4-24-24-4224-2-2-2-2-4-4-21-211-4222-1-122-1-1-1-1-21-211422-222-1-122-1-1-1-1-2-211-2-21111000000000000000000
χ4844-4-24-2-44224-2-22244-21-211-4222-1-122-1-1-1-1-21-211-4-2-22-2-211-2-2111122-1-122-1-1-1-1000000000000000000
χ4944-4-2-244-422-24-244221-2-2112-4-1-12222-1-1-1-11-2-211-2-42-2-1-12222-1-1-1-111-2-2-2-21111000000000000000000
χ5044-4-2-24-4422-24-2-4-4-2-21-2-2112-4-1-12222-1-1-1-11-2-21124-2211-2-2-2-21111-1-12222-1-1-1-1000000000000000000
χ5144-4-2-2-24-422-2-2-2-2-222111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-222-2-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000
χ5244-4-2-2-24-422-2-2-2-2-222111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-222-2-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000
χ5344-4-2-2-2-4422-2-2-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322-2-22111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000
χ5444-4-2-2-2-4422-2-2-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322-2-22111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000
χ554-404440000-4-4-4000044444000000000000-4-4-4-4-4000000000000000000000000000000000000000000
χ564-4044-20000-42-423−23004-2-2-2-2000000000000-42222000000000000000023−2323−2323−2323−23000000000000000000
χ574-4044-20000-42-4−2323004-2-2-2-2000000000000-422220000000000000000−2323−2323−2323−2323000000000000000000
χ584-404-2400002-4-40023−23-24-2-2-20000000000002-4222000023−230023−2323−2323−230000000000000000000000000000
χ594-404-2400002-4-400−2323-24-2-2-20000000000002-42220000−232300−2323−2323−23230000000000000000000000000000
χ604-404-2-2000022-423−2323−23-2-21110000003-33-33-322-1-1-1000023−2300−33−33−330023−23−33−33−33000000000000000000
χ614-404-2-2000022-423−23−2323-2-2111000000-33-33-3322-1-1-10000−2323003−33−33−30023−23−33−33−33000000000000000000
χ624-404-2-2000022-4−232323−23-2-2111000000-33-33-3322-1-1-1000023−2300−33−33−3300−23233−33−33−3000000000000000000
χ634-404-2-2000022-4−2323−2323-2-21110000003-33-33-322-1-1-10000−2323003−33−33−300−23233−33−33−3000000000000000000
χ644-40-24400−2i32i3-4-420000-2-24-2-200−2i32i3−2i32i300−2i32i32i3−2i322-422000000000000000000000000000000000000000000
χ654-40-244002i3−2i3-4-420000-2-24-2-2002i3−2i32i3−2i3002i3−2i3−2i32i322-422000000000000000000000000000000000000000000
χ664-40-24-200−2i32i3-42223−2300-21-21100−2i32i3i3−i300i3−i3−i3i32-12-1-10000003i−3i003i−3i−3i3i00−3323−23−33−33000000000000000000
χ674-40-24-200−2i32i3-422−232300-21-21100−2i32i3i3−i300i3−i3−i3i32-12-1-1000000−3i3i00−3i3i3i−3i003−3−23233−33−3000000000000000000
χ684-40-24-2002i3−2i3-42223−2300-21-211002i3−2i3−i3i300−i3i3i3−i32-12-1-1000000−3i3i00−3i3i3i−3i00−3323−23−33−33000000000000000000
χ694-40-24-2002i3−2i3-422−232300-21-211002i3−2i3−i3i300−i3i3i3−i32-12-1-10000003i−3i003i−3i−3i3i003−3−23233−33−3000000000000000000
χ704-40-2-2400−2i32i32-420023−231-2-21100i3−i3−2i32i300i3−i3−i3i3-122-1-10000−330023−23−33−333i−3i00003i−3i−3i3i000000000000000000
χ714-40-2-2400−2i32i32-4200−23231-2-21100i3−i3−2i32i300i3−i3−i3i3-122-1-100003−300−23233−33−3−3i3i0000−3i3i3i−3i000000000000000000
χ724-40-2-24002i3−2i32-420023−231-2-21100−i3i32i3−2i300−i3i3i3−i3-122-1-10000−330023−23−33−33−3i3i0000−3i3i3i−3i000000000000000000
χ734-40-2-24002i3−2i32-4200−23231-2-21100−i3i32i3−2i300−i3i3i3−i3-122-1-100003−300−23233−33−33i−3i00003i−3i−3i3i000000000000000000
χ744-40-2-2-200−2i32i322223−2323−23111−1−3i32−1+3i3200i3−i3i3−i33-3−3−i323+i32−3+i323−i32-1-1-11+3i321−3i320000−333i−3i−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ113i−3i−33−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000000
χ754-40-2-2-200−2i32i322223−23−2323111−1+3i32−1−3i3200i3−i3i3−i3-333−i32−3+i323+i32−3−i32-1-1-11−3i321+3i3200003−33i−3i3−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−3i3i−33−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000
χ764-40-2-2-200−2i32i3222−232323−23111−1+3i32−1−3i3200i3−i3i3−i3-333−i32−3+i323+i32−3−i32-1-1-11−3i321+3i320000−33−3i3i−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ113i−3i3−33−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000
χ774-40-2-2-200−2i32i3222−2323−2323111−1−3i32−1+3i3200i3−i3i3−i33-3−3−i323+i32−3+i323−i32-1-1-11+3i321−3i3200003−3−3i3i3−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11−3i3i3−33−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000000
χ784-40-2-2-2002i3−2i322223−2323−23111−1+3i32−1−3i3200−i3i3−i3i33-3−3+i323−i32−3−i323+i32-1-1-11−3i321+3i320000−33−3i3i−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11−3i3i−33−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000
χ794-40-2-2-2002i3−2i322223−23−2323111−1−3i32−1+3i3200−i3i3−i3i3-333+i32−3−i323−i32−3+i32-1-1-11+3i321−3i3200003−3−3i3i3−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ113i−3i−33−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000000
χ804-40-2-2-2002i3−2i3222−232323−23111−1−3i32−1+3i3200−i3i3−i3i3-333+i32−3−i323−i32−3+i32-1-1-11+3i321−3i320000−333i−3i−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−3i3i3−33−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000000
χ814-40-2-2-2002i3−2i3222−2323−2323111−1+3i32−1−3i3200−i3i3−i3i33-3−3+i323−i32−3−i323+i32-1-1-11−3i321+3i3200003−33i−3i3−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113i−3i3−33−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000

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