Finite Group Databasebeta

← Group #11720794

Character table — Group #11720794

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49
size11111122244412121212121212121212121212121212181818181818363636363636363636363636363636
order1233662662663366666666666666441212121226688882424242424242424
χ11111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii
χ5111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11-11-111-1-111-1-1
χ6111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-1-111-1-111
χ7111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111i−i−iiii−i−i−i−iii
χ8111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111−iii−i−i−iiiii−i−i
χ9222222-2-2-20002222-2-2-2-2000000002-222-2-2000000000000000
χ10222222-2-2-20002222-2-2-2-200000000-22-2-222000000000000000
χ1133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32ii−i−iζ7ζ11ζ7ζ11−ζ7−ζ11−ζ7−ζ11
χ1233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−i−iii−ζ7−ζ11−ζ7−ζ11ζ7ζ11ζ7ζ11
χ1333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-1-11+i321−i321+i321−i32-11+i321−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ1433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ1533−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32i−i−iiζ7ζ11−ζ7−ζ11−ζ7−ζ11ζ7ζ11
χ1633−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32−iii−i−ζ7−ζ11ζ7ζ11ζ7ζ11−ζ7−ζ11
χ1733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i321-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ1833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i320000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i32-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ1933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32ii−i−iζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ2033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−i−iii−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ2133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-11−i321+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ2333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32i−i−iiζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ2433−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32−iii−i−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ2533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i321-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ2633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i320000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i32-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ274444444444441-21-211-2-21111-2-2-2-2000000000000000000000
χ28444444444444-21-21-2-211-2-2-2-21111000000000000000000000
χ29444444444-4-4-41-21-211-2-2-1-1-1-12222000000000000000000000
χ30444444444-4-4-4-21-21-2-2112222-1-1-1-1000000000000000000000
χ31444444-4-4-40001-21-2-1-12233-3-30000000000000000000000000
χ32444444-4-4-40001-21-2-1-122-3-3330000000000000000000000000
χ33444444-4-4-4000-21-2122-1-1000033-3-3000000000000000000000
χ34444444-4-4-4000-21-2122-1-10000-3-333000000000000000000000
χ354-444-4-40000001-2-123-300−i3i3−i3i300−2i32i3000000000000000000000
χ364-444-4-40000001-2-123-300i3−i3i3−i3002i3−2i3000000000000000000000
χ374-444-4-40000001-2-12-3300−i3i3i3−i3−2i32i300000000000000000000000
χ384-444-4-40000001-2-12-3300i3−i3−i3i32i3−2i300000000000000000000000
χ394-444-4-400000044-4-4000000000000000000000000000000000
χ404-444-4-4000000-212-1003-300−2i32i3−i3i3i3−i3000000000000000000000
χ414-444-4-4000000-212-1003-3002i3−2i3i3−i3−i3i3000000000000000000000
χ424-444-4-4000000-212-100-33−2i32i300i3−i3i3−i3000000000000000000000
χ434-444-4-4000000-212-100-332i3−2i300−i3i3−i3i3000000000000000000000
χ4466−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i300000000000000000002-2−1−i3−1+i31+i31−i3000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-63+3i33−3i30000000000000000000-221+i31−i3−1−i3−1+i3000000000000000
χ4666−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i300000000000000000002-2−1+i3−1−i31−i31+i3000000000000000
χ4766−3+3i3−3−3i3−3+3i3−3−3i3-63−3i33+3i30000000000000000000-221−i31+i3−1+i3−1−i3000000000000000
χ4812-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000000
χ4912-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000000

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