Finite Group Databasebeta

← Group #88926

Character table — Group #88926

Order 432.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size112244446888899121212121818181818181818545454
order1236336643366441212121288121224242424288
χ1111111111111111111111111111111
χ21111111111111111111-1-111-1-1-1-11-1-1
χ31111111111111-1-11111i−i-1-1ii−i−i-1i−i
χ41111111111111-1-11111−ii-1-1−i−iii-1−ii
χ511111111-1111111-1-1-1-111111111-1-1-1
χ611111111-1111111-1-1-1-1-1-111-1-1-1-1-111
χ711111111-11111-1-1-1-1-1-1i−i-1-1ii−i−i1−ii
χ811111111-11111-1-1-1-1-1-1−ii-1-1−i−iii1i−i
χ922-1-122220-1-1-1-122000022-1-1-1-1-1-1000
χ1022-1-122220-1-1-1-1220000-2-2-1-11111000
χ1122-1-122220-1-1-1-1-2-200002i−2i11−i−iii000
χ1222-1-122220-1-1-1-1-2-20000−2i2i11ii−i−i000
χ132-22-222-2-2022-2-22i−2i0000002i−2i0000000
χ142-22-222-2-2022-2-2−2i2i000000−2i2i0000000
χ152-2-1122-2-20-1-1112i−2i000000−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000
χ162-2-1122-2-20-1-1112i−2i000000−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000
χ172-2-1122-2-20-1-111−2i2i000000i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000
χ182-2-1122-2-20-1-111−2i2i000000i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000
χ1944441-21-241-21-20011-2-200000000000
χ2044441-21-2-41-21-200-1-12200000000000
χ214444-21-214-21-2100-2-21100000000000
χ224444-21-21-4-21-210022-1-100000000000
χ234-44-41-2-1201-2-12003i−3i0000000000000
χ244-44-41-2-1201-2-1200−3i3i0000000000000
χ254-44-4-212-10-212-100003i−3i00000000000
χ264-44-4-212-10-212-10000−3i3i00000000000
χ2788-4-42-42-40-12-1200000000000000000
χ2888-4-4-42-4202-12-100000000000000000
χ298-8-442-4-240-121-200000000000000000
χ308-8-44-424-202-1-2100000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.