Finite Group Databasebeta

← Group #3712

Character table — Group #3712

Order 144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size11112222222244446666666666661818
order12443366121212123612128888242424242424242424
χ1111111111111111111111111111111
χ2111111111111111111-1-11111-1-1-1-1-1-1
χ31111111111111111-1-111-1-1-1-11111-1-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-11111-1-1-1-111-1-1i−ii−iii−i−iii−i−i1-1
χ611-1-11111-1-1-1-111-1-1i−i−iiii−i−i−i−iii-11
χ711-1-11111-1-1-1-111-1-1−iii−i−i−iiiii−i−i-11
χ811-1-11111-1-1-1-111-1-1−ii−ii−i−iii−i−iii1-1
χ922222-12-122-1-1-1-1-1-100220000-1-1-1-100
χ1022222-12-122-1-1-1-1-1-100-2-20000111100
χ112222-12-12-1-122-1-1-1-12200-1-1-1-1000000
χ122222-12-12-1-122-1-1-1-1-2-2001111000000
χ1322-2-22-12-1-2-211-1-111002i−2i0000−i−iii00
χ1422-2-22-12-1-2-211-1-11100−2i2i0000ii−i−i00
χ1522-2-2-12-1211-2-2-1-1112i−2i00−i−iii000000
χ1622-2-2-12-1211-2-2-1-111−2i2i00ii−i−i000000
χ172-22i−2i22-2-22i−2i2i−2i2-22i−2i00000000000000
χ182-22i−2i2-1-212i−2i−ii-11−ii00000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300
χ192-22i−2i2-1-212i−2i−ii-11−ii00000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300
χ202-22i−2i-121-2−ii2i−2i-11−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ212-22i−2i-121-2−ii2i−2i-11−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ222-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i00000000000000
χ232-2−2i2i2-1-21−2i2ii−i-11i−i00000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300
χ242-2−2i2i2-1-21−2i2ii−i-11i−i00000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300
χ252-2−2i2i-121-2i−i−2i2i-11i−i0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ262-2−2i2i-121-2i−i−2i2i-11i−i0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ274444-2-2-2-2-2-2-2-2111100000000000000
χ2844-4-4-2-2-2-2222211-1-100000000000000
χ294-44i−4i-2-222−2i2i−2i2i1-1i−i00000000000000
χ304-4−4i4i-2-2222i−2i2i−2i1-1−ii00000000000000

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