Finite Group Databasebeta

← Group #150436

Character table — Group #150436

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444488888888888888888161616161616161616323232323232
order12222222244444444444444488888888488888888448888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-111-1-1-111111111-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111111111-1-1-111-1-1-111111111-1−i−i−i−iiiii-1-1−i−iii
χ71111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911111-1-11-1-1-1-1-111-111-111-1-1-11111-1-1-1-11ii−i−iii−i−i1-1i−ii−i
χ1011111-1-11-1-1-1-1-111-111-111-1-1-11111-1-1-1-11−i−iii−i−iii1-1−ii−ii
χ1111111-1-11-1-1-1-1-111-111-111-1-1-1-1-1-1-111111ii−i−iii−i−i-11−ii−ii
χ1211111-1-11-1-1-1-1-111-111-111-1-1-1-1-1-1-111111−i−iii−i−iii-11i−ii−i
χ1311111-1-11-1-1-1-1-111-1-1-11111111111-1-1-1-1-111-1-1-1-111-111-1-11
χ1411111-1-11-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-11111-1-1-11-111-1
χ1511111-1-11-1-1-1-1-111-1-1-1111111-1-1-1-11111-111-1-1-1-1111-1-111-1
χ1611111-1-11-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-11111-1-11-11-1-11
χ17222222222-2-2-2-2222222-2-2-2-2200000000-200000000000000
χ18222222222-2-2-2-2222-2-2-2-2-222-200000000200000000000000
χ1922222-2-22-2222222-222-2-2-222-200000000-200000000000000
χ2022222-2-22-2222222-2-2-22-2-2-2-2200000000200000000000000
χ212-2-22200-202i2i−2i−2i2-202-20002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000
χ222-2-22200-202i2i−2i−2i2-202-20002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000
χ232-2-22200-202i2i−2i−2i2-20-22000−2i2i00000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i000000
χ242-2-22200-202i2i−2i−2i2-20-22000−2i2i0000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i000000
χ252-2-22200-20−2i−2i2i2i2-202-2000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000
χ262-2-22200-20−2i−2i2i2i2-202-2000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000
χ272-2-22200-20−2i−2i2i2i2-20-220002i−2i00000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i000000
χ282-2-22200-20−2i−2i2i2i2-20-220002i−2i0000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i000000
χ294444444440000-4-4-40000000000000000000000000000000
χ3044444-4-44-40000-4-440000000000000000000000000000000
χ314444-444-4-400000000000000022-2-222-2-2000000000000000
χ324444-444-4-4000000000000000-2-222-2-222000000000000000
χ334444-4-4-4-4400000000000000022-2-2-2-222000000000000000
χ344444-4-4-4-44000000000000000-2-22222-2-2000000000000000
χ3544-4-404-4002-22-20000002-20000022−220022−22000000000000000
χ3644-4-404-4002-22-20000002-200000−222200−2222000000000000000
χ3744-4-404-400-22-22000000-2200022−220022−2200000000000000000
χ3844-4-404-400-22-22000000-22000−222200−222200000000000000000
χ3944-4-40-44002-22-2000000-2200022−2200−222200000000000000000
χ4044-4-40-44002-22-2000000-22000−22220022−2200000000000000000
χ4144-4-40-4400-22-220000002-20000022−2200−2222000000000000000
χ4244-4-40-4400-22-220000002-200000−22220022−22000000000000000
χ434-4-44400-400000-4400040000-400000000000000000000000
χ444-4-44400-400000-44000-40000400000000000000000000000
χ458-88-8000004i−4i−4i4i0000000000000000000000000000000000
χ468-88-800000−4i4i4i−4i0000000000000000000000000000000000
χ478-8-88-8008000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).