Finite Group Databasebeta

← Group #94643

Character table — Group #94643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size1111224444448888888888881616161632323232323232323232
order12222244444488888888888822444444448888
χ111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii
χ51111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ9222222222222-2-2-2-20000000022-2-20000000000
χ10222222222222-2-2-2-200000000-2-2220000000000
χ112-2-22-22222-2-2-2000000000000002i−2i001+i−1−i1−i−1+i0000
χ122-2-22-22222-2-2-2000000000000002i−2i00−1−i1+i−1+i1−i0000
χ132-2-22-22222-2-2-200000000000000−2i2i001−i−1+i1+i−1−i0000
χ142-2-22-22222-2-2-200000000000000−2i2i00−1+i1−i−1−i1+i0000
χ152-2-22-222-2-2-2220000000000002-200000000i2−i2i2−i2
χ162-2-22-222-2-2-2220000000000002-200000000−i2i2−i2i2
χ172-2-22-222-2-2-222000000000000-22000000002−2−22
χ182-2-22-222-2-2-222000000000000-2200000000−222−2
χ194444444-4-44-4-400000000000000000000000000
χ20444444-400-40000002222-2-2-2-200000000000000
χ21444444-400-4000000-2-2-2-2222200000000000000
χ224444-4-400000022-2-200002222−22−2200000000000000
χ234444-4-400000022-2-20000−22−22222200000000000000
χ244444-4-4000000-2-2222222−22−22000000000000000000
χ254444-4-4000000-2-222−22−222222000000000000000000
χ264-44-40002-202-20022−22ζ+2i+ζ3−ζ−2i−ζ3ζ−2i+ζ3−ζ+2i−ζ3i2−i2i2−i200000000000000
χ274-44-40002-202-20022−22−ζ−2i−ζ3ζ+2i+ζ3−ζ+2i−ζ3ζ−2i+ζ3−i2i2−i2i200000000000000
χ284-44-40002-202-200−2222ζ−2i+ζ3−ζ+2i−ζ3ζ+2i+ζ3−ζ−2i−ζ3i2−i2i2−i200000000000000
χ294-44-40002-202-200−2222−ζ+2i−ζ3ζ−2i+ζ3−ζ−2i−ζ3ζ+2i+ζ3−i2i2−i2i200000000000000
χ304-44-4000-220-2222−2200i2−i2i2−i2−ζ+2i−ζ3ζ−2i+ζ3−ζ−2i−ζ3ζ+2i+ζ300000000000000
χ314-44-4000-220-2222−2200−i2i2−i2i2ζ−2i+ζ3−ζ+2i−ζ3ζ+2i+ζ3−ζ−2i−ζ300000000000000
χ324-44-4000-220-22−222200i2−i2i2−i2−ζ−2i−ζ3ζ+2i+ζ3−ζ+2i−ζ3ζ−2i+ζ300000000000000
χ334-44-4000-220-22−222200−i2i2−i2i2ζ+2i+ζ3−ζ−2i−ζ3ζ−2i+ζ3−ζ+2i−ζ300000000000000
χ344-4-44-44-40040000000000000000002-200000000
χ354-4-44-44-4004000000000000000000-2200000000
χ3688-8-80004-40-4400000000000000000000000000
χ3788-8-8000-4404-400000000000000000000000000
χ388-8-888-800000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.