Finite Group Databasebeta

← Group #93205

Character table — Group #93205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35
size111122448888888816161616161616161616163232323232323232
order1222442422248888488161616161616161624444488
χ111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111-1-11-1-1-1-1-111iiii−i−i−i−i11ii−i−i-1-1
χ6111111111-1-11-1-1-1-1-111iiii−i−i−i−i-1-1−i−iii11
χ7111111111-1-11-1-1-1-1-111−i−i−i−iiiii11−i−iii-1-1
χ8111111111-1-11-1-1-1-1-111−i−i−i−iiiii-1-1ii−i−i11
χ9222222222222-2-2-2-22-2-20000000000000000
χ10222222222-2-222222-2-2-20000000000000000
χ112222-2-22-2200-22i2i−2i−2i00000000000001+i−1−i1−i−1+i00
χ122222-2-22-2200-22i2i−2i−2i0000000000000−1−i1+i−1+i1−i00
χ132222-2-22-2200-2−2i−2i2i2i00000000000001−i−1+i1+i−1−i00
χ142222-2-22-2200-2−2i−2i2i2i0000000000000−1+i1−i−1−i1+i00
χ152222-2-22-2-22220000-20022−2−222−2−200000000
χ162222-2-22-2-22220000-200−2−222−2−22200000000
χ172222-2-22-2-2-2-220000200i2i2−i2−i2−i2−i2i2i200000000
χ182222-2-22-2-2-2-220000200−i2−i2i2i2i2i2−i2−i200000000
χ1944444444-400-400000000000000000000000
χ20444444-4-400000000000000000000000002-2
χ21444444-4-40000000000000000000000000-22
χ224444-4-4-4400000000000000000002-2000000
χ234444-4-4-440000000000000000000-22000000
χ2444-4-44i−4i0000002ζ2−2ζ22ζ6−2ζ6000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ700000000
χ2544-4-44i−4i0000002ζ2−2ζ22ζ6−2ζ6000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ700000000
χ2644-4-44i−4i000000−2ζ22ζ2−2ζ62ζ6000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ700000000
χ2744-4-44i−4i000000−2ζ22ζ2−2ζ62ζ6000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ700000000
χ2844-4-4−4i4i0000002ζ6−2ζ62ζ2−2ζ2000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ500000000
χ2944-4-4−4i4i0000002ζ6−2ζ62ζ2−2ζ2000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ500000000
χ3044-4-4−4i4i000000−2ζ62ζ6−2ζ22ζ2000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ500000000
χ3144-4-4−4i4i000000−2ζ62ζ6−2ζ22ζ2000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ500000000
χ328-88-8000004-4000000000000000000000000
χ338-88-800000-44000000000000000000000000
χ348-8-88000000000000022−220000000000000000
χ358-8-880000000000000−22220000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.