Finite Group Databasebeta

← Group #134821

Character table — Group #134821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444444444448888888888888888161616163232323232323232
order12222244442244444488882224448888888888448888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ8111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-11111-111-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ1011111111111111-1-1-1-11111-111-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ1111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111i−i−iii−i−ii
χ1411111111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111−iii−i−iii−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1i−i−ii−iii−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−iii−ii−i−ii
χ172222222222-2-2-2-222-2-22222-200200-2-222-2-20000000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-2-20020022-2-2220000000000000000
χ192222222222-2-2-2-2-2-2222222200-200-2-2-2-2220000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2200-2002222-2-20000000000000000
χ21222222-2-2-2-222-2-222220000-222-2-2-200000000002-20000000000
χ22222222-2-2-2-222-2-222220000-2-2-2-2220000000000-220000000000
χ23222222-2-2-2-222-2-2-2-2-2-200002222-2-20000000000-220000000000
χ24222222-2-2-2-222-2-2-2-2-2-200002-2-222200000000002-20000000000
χ25222222-2-2-2-2-2-22222-2-20000200-2000000002i2i−2i−2i002i−2i00000000
χ26222222-2-2-2-2-2-22222-2-20000200-200000000−2i−2i2i2i00−2i2i00000000
χ27222222-2-2-2-2-2-222-2-2220000-2002000000002i2i−2i−2i00−2i2i00000000
χ28222222-2-2-2-2-2-222-2-2220000-200200000000−2i−2i2i2i002i−2i00000000
χ294444-4-444-4-40000000000000000004i−4i00000000000000000000
χ304444-4-444-4-4000000000000000000−4i4i00000000000000000000
χ314444-4-4-4-4440000000044-4-40000000000000000000000000000
χ324444-4-4-4-44400000000-4-4440000000000000000000000000000
χ3344-4-4004i−4i00000000002i2−2i222−2202-202i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ3444-4-4004i−4i00000000002i2−2i222−220-220−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ3544-4-4004i−4i0000000000−2i22i2−222202-202i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ3644-4-4004i−4i0000000000−2i22i2−22220-220−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ3744-4-400−4i4i00000000002i2−2i2−222202-20−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ3844-4-400−4i4i00000000002i2−2i2−22220-2202i−2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ3944-4-400−4i4i0000000000−2i22i222−2202-20−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ4044-4-400−4i4i0000000000−2i22i222−220-2202i−2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ414-44-44-40000004i−4i00000000000000002i2−2i222−220000000000000000
χ424-44-44-40000004i−4i0000000000000000−2i22i2−22220000000000000000
χ434-44-44-4000000−4i4i00000000000000002i2−2i2−22220000000000000000
χ444-44-44-4000000−4i4i0000000000000000−2i22i222−220000000000000000
χ454-44-4-4400004-4004i−4i4i−4i00000000000000000000000000000000
χ464-44-4-4400004-400−4i4i−4i4i00000000000000000000000000000000
χ474-44-4-440000-44004i−4i−4i4i00000000000000000000000000000000
χ484-44-4-440000-4400−4i4i4i−4i00000000000000000000000000000000
χ498-8-8800008-80000000000000000000000000000000000000000
χ508-8-880000-880000000000000000000000000000000000000000

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