Finite Group Databasebeta

← Group #151060

Character table — Group #151060

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1122222224444444444444488888881616161616161616161616161616161632323232
order1224488882444448888161616168161616161616161616161616161632323232323232328888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-111-1-11111-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i
χ6111111111-1-111-1-111-1-11111-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−iii
χ7111111111-1-111-1-111-1-11111-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii
χ8111111111-1-111-1-111-1-11111-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i
χ911111-1-11111-1-1-1-1-11-1-11111111-1-1-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011111-1-11111-1-1-1-1-11-1-11111111-1-1-1-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ1111111-1-11111-1-1-1-1-11-1-11111111-1-1-1-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ1211111-1-11111-1-1-1-1-11-1-11111111-1-1-1-1−i−iii−i−iii-1-111-1-111i−ii−i
χ1311111-1-111-1-1-1-111-11111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11
χ1411111-1-111-1-1-1-111-11111111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-111-1
χ1511111-1-111-1-1-1-111-11111111-1-1-1-1-111-1-11111-1-111-1-1-1-111-111-1
χ1611111-1-111-1-1-1-111-11111111-1-1-1-1-111-1-11111-1-1-1-11111-1-11-1-11
χ172222222222222222222-2-2-2-22-2-2-2-2-2-200000000000000000000
χ18222222222-2-222-2-222-2-2-2-2-2-2-222-2-22200000000000000000000
χ192222222-2-222-2-2-2-22-2220000-200000000000000i2−i2i2−i2i2−i2i2−i20000
χ202222222-2-222-2-2-2-22-2220000-200000000000000−i2i2−i2i2−i2i2−i2i20000
χ212222222-2-2-2-2-2-2222-2-2-20000200000000000000i2−i2i2−i2−i2i2−i2i20000
χ222222222-2-2-2-2-2-2222-2-2-20000200000000000000−i2i2−i2i2i2−i2i2−i20000
χ2322222-2-22222-2-2-2-2-22-2-2-2-2-2-22-2-2222200000000000000000000
χ2422222-2-222-2-2-2-222-2222-2-2-2-2-22222-2-200000000000000000000
χ2522222-2-2-2-2222222-2-2-2-20000-200000000000000i2−i2−i2i2i2−i2−i2i20000
χ2622222-2-2-2-2222222-2-2-2-20000-200000000000000−i2i2i2−i2−i2i2i2−i20000
χ2722222-2-2-2-2-2-222-2-2-2-2220000200000000000000i2−i2−i2i2−i2i2i2−i20000
χ2822222-2-2-2-2-2-222-2-2-2-2220000200000000000000−i2i2i2−i2i2−i2−i2i20000
χ2922-22-2002200002i−2i0-22i−2i22-2-2000002i−2i002ζ3−2ζ32ζ−2ζ00000000000000
χ3022-22-2002200002i−2i0-22i−2i22-2-2000002i−2i00−2ζ32ζ3−2ζ2ζ00000000000000
χ3122-22-2002200002i−2i0-22i−2i-2-22200000−2i2i2ζ−2ζ00002ζ3−2ζ3000000000000
χ3222-22-2002200002i−2i0-22i−2i-2-22200000−2i2i−2ζ2ζ0000−2ζ32ζ3000000000000
χ3322-22-200220000−2i2i0-2−2i2i22-2-200000−2i2i002ζ−2ζ2ζ3−2ζ300000000000000
χ3422-22-200220000−2i2i0-2−2i2i22-2-200000−2i2i00−2ζ2ζ−2ζ32ζ300000000000000
χ3522-22-200220000−2i2i0-2−2i2i-2-222000002i−2i2ζ3−2ζ300002ζ−2ζ000000000000
χ3622-22-200220000−2i2i0-2−2i2i-2-222000002i−2i−2ζ32ζ30000−2ζ2ζ000000000000
χ37444-4-400004-4000000002i2−2i22i2−2i202i2−2i2000000000000000000000000
χ38444-4-400004-400000000−2i22i2−2i22i20−2i22i2000000000000000000000000
χ39444-4-40000-44000000002i2−2i22i2−2i20−2i22i2000000000000000000000000
χ40444-4-40000-4400000000−2i22i2−2i22i202i2−2i2000000000000000000000000
χ4144-44-400-4-400004i−4i04−4i4i0000000000000000000000000000000
χ4244-44-400-4-40000−4i4i044i−4i0000000000000000000000000000000
χ4344-4-444400000000-40002i2−2i2−2i22i20002i2−2i20000000000000000000000
χ4444-4-444400000000-4000−2i22i22i2−2i2000−2i22i20000000000000000000000
χ4544-4-44-4-40000000040002i2−2i2−2i22i2000−2i22i20000000000000000000000
χ4644-4-44-4-4000000004000−2i22i22i2−2i20002i2−2i20000000000000000000000
χ478-800042−424i2−4i2004i−4i0000000000000000000000000000000000000
χ488-800042−42−4i24i200−4i4i0000000000000000000000000000000000000
χ498-8000−42424i2−4i200−4i4i0000000000000000000000000000000000000
χ508-8000−4242−4i24i2004i−4i0000000000000000000000000000000000000

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