Finite Group Databasebeta

← Group #97721

Character table — Group #97721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422222244444444444444444444424444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1111-1-11111111111-1-1-11-1-11-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-111-11-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-111-1-11111111-1-1iiii−i−i−i−i-1-1-1-11-111ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-111-1-11111111-1-1−i−i−i−iiiii-1-1-1-11-111−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-111-1-111-1-111111iiii−i−i−i−i1-1-11-11-1-1−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-1-1-111-1-111-1-111111−i−i−i−iiiii1-1-11-11-1-1ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1iiii−i−i−i−i111-1-111-1ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1−i−i−i−iiiii111-1-111-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-111iiii−i−i−i−i-11111-1-11−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-111−i−i−i−iiiii-11111-1-11ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2220022-2002200000000000-200-20000000000000
χ1822222222222222-2-2-2-2-2-22200-2-2-200-2-20000000000020020000000000000
χ19222222222222-2-22-22-222-2-22200-2-2-200000000000-2200000000000000000
χ20222222222222-2-22-22-222-2-2-2-200-222000000000002-200000000000000000
χ21222222222222-2-2-22-22-2-2-2-20000200000000000020002-20-2000000000000
χ22222222222222-2-2-22-22-2-2-2-200002000000000000-2000-2202000000000000
χ2322222222-2-2-2-2222222-2-2-2-20022-200-2-200000000000200-20000000000000
χ2422222222-2-2-2-2222222-2-2-2-200-2-2-2002200000000000-20020000000000000
χ2522222222-2-2-2-2-2-22-22-2-2-222000020000000000002000-2-202000000000000
χ2622222222-2-2-2-2-2-22-22-2-2-22200002000000000000-2000220-2000000000000
χ2722222222-2-2-2-2-2-2-22-2222222200-2-2-2000000000002-200000000000000000
χ2822222222-2-2-2-2-2-2-22-222222-2-200-22200000000000-2200000000000000000
χ292-2222-2-2-22i−2i2i−2i2-20000002i−2i002-20002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i00000000
χ302-2222-2-2-22i−2i2i−2i2-20000002i−2i002-20002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i00000000
χ312-2222-2-2-22i−2i2i−2i2-20000002i−2i00-22000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i00000000
χ322-2222-2-2-22i−2i2i−2i2-20000002i−2i00-22000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i00000000
χ332-2222-2-2-2−2i2i−2i2i2-2000000−2i2i002-2000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i00000000
χ342-2222-2-2-2−2i2i−2i2i2-2000000−2i2i002-2000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i00000000
χ352-2222-2-2-2−2i2i−2i2i2-2000000−2i2i00-220002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i00000000
χ362-2222-2-2-2−2i2i−2i2i2-2000000−2i2i00-220002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i00000000
χ37444-4-44-4-4000000040-400000000000002-22-22-22-200000000000000000000
χ38444-4-44-4-4000000040-40000000000000-22-22-22-2200000000000000000000
χ39444-4-44-4-40000000-40400000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ40444-4-44-4-40000000-4040000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4144-44-4-44-400000000004-400000004i−4i000000000000000000000000000000
χ4244-44-4-44-400000000004-40000000−4i4i000000000000000000000000000000
χ4344-44-4-44-40000000000-44004i−4i00000000000000000000000000000000000
χ4444-44-4-44-40000000000-4400−4i4i00000000000000000000000000000000000
χ4544-4-44-4-444i−4i−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4644-4-44-4-444i−4i−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ4744-4-44-4-44−4i4i4i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4844-4-44-4-44−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ494-4444-4-4-44i−4i4i−4i-44000000−4i4i0000000000000000000000000000000000000
χ504-4444-4-4-4−4i4i−4i4i-440000004i−4i0000000000000000000000000000000000000
χ514-44-4-4-44400000040-4000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ524-44-4-4-44400000040-400000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ534-44-4-4-444000000-404000000000000002-2-222-2-2200000000000000000000
χ544-44-4-4-444000000-40400000000000000-222-2-222-200000000000000000000
χ554-4-4-4444-444-4-40000000000000000000000000000000000000002i−2i2i−2i0000
χ564-4-4-4444-444-4-4000000000000000000000000000000000000000−2i2i−2i2i0000
χ574-4-4-4444-4-4-4440000000000000000000000000000000000000002-2-220000
χ584-4-4-4444-4-4-444000000000000000000000000000000000000000-222-20000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

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