Finite Group Databasebeta

← Group #97757

Character table — Group #97757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444448888888824444444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111
χ51111111111111111111111-1-11-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-11-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-11111
χ911111111-1-1-1-111-1-111-1-1-1-11111111-1-1iiii−i−i−i−i1-1-11-11-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-111-1-1-1-11111111-1-1−i−i−i−iiiii1-1-11-11-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-111-1-1-1-111111-1-111iiii−i−i−i−i-11-1-11-11-1ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-111-1-111-1-1-1-111111-1-111−i−i−i−iiiii-11-1-11-11-1−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1iiii−i−i−i−i-1111-1-111−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1−i−i−i−iiiii-1111-1-111ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-111-1-111-1-1-1-1-1-11-1-1-1-111iiii−i−i−i−i1-11-111-11−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-111-1-111-1-1-1-1-1-11-1-1-1-111−i−i−i−iiiii1-11-111-11ii−i−i−i−iiiii−i−i
χ172222222222222222-2-2-2-2-2-200-200222200000000000-2-2000000000000000
χ182222222222222222-2-2-2-2-2-200-200-2-2-2-20000000000022000000000000000
χ19222222222222-2-2-2-2222-2-2222-2-2-20000000000000020000-2000000000000
χ20222222222222-2-2-2-2222-2-22-2-2-22200000000000000-200002000000000000
χ21222222222222-2-2-2-2-2-2-222-20020000000000000022000-2-20000000000000
χ22222222222222-2-2-2-2-2-2-222-200200000000000000-2-2000220000000000000
χ2322222222-2-2-2-222-2-2-2-2222200-20022-2-200000000000-22000000000000000
χ2422222222-2-2-2-222-2-2-2-2222200-200-2-222000000000002-2000000000000000
χ2522222222-2-2-2-2-2-22222-222-222-2-2-200000000000000-200002000000000000
χ2622222222-2-2-2-2-2-22222-222-2-2-2-2220000000000000020000-2000000000000
χ2722222222-2-2-2-2-2-222-2-22-2-22002000000000000002-2000-220000000000000
χ2822222222-2-2-2-2-2-222-2-22-2-2200200000000000000-220002-20000000000000
χ292-2222-2-2-222-2-22-2-22000000000002i−2i2i−2i22−2−222−2−20000000000000000i2−i2i2−i2
χ302-2222-2-2-222-2-22-2-22000000000002i−2i2i−2i−2−222−2−2220000000000000000−i2i2−i2i2
χ312-2222-2-2-222-2-22-2-2200000000000−2i2i−2i2i22−2−222−2−20000000000000000−i2i2−i2i2
χ322-2222-2-2-222-2-22-2-2200000000000−2i2i−2i2i−2−222−2−2220000000000000000i2−i2i2−i2
χ332-2222-2-2-2-2-2222-22-2000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000−222−2
χ342-2222-2-2-2-2-2222-22-2000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i200000000000000002−2−22
χ352-2222-2-2-2-2-2222-22-200000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200000000000000002−2−22
χ362-2222-2-2-2-2-2222-22-200000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000−222−2
χ37444-4-44-4-44-44-40000000000000000000000000000000000000002-22-20000
χ38444-4-44-4-44-44-4000000000000000000000000000000000000000-22-220000
χ39444-4-44-4-4-44-440000000000000000000000000000000000000002i−2i−2i2i0000
χ40444-4-44-4-4-44-44000000000000000000000000000000000000000−2i2i2i−2i0000
χ4144-44-4-44-4000000000004i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4244-44-4-44-4000000000004i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4344-44-4-44-400000000000−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ4444-44-4-44-400000000000−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4544-4-44-4-44000000004-400000004i−4i00000000000000000000000000000000
χ4644-4-44-4-44000000004-40000000−4i4i00000000000000000000000000000000
χ4744-4-44-4-4400000000-4400004i−4i00000000000000000000000000000000000
χ4844-4-44-4-4400000000-440000−4i4i00000000000000000000000000000000000
χ494-4444-4-4-444-4-4-444-40000000000000000000000000000000000000000000
χ504-4444-4-4-4-4-444-44-440000000000000000000000000000000000000000000
χ514-44-4-4-4444-4-44000000000000000000000000000000000002-22-200000000
χ524-44-4-4-4444-4-4400000000000000000000000000000000000-22-2200000000
χ534-44-4-4-444-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ544-44-4-4-444-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ554-4-44-44-440000000000400-40000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ564-4-44-44-440000000000400-4000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ574-4-44-44-440000000000-40040000000002-2-22-222-200000000000000000000
χ584-4-44-44-440000000000-4004000000000-222-22-2-2200000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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