Finite Group Databasebeta

← Group #97751

Character table — Group #97751

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
χ31111111111111111111111111-1-111-1-111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1111-1-11111111111-1-1-1-11-11-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111-11-1-11-11-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-111111-1-1-1-11111
χ911111111-1-1-1-111-1-111-1-1-1-111111-1-111iiii−i−i−i−i-1-1-11-11-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-111-1-1-1-111111-1-111−i−i−i−iiiii-1-1-11-11-11−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-1iiii−i−i−i−i1-1111-11-1−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-1−i−i−i−iiiii1-1111-11-1ii−i−iii−i−i−i−iii
χ1311111111-1-1-1-111-1-111-1-1-1-1-1-11111111iiii−i−i−i−i111-1-1-1-1-1ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-111-1-111-1-1-1-1-1-11111111−i−i−i−iiiii111-1-1-1-1-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1iiii−i−i−i−i-11-1-11111−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1−i−i−i−iiiii-11-1-11111ii−i−i−i−iiiii−i−i
χ172222222222222222-2-2-2-2-2-222-2002200000000000-20-20000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-200-2-2000000000002020000000000000000
χ19222222222222-2-2-2-2222-2-2200-22200-2-200000000000020-20000000000000
χ20222222222222-2-2-2-2222-2-2200-2-2-20022000000000000-2020000000000000
χ21222222222222-2-2-2-2-2-2-222-20020000000000000020-20020-2000000000000
χ22222222222222-2-2-2-2-2-2-222-200200000000000000-20200-202000000000000
χ2322222222-2-2-2-222-2-2-2-2222222-200-2-20000000000020-20000000000000000
χ2422222222-2-2-2-222-2-2-2-22222-2-2-2002200000000000-2020000000000000000
χ2522222222-2-2-2-2-2-22222-222-200-22200-2-2000000000000-2020000000000000
χ2622222222-2-2-2-2-2-22222-222-200-2-2-2002200000000000020-20000000000000
χ2722222222-2-2-2-2-2-222-2-22-2-220020000000000000020-200-202000000000000
χ2822222222-2-2-2-2-2-222-2-22-2-2200200000000000000-2020020-2000000000000
χ292-2-2-222-2222-2-22-22-20000002-20002-200i2i2−i2−i2i2i2−i2−i20000000000000000i2−i2i2−i2
χ302-2-2-222-2222-2-22-22-20000002-20002-200−i2−i2i2i2−i2−i2i2i20000000000000000−i2i2−i2i2
χ312-2-2-222-2222-2-22-22-2000000-22000-2200i2i2−i2−i2i2i2−i2−i20000000000000000−i2i2−i2i2
χ322-2-2-222-2222-2-22-22-2000000-22000-2200−i2−i2i2i2−i2−i2i2i20000000000000000i2−i2i2−i2
χ332-2-2-222-22-2-2222-2-220000002-2000-220022−2−2−2−22200000000000000002−2−22
χ342-2-2-222-22-2-2222-2-220000002-2000-2200−2−22222−2−20000000000000000−222−2
χ352-2-2-222-22-2-2222-2-22000000-220002-20022−2−2−2−2220000000000000000−222−2
χ362-2-2-222-22-2-2222-2-22000000-220002-200−2−22222−2−200000000000000002−2−22
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
χ4144-44-4-4-44000000000004i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4244-44-4-4-44000000000004i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4344-44-4-4-4400000000000−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ4444-44-4-4-4400000000000−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4544-4-44-44-4000000004-4000000000004i−4i0000000000000000000000000000
χ4644-4-44-44-4000000004-400000000000−4i4i0000000000000000000000000000
χ4744-4-44-44-400000000-4400000004i−4i00000000000000000000000000000000
χ4844-4-44-44-400000000-440000000−4i4i00000000000000000000000000000000
χ494-44-4-4-4440000000000400-40000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ504-44-4-4-4440000000000400-4000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ514-44-4-4-4440000000000-40040000000002-2-222-2-2200000000000000000000
χ524-44-4-4-4440000000000-4004000000000-222-2-222-200000000000000000000
χ534-4-44-444-44-4-44000000000000000000000000000000000002-22-200000000
χ544-4-44-444-44-4-4400000000000000000000000000000000000-22-2200000000
χ554-4-44-444-4-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ564-4-44-444-4-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ574-4-4-444-4444-4-4-44-440000000000000000000000000000000000000000000
χ584-4-4-444-44-4-444-444-40000000000000000000000000000000000000000000
χ598-8888-8-8-8000000000000000000000000000000000000000000000000000

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