Finite Group Databasebeta

← Group #97833

Character table — Group #97833

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444444444444448888888822444444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-11111111-1-1iiii−i−i−i−i1-1-1-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-11111111-1-1−i−i−i−iiiii1-1-1-11-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-111111-1-111iiii−i−i−i−i-11-1-1-11-11ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-111111-1-111−i−i−i−iiiii-11-1-1-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-1iiii−i−i−i−i-1111-111-1−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-111-1-1−i−i−i−iiiii-1111-111-1ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-111iiii−i−i−i−i1-1111-1-11−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-111−i−i−i−iiiii1-1111-1-11ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-22-2-2-22-20000222200000000000000-2-2000000000000
χ1822222222222222-2-2-22-2-2-22-20000-2-2-2-20000000000000022000000000000
χ19222222222222-2-222-2-222-2-2-222-2-200000000000000-220000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222000000000000002-20000000000000000
χ21222222222222-2-2-2-22-2-2-22-2200000000000000002200-2-200000000000000
χ22222222222222-2-2-2-22-2-2-22-220000000000000000-2-2002200000000000000
χ2322222222-2-2-2-222-2-22-2222-2-2000022-2-200000000000000-22000000000000
χ2422222222-2-2-2-222-2-22-2222-2-20000-2-222000000000000002-2000000000000
χ2522222222-2-2-2-2-2-22222-2-222-222-2-2000000000000002-20000000000000000
χ2622222222-2-2-2-2-2-22222-2-222-2-2-22200000000000000-220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2222-22200000000000000002-200-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-2220000000000000000-22002-200000000000000
χ2922-22-2-22-222-2-22-2000-20002000002i−2i2i−2i22−2−222−2−2000000000000i2−i2i2−i20000
χ3022-22-2-22-222-2-22-2000-20002000002i−2i2i−2i−2−222−2−222000000000000−i2i2−i2i20000
χ3122-22-2-22-222-2-22-2000-2000200000−2i2i−2i2i22−2−222−2−2000000000000−i2i2−i2i20000
χ3222-22-2-22-222-2-22-2000-2000200000−2i2i−2i2i−2−222−2−222000000000000i2−i2i2−i20000
χ3322-22-2-22-2-2-2222-20002000-2000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000−222−20000
χ3422-22-2-22-2-2-2222-20002000-2000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000002−2−220000
χ3522-22-2-22-2-2-2222-20002000-200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000002−2−220000
χ3622-22-2-22-2-2-2222-20002000-200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000−222−20000
χ37444-44-4-4-4000000004000-400000000002-22-22-22-200000000000000000000
χ38444-44-4-4-4000000004000-40000000000-22-22-22-2200000000000000000000
χ39444-44-4-4-400000000-4000400000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ40444-44-4-4-400000000-400040000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4144-44-4-44-444-4-4-440004000-40000000000000000000000000000000000000
χ4244-44-4-44-4-4-444-44000-400040000000000000000000000000000000000000
χ4344-4-4-44-4400000000004i−4i000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4444-4-4-44-4400000000004i−4i00000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4544-4-4-44-440000000000−4i4i000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ4644-4-4-44-440000000000−4i4i00000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ474-444-44-4-40000004-40000000004i−4i00000000000000000000000000000000
χ484-444-44-4-40000004-4000000000−4i4i00000000000000000000000000000000
χ494-444-44-4-4000000-4400000004i−4i0000000000000000000000000000000000
χ504-444-44-4-4000000-440000000−4i4i0000000000000000000000000000000000
χ514-44-4-4-4444-44-400000000000000000000000000000000000000000002i−2i2i−2i
χ524-44-4-4-4444-44-40000000000000000000000000000000000000000000−2i2i−2i2i
χ534-44-4-4-444-44-4400000000000000000000000000000000000000000002-2-22
χ544-44-4-4-444-44-440000000000000000000000000000000000000000000-222-2
χ554-4-4-4444-44-4-44000000000000000000000000000000000002-22-200000000
χ564-4-4-4444-44-4-4400000000000000000000000000000000000-22-2200000000
χ574-4-4-4444-4-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ584-4-4-4444-4-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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