Finite Group Databasebeta

← Group #100731

Character table — Group #100731

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444448888888888888888888888888881616161616161616161616163232
order12222222444444444422444444444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-111-1-1-1-111-1111-1-1-1-11ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-1-1-1-111-1111-1-1-1-11ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-111-1-1-1-111-1111-1-1-1-11−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-111-1-1-1-111-1111-1-1-1-11−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-111-1-1-1-1-1-1-11-1-111111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-111-1-1-1-1-1-1-11-1-111111ii−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-111-1-1-1-1-1-1-11-1-111111−i−iii−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-1-1-1-1-1-1-11-1-111111−i−iii−i−iiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-11
χ1722222222222222-2-2-2-2222-2-2-222-2-2-2000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-22-222-2-222-2000000000000000000000000000000
χ19222222222222-2-222-2-200-2-200000020000000022-2-222-2-200000000000000
χ20222222222222-2-222-2-200-2-2000000200000000-2-222-2-22200000000000000
χ21222222222222-2-2-2-22200-22000000-22222-2-2-2-20000000000000000000000
χ22222222222222-2-2-2-22200-22000000-2-2-2-2-222220000000000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-222-2000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-22222-2-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-20022000000-22i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2622222222-2-2-2-2-2-222-2-20022000000-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222002-20000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-222002-2000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-22-2-2-200002-22i−2i2i−2i00002i−2i2-20001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ30222-22-2-2-200002-22i−2i2i−2i00002i−2i2-2000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ31222-22-2-2-200002-22i−2i2i−2i0000−2i2i-220001+i−1−i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ32222-22-2-2-200002-22i−2i2i−2i0000−2i2i-22000−1−i1+i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ33222-22-2-2-200002-2−2i2i−2i2i00002i−2i-220001−i−1+i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ34222-22-2-2-200002-2−2i2i−2i2i00002i−2i-22000−1+i1−i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ35222-22-2-2-200002-2−2i2i−2i2i0000−2i2i2-20001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ36222-22-2-2-200002-2−2i2i−2i2i0000−2i2i2-2000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ37222-22-2-2-20000-222i−2i−2i2i2-20000002i−2i01−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ38222-22-2-2-20000-222i−2i−2i2i2-20000002i−2i0−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ39222-22-2-2-20000-222i−2i−2i2i-22000000−2i2i01−i−1+i1+i−1−i−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ40222-22-2-2-20000-222i−2i−2i2i-22000000−2i2i0−1+i1−i−1−i1+i1−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ41222-22-2-2-20000-22−2i2i2i−2i2-2000000−2i2i01+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ42222-22-2-2-20000-22−2i2i2i−2i2-2000000−2i2i0−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ43222-22-2-2-20000-22−2i2i2i−2i-220000002i−2i01+i−1−i1−i−1+i−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ44222-22-2-2-20000-22−2i2i2i−2i-220000002i−2i0−1−i1+i−1+i1−i1+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ4544-44-44-4-44i−4i4i−4i000000000000000000000000000000000000000002-22i−2i00
χ4644-44-44-4-44i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i00
χ4744-44-44-4-4−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i00
χ4844-44-44-4-4−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i00
χ494-444-4-44-44i−4i−4i4i00000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ504-444-4-44-44i−4i−4i4i0000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ514-444-4-44-4−4i4i4i−4i00000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ524-444-4-44-4−4i4i4i−4i0000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ534-4-444-4-4444-4-40000000000000000000000000000000002i−2i2i−2i0000000000
χ544-4-444-4-4444-4-4000000000000000000000000000000000−2i2i−2i2i0000000000
χ554-4-444-4-44-4-4440000000000000000000000000000000002-2-220000000000
χ564-4-444-4-44-4-444000000000000000000000000000000000-222-20000000000
χ5788-8-8-8-888000000000000000000000000000000000000000000000000000
χ588-88-8-88-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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