Finite Group Databasebeta

← Group #138564

Character table — Group #138564

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222444444888824448816161616161616162444888888161616161616161616161616444488882488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ91111-1-111-1-1-1-1-1-1-11-1111iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−iii−i−i11-1-11-1i−i
χ101111-1-111-1-1-1-1-1-1-11-1111iiii−i−i−i−i11-1-11-111-1-1ii−i−iiiii−i−i−i−i−i−iii-1-111-11−ii
χ111111-1-111-1-1-1-1-1-1-11-1111iiii−i−i−i−i-1-1111-1-1-111ii−i−i−i−i−i−iiiiiii−i−i11-1-1-11−ii
χ121111-1-111-1-1-1-1-1-1-11-1111iiii−i−i−i−i-1-1111-1-1-111ii−i−i−i−i−i−iiiii−i−iii-1-1111-1i−i
χ131111-1-111-1-1-1-1-1-1-11-1111−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiiiii−i−i-1-111-11i−i
χ141111-1-111-1-1-1-1-1-1-11-1111−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−i−i−iiiii−i−iii11-1-11-1−ii
χ151111-1-111-1-1-1-1-1-1-11-1111−i−i−i−iiiii-1-1111-1-1-111−i−iiiiiii−i−i−i−iii−i−i-1-1111-1−ii
χ161111-1-111-1-1-1-1-1-1-11-1111−i−i−i−iiiii-1-1111-1-1-111−i−iiiiiii−i−i−i−i−i−iii11-1-1-11i−i
χ1722222222222222-2-2-2-222222222220000-2-20000-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000
χ192222222222-2-2-2-22222-2-2000000002222-2-2-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-22222-2-200000000-2-2-2-2-2-22222000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-200i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2ii2−i2i2−i22−22−22−22−2000000000000
χ24222222-2-2-2-2000022-2-200i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2ii2−i2i2−i2−22−22−22−22000000000000
χ25222222-2-2-2-2000022-2-200−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i−i2i2−i2i2−22−22−22−22000000000000
χ26222222-2-2-2-2000022-2-200−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i−i2i2−i2i22−22−22−22−2000000000000
χ27222222-2-2-2-20000-2-22200i2i2−i2−i2i2i2−i2−i22-2-22000000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ28222222-2-2-2-20000-2-22200i2i2−i2−i2i2i2−i2−i2-222-2000000−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ29222222-2-2-2-20000-2-22200−i2−i2i2i2−i2−i2i2i22-2-22000000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ30222222-2-2-2-20000-2-22200−i2−i2i2i2−i2−i2i2i2-222-2000000i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-222-2-222222-22-2-2-20000000000002-20000000022-2-2-2-222000000000000
χ322222-2-222-2-222222-22-2-2-20000000000002-200000000-2-22222-2-2000000000000
χ332222-2-222-2-22222-22-22-2-20000000022-2-2-22-2-222000000000000000000000000
χ342222-2-222-2-22222-22-22-2-200000000-2-222-2222-2-2000000000000000000000000
χ352222-2-222-2-2-2-2-2-22-22-2222i2i2i2i−2i−2i−2i−2i0000-220000−2i−2i2i2i00000000000000000000
χ362222-2-222-2-2-2-2-2-22-22-222−2i−2i−2i−2i2i2i2i2i0000-2200002i2i−2i−2i00000000000000000000
χ372222-2-2-2-22200002-2-220022−2−2−2−2222-22-2000000−222−22−2−22−222−2000000000000
χ382222-2-2-2-22200002-2-220022−2−2−2−222-22-22000000−222−2−222−22−2−22000000000000
χ392222-2-2-2-22200002-2-2200−2−22222−2−22-22-20000002−2−22−222−22−2−22000000000000
χ402222-2-2-2-22200002-2-2200−2−22222−2−2-22-220000002−2−222−2−22−222−2000000000000
χ412222-2-2-2-2220000-222-20022−2−2−2−2220000002i−2i−2i2i2−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ422222-2-2-2-2220000-222-20022−2−2−2−222000000−2i2i2i−2i2−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ432222-2-2-2-2220000-222-200−2−22222−2−20000002i−2i−2i2i−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ442222-2-2-2-2220000-222-200−2−22222−2−2000000−2i2i2i−2i−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ4522-2-22i−2i2-22i−2i2i2i−2i−2i00002-22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000001+i−1−i1−i−1+i2−2i2−i20000
χ4622-2-22i−2i2-22i−2i2i2i−2i−2i00002-22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000−1−i1+i−1+i1−i−22−i2i20000
χ4722-2-22i−2i2-22i−2i2i2i−2i−2i00002-2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000001+i−1−i1−i−1+i−22−i2i20000
χ4822-2-22i−2i2-22i−2i2i2i−2i−2i00002-2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000−1−i1+i−1+i1−i2−2i2−i20000
χ4922-2-2−2i2i2-2−2i2i−2i−2i2i2i00002-22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000001−i−1+i1+i−1−i−22i2−i20000
χ5022-2-2−2i2i2-2−2i2i−2i−2i2i2i00002-22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000−1+i1−i−1−i1+i2−2−i2i20000
χ5122-2-2−2i2i2-2−2i2i−2i−2i2i2i00002-2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000001−i−1+i1+i−1−i2−2−i2i20000
χ5222-2-2−2i2i2-2−2i2i−2i−2i2i2i00002-2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000−1+i1−i−1−i1+i−22i2−i20000
χ5344-4-44i−4i4-44i−4i−4i−4i4i4i0000-44000000000000000000000000000000000000000000
χ5444-4-44i−4i-44−4i4i00000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000
χ5544-4-44i−4i-44−4i4i0000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000
χ5644-4-4−4i4i4-4−4i4i4i4i−4i−4i0000-44000000000000000000000000000000000000000000
χ5744-4-4−4i4i-444i−4i00000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000
χ5844-4-4−4i4i-444i−4i0000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000
χ598-88-80000004i2−4i24i2−4i2000000000000000000000000000000000000000000000000
χ608-88-8000000−4i24i2−4i24i2000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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