Finite Group Databasebeta

← Group #102206

Character table — Group #102206

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222222-2-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i002-200i2i2−i2−i2i2i2−i2−i222−2−222−2−2002ζ3−2ζ32ζ−2ζ001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ30222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i002-200i2i2−i2−i2i2i2−i2−i222−2−222−2−200−2ζ32ζ3−2ζ2ζ00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ31222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i002-200−i2−i2i2i2−i2−i2i2i2−2−222−2−222002ζ3−2ζ32ζ−2ζ00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ32222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i002-200−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−2ζ32ζ3−2ζ2ζ001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ33222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00-2200i2i2−i2−i2−i2−i2i2i222−2−2−2−2222ζ−2ζ00002ζ3−2ζ31−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ34222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00-2200i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2ζ2ζ0000−2ζ32ζ3−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ35222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00-2200−i2−i2i2i2i2i2−i2−i2−2−22222−2−22ζ−2ζ00002ζ3−2ζ3−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ36222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00-2200−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−2ζ2ζ0000−2ζ32ζ31−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ37222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00-2200i2i2−i2−i2−i2−i2i2i2−2−22222−2−22ζ3−2ζ300002ζ−2ζ1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ38222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00-2200i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2ζ32ζ30000−2ζ2ζ−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ39222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00-2200−i2−i2i2i2i2i2−i2−i222−2−2−2−2222ζ3−2ζ300002ζ−2ζ−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ40222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00-2200−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2ζ32ζ30000−2ζ2ζ1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ41222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i002-200i2i2−i2−i2i2i2−i2−i2−2−222−2−222002ζ−2ζ2ζ3−2ζ3001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ42222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i002-200i2i2−i2−i2i2i2−i2−i2−2−222−2−22200−2ζ2ζ−2ζ32ζ300−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ43222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i002-200−i2−i2i2i2−i2−i2i2i222−2−222−2−2002ζ−2ζ2ζ3−2ζ300−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ44222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i002-200−i2−i2i2i2−i2−i2i2i222−2−222−2−200−2ζ2ζ−2ζ32ζ3001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ452-2-222-22-222-2-22i2i−2i−2i2i−2i2i−2i000000000000002i−2i2i−2i00002-22-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ462-2-222-22-222-2-22i2i−2i−2i2i−2i2i−2i000000000000002i−2i2i−2i00002-22-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ472-2-222-22-222-2-22i2i−2i−2i2i−2i2i−2i00000000000000−2i2i−2i2i0000-22-2200000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ482-2-222-22-222-2-22i2i−2i−2i2i−2i2i−2i00000000000000−2i2i−2i2i0000-22-220000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ492-2-222-22-222-2-2−2i−2i2i2i−2i2i−2i2i000000000000002i−2i2i−2i0000-22-2200000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ502-2-222-22-222-2-2−2i−2i2i2i−2i2i−2i2i000000000000002i−2i2i−2i0000-22-220000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ512-2-222-22-222-2-2−2i−2i2i2i−2i2i−2i2i00000000000000−2i2i−2i2i00002-22-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ522-2-222-22-222-2-2−2i−2i2i2i−2i2i−2i2i00000000000000−2i2i−2i2i00002-22-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ5344-44-44-4-400004-44-400004-44-44-4000000000000000000000000000000000000000000000000
χ5444-44-44-4-400004-44-40000-44-44-44000000000000000000000000000000000000000000000000
χ5544-44-44-4-40000-44-4400004-44-4-44000000000000000000000000000000000000000000000000
χ5644-44-44-4-40000-44-440000-44-444-4000000000000000000000000000000000000000000000000
χ5744-4-44-4-444-44-4000000004i−4i−4i4i00004i−4i00000000000000000000000000000000000000000000
χ5844-4-44-4-444-44-400000000−4i4i4i−4i0000−4i4i00000000000000000000000000000000000000000000
χ5944-4-44-4-44-44-44000000004i−4i−4i4i0000−4i4i00000000000000000000000000000000000000000000
χ6044-4-44-4-44-44-4400000000−4i4i4i−4i00004i−4i00000000000000000000000000000000000000000000
χ614-444-4-4-4400004i−4i−4i4i000000000000002i2−2i22i2−2i2000022−2222−2200000000000000000000000000000000
χ624-444-4-4-4400004i−4i−4i4i00000000000000−2i22i2−2i22i20000−2222−222200000000000000000000000000000000
χ634-444-4-4-440000−4i4i4i−4i000000000000002i2−2i22i2−2i20000−2222−222200000000000000000000000000000000
χ644-444-4-4-440000−4i4i4i−4i00000000000000−2i22i2−2i22i2000022−2222−2200000000000000000000000000000000
χ654-44-444-4-44-4-440000000000000000004-4-440000000000000000000000000000000000000000
χ664-44-444-4-44-4-44000000000000000000-444-40000000000000000000000000000000000000000
χ674-44-444-4-4-444-4000000000000000000000000004-4-4400000000000000000000000000000000
χ684-44-444-4-4-444-400000000000000000000000000-444-400000000000000000000000000000000
χ694-4-444-44-4-4-4444i4i−4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ704-4-444-44-4-4-444−4i−4i4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ714-4-4-4-4444000000004-4-440000000000000022−22−2222000022−22−22220000000000000000000000000000
χ724-4-4-4-4444000000004-4-4400000000000000−222222−220000−222222−220000000000000000000000000000
χ734-4-4-4-444400000000-444-40000000000000022−22−22220000−222222−220000000000000000000000000000
χ744-4-4-4-444400000000-444-400000000000000−222222−22000022−22−22220000000000000000000000000000

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