Finite Group Databasebeta

← Group #98261

Character table — Group #98261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ71111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ81111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11-111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11-111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-11-1-1ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2222222-2-2-222-2-2-2-20000000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000000000
χ19222222222222-2-222-2-222-2-22222-2-222-2-2-222-2-20000000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-222-222-2-2220000000000000000000000000000000000
χ2122222222-2-2-2-222222222220000-2-2-2-2-20000002222000000000000000000-2-20000000000
χ2222222222-2-2-2-222222222220000-2-2-2-2-2000000-2-2-2-2000000000000000000220000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-2222000000000000000000000000002-2002-200000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-222200000000000000000000000000-2200-2200000000
χ2522222222-2-2-2-2-2-222-2-222-2-2000022-2-22000000000000000000000000002-200-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-2000022-2-2200000000000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-200000022-2-2000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002222-2000000-2-2220000000000000000002-20000000000
χ29222-2-22-2-2000022-2-2-2-2222-20000000000000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-22-2-2000022-2-2-2-2222-20000000000000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-22-2-2000022-2-2-2-2222-2000000000000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-22-2-2000022-2-2-2-2222-2000000000000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-22-2-20000-2-22222-2-22-20000000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000
χ34222-2-22-2-20000-2-22222-2-22-20000000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000
χ35222-2-22-2-20000-2-22222-2-22-2000000000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000
χ36222-2-22-2-20000-2-22222-2-22-2000000000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000
χ3722-22-2-22-222-2-2002i−2i002i−2i0022-2-2002i−2i0002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i0000
χ3822-22-2-22-222-2-2002i−2i002i−2i0022-2-2002i−2i0002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i0000
χ3922-22-2-22-222-2-2002i−2i002i−2i00-2-222002i−2i000−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i0000
χ4022-22-2-22-222-2-2002i−2i002i−2i00-2-222002i−2i000−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i0000
χ4122-22-2-22-222-2-200−2i2i00−2i2i0022-2-200−2i2i000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i0000
χ4222-22-2-22-222-2-200−2i2i00−2i2i0022-2-200−2i2i000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i0000
χ4322-22-2-22-222-2-200−2i2i00−2i2i00-2-22200−2i2i0002i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i0000
χ4422-22-2-22-222-2-200−2i2i00−2i2i00-2-22200−2i2i0002i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i0000
χ452-222-2-2-222-22-22i−2i002i−2i00002i−2i2i−2i2i−2i0002-200000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000001+i−1−i1−i−1+i
χ462-222-2-2-222-22-22i−2i002i−2i00002i−2i2i−2i2i−2i0002-20000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−1−i1+i−1+i1−i
χ472-222-2-2-222-22-22i−2i002i−2i0000−2i2i−2i2i2i−2i000-2200000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−1−i1+i−1+i1−i
χ482-222-2-2-222-22-22i−2i002i−2i0000−2i2i−2i2i2i−2i000-220000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000001+i−1−i1−i−1+i
χ492-222-2-2-222-22-2−2i2i00−2i2i00002i−2i2i−2i−2i2i000-2200000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−1+i1−i−1−i1+i
χ502-222-2-2-222-22-2−2i2i00−2i2i00002i−2i2i−2i−2i2i000-220000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000001−i−1+i1+i−1−i
χ512-222-2-2-222-22-2−2i2i00−2i2i0000−2i2i−2i2i−2i2i0002-200000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000001−i−1+i1+i−1−i
χ522-222-2-2-222-22-2−2i2i00−2i2i0000−2i2i−2i2i−2i2i0002-20000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−1+i1−i−1−i1+i
χ53444-4-44-4-400004444-4-4-4-4-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-40000-4-4-4-44444-440000000000000000000000000000000000000000000000000
χ5544-44-4-44-4-4-444004i−4i004i−4i00000000−4i4i00000000000000000000000000000000000000000
χ5644-44-4-44-4-4-44400−4i4i00−4i4i000000004i−4i00000000000000000000000000000000000000000
χ5744-4-44-4-440000004i−4i00−4i4i0000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ5844-4-44-4-440000004i−4i00−4i4i000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ5944-4-44-4-44000000−4i4i004i−4i0000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ6044-4-44-4-44000000−4i4i004i−4i000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ614-444-4-4-44-44-444i−4i004i−4i00000000−4i4i0000000000000000000000000000000000000000000
χ624-444-4-4-44-44-44−4i4i00−4i4i000000004i−4i0000000000000000000000000000000000000000000
χ634-44-44-44-400004i−4i00−4i4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ644-44-44-44-400004i−4i00−4i4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ654-44-44-44-40000−4i4i004i−4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ664-44-44-44-40000−4i4i004i−4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ674-4-4444-4-44-4-4400000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ684-4-4444-4-44-4-440000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ694-4-4444-4-4-444-4000000000000000000000004i−4i0000000000000000000000000000000000
χ704-4-4444-4-4-444-400000000000000000000000−4i4i0000000000000000000000000000000000
χ718-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000

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