Finite Group Databasebeta

← Group #142068

Character table — Group #142068

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444448888888888884444881616161616161616161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ9111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ14111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ15111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ19222222-2-2-2-22222-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000
χ20222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ212222-2-2222222-2-2-2-200002i−2i00002i−2i00002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ222222-2-2222222-2-2-2-200002i−2i00002i−2i00002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ232222-2-2222222-2-2-2-20000−2i2i0000−2i2i0000−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
χ242222-2-2222222-2-2-2-20000−2i2i0000−2i2i0000−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000
χ252222-2-222-2-2-2-222-222i2i−2i−2i002i2i−2i−2i0000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ262222-2-222-2-2-2-222-222i2i−2i−2i002i2i−2i−2i000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ272222-2-222-2-2-2-222-22−2i−2i2i2i00−2i−2i2i2i0000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ282222-2-222-2-2-2-222-22−2i−2i2i2i00−2i−2i2i2i000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ292222-2-2-2-222-2-2222-22i2i−2i−2i00−2i−2i2i2i0000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ302222-2-2-2-222-2-2222-22i2i−2i−2i00−2i−2i2i2i000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ312222-2-2-2-222-2-2222-2−2i−2i2i2i002i2i−2i−2i0000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ322222-2-2-2-222-2-2222-2−2i−2i2i2i002i2i−2i−2i000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ332222-2-2-2-2-2-222-2-22200002i−2i00002i−2i0000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ342222-2-2-2-2-2-222-2-22200002i−2i00002i−2i0000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ352222-2-2-2-2-2-222-2-2220000−2i2i0000−2i2i00002i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ362222-2-2-2-2-2-222-2-2220000−2i2i0000−2i2i00002i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ3722-2-22-200002-22-2000000222-22-2-2-22-2000000002-22-22-22-20000000000000000
χ3822-2-22-200002-22-2000000222-22-2-2-22-200000000-22-22-22-220000000000000000
χ3922-2-22-200002-22-200000022-22-22-2-2-2200002-22-2000000002-22-2000000000000
χ4022-2-22-200002-22-200000022-22-22-2-2-220000-22-2200000000-22-22000000000000
χ4122-2-22-200002-22-2000000-2-22-22-222-2200002i−2i2i−2i00000000−2i2i−2i2i000000000000
χ4222-2-22-200002-22-2000000-2-22-22-222-220000−2i2i−2i2i000000002i−2i2i−2i000000000000
χ4322-2-22-200002-22-2000000-2-2-22-22222-2000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4422-2-22-200002-22-2000000-2-2-22-22222-200000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4522-2-2-2200002-2-22002i−2i2i−2i2i−2i0000−2i2i002-2001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000
χ4622-2-2-2200002-2-22002i−2i2i−2i2i−2i0000−2i2i002-200−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000000000
χ4722-2-2-2200002-2-22002i−2i2i−2i−2i2i00002i−2i00-22001−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i000000000000
χ4822-2-2-2200002-2-22002i−2i2i−2i−2i2i00002i−2i00-2200−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i000000000000
χ4922-2-2-2200002-2-2200−2i2i−2i2i2i−2i0000−2i2i00-22001+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i000000000000
χ5022-2-2-2200002-2-2200−2i2i−2i2i2i−2i0000−2i2i00-2200−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i000000000000
χ5122-2-2-2200002-2-2200−2i2i−2i2i−2i2i00002i−2i002-2001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i000000000000
χ5222-2-2-2200002-2-2200−2i2i−2i2i−2i2i00002i−2i002-200−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i000000000000
χ5344444444-4-4-4-4-4-44-40000000000000000000000000000000000000000000000
χ54444444-4-444-4-4-4-4-440000000000000000000000000000000000000000000000
χ5544-4-44-40000-44-44004-4-44000000000000000000000000000000000000000000
χ5644-4-44-40000-44-4400-444-4000000000000000000000000000000000000000000
χ5744-4-4-440000-444-4000000004i−4i−4i4i000000000000000000000000000000000000
χ5844-4-4-440000-444-400000000−4i4i4i−4i000000000000000000000000000000000000
χ598-88-8008-8000000000000000000000000000000000000000000000000000000
χ608-88-800-88000000000000000000000000000000000000000000000000000000
χ618-8-8800008-80000000000000000000000000000000000000000000000000000
χ628-8-880000-880000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).