Finite Group Databasebeta

← Group #138293

Character table — Group #138293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222222244444424444444448888888888888888888888888816161616161616162444
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
χ51111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2-2-22-22222-2-2-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-2-2-2-2-2-22-22222-2-2-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-2-2-2-2-2-22-2-2-2-2-2222200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2222222222-2-2-2-2-2-22-2-2-2-2-2222200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ23222222-2-2-2-222-2-2-220000000022-2-22-20000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ24222222-2-2-2-222-2-2-220000000022-2-22-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ25222222-2-2-2-222-2-2-2200000000-2-222-2200002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ26222222-2-2-2-222-2-2-2200000000-2-222-220000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ272222-2-2222222-2-2-2-222-2-222-2-22222-2-2-2-2220000000000000000000000000000
χ282222-2-2222222-2-2-2-2-2-222-2-2222222-2-222-2-20000000000000000000000000000
χ292222-2-222-2-2-2-222-2222-2-2-2-222000000000000000000000000002−2−222−2−220000
χ302222-2-222-2-2-2-222-2222-2-2-2-22200000000000000000000000000−222−2−222−20000
χ312222-2-222-2-2-2-222-22-2-22222-2-2000000000000000000000000002−2−22−222−20000
χ322222-2-222-2-2-2-222-22-2-22222-2-200000000000000000000000000−222−22−2−220000
χ332222-2-2-2-2-2-222222-20000000022-2-2-22000022-2-2-2-22200000000000000000000
χ342222-2-2-2-2-2-222222-20000000022-2-2-220000-2-22222-2-200000000000000000000
χ352222-2-2-2-2-2-222222-200000000-2-2222-200000000000022-2-2-2-222000000000000
χ362222-2-2-2-2-2-222222-200000000-2-2222-2000000000000-2-22222-2-2000000000000
χ3722-2-2002-22-22-20000002i−2i002i−2i2i−2i2i−2i002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-2-2002-22-22-20000002i−2i002i−2i2i−2i2i−2i002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-2-2002-22-22-20000002i−2i002i−2i−2i2i−2i2i00-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4022-2-2002-22-22-20000002i−2i002i−2i−2i2i−2i2i00-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4122-2-2002-22-22-2000000−2i2i00−2i2i2i−2i2i−2i00-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4222-2-2002-22-22-2000000−2i2i00−2i2i2i−2i2i−2i00-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4322-2-2002-22-22-2000000−2i2i00−2i2i−2i2i−2i2i002-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4422-2-2002-22-22-2000000−2i2i00−2i2i−2i2i−2i2i002-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4522-2-200-22-222-200002i−2i002i−2i002i−2i−2i2i00002-21+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ4622-2-200-22-222-200002i−2i002i−2i002i−2i−2i2i00002-2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ4722-2-200-22-222-200002i−2i002i−2i00−2i2i2i−2i0000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ4822-2-200-22-222-200002i−2i002i−2i00−2i2i2i−2i0000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ4922-2-200-22-222-20000−2i2i00−2i2i002i−2i−2i2i0000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5022-2-200-22-222-20000−2i2i00−2i2i002i−2i−2i2i0000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5122-2-200-22-222-20000−2i2i00−2i2i00−2i2i2i−2i00002-21−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5222-2-200-22-222-20000−2i2i00−2i2i00−2i2i2i−2i00002-2−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ53444444-4-444-4-444-4-40000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000
χ5544-4-4004-4-44-440000004i−4i00−4i4i00000000000000000000000000000000000000
χ5644-4-4004-4-44-44000000−4i4i004i−4i00000000000000000000000000000000000000
χ5744-4-400-444-4-4400004i−4i00−4i4i0000000000000000000000000000000000000000
χ5844-4-400-444-4-440000−4i4i004i−4i0000000000000000000000000000000000000000
χ598-88-8000000008i−8i000000000000000000000000000000000000000000000000
χ608-88-800000000−8i8i000000000000000000000000000000000000000000000000
χ618-8-888-800000000000000000000000000000000000000000000000000000000
χ628-8-88-8800000000000000000000000000000000000000000000000000000000

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