Finite Group Databasebeta

← Group #138294

Character table — Group #138294

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222222244444424444444448888444444444444444488888816161616161616162444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1ii−i−iii−i−i1-11-1
χ10111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1−i−iii−i−iii-11-11
χ11111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1ii−i−iii−i−i-11-11
χ12111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1−i−iii−i−iii1-11-1
χ13111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111ii−i−i−i−iii1-1-11
χ14111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111−i−iiiii−i−i-111-1
χ15111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111ii−i−i−i−iii-111-1
χ16111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111−i−iiiii−i−i1-1-11
χ17222222222222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-22222000000000000
χ1922222222-2-2-2-2-2-22-22222-2-2-2-2000000000000000000000000002−22−22−22−20000
χ2022222222-2-2-2-2-2-22-22222-2-2-2-200000000000000000000000000−22−22−22−220000
χ2122222222-2-2-2-2-2-22-2-2-2-2-22222000000000000000000000000002−22−2−22−220000
χ2222222222-2-2-2-2-2-22-2-2-2-2-2222200000000000000000000000000−22−222−22−20000
χ23222222-2-222-2-222-2-222-2-222-2-222220000000000000000-2-2-2-222000000000000
χ24222222-2-222-2-222-2-2-2-222-2-22222220000000000000000-2-222-2-2000000000000
χ25222222-2-2-2-222-2-2-2222-2-2-2-22200000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ26222222-2-2-2-222-2-2-2222-2-2-2-22200000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ27222222-2-2-2-222-2-2-22-2-22222-2-200000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ28222222-2-2-2-222-2-2-22-2-22222-2-200000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ292222-2-222-2-2-2-222-220000000022-2-20000000022-2-222-2-22-20000000000000000
χ302222-2-222-2-2-2-222-220000000022-2-200000000-2-222-2-2222-20000000000000000
χ312222-2-222-2-2-2-222-2200000000-2-22222-2-222-2-200000000-220000000000000000
χ322222-2-222-2-2-2-222-2200000000-2-222-2-222-2-22200000000-220000000000000000
χ332222-2-2-2-2-2-222222-20000000022-2-22i2i−2i−2i−2i−2i2i2i00000000-220000000000000000
χ342222-2-2-2-2-2-222222-20000000022-2-2−2i−2i2i2i2i2i−2i−2i00000000-220000000000000000
χ352222-2-2-2-2-2-222222-200000000-2-222000000002i2i−2i−2i−2i−2i2i2i2-20000000000000000
χ362222-2-2-2-2-2-222222-200000000-2-22200000000−2i−2i2i2i2i2i−2i−2i2-20000000000000000
χ3722-2-22-2002-2002-200002i−2i002i−2i2i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002-200000000000000
χ3822-2-22-2002-2002-200002i−2i002i−2i2i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-200000000000000
χ3922-2-22-2002-2002-200002i−2i002i−2i−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00-2200000000000000
χ4022-2-22-2002-2002-200002i−2i002i−2i−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00-2200000000000000
χ4122-2-22-2002-2002-20000−2i2i00−2i2i2i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00-2200000000000000
χ4222-2-22-2002-2002-20000−2i2i00−2i2i2i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00-2200000000000000
χ4322-2-22-2002-2002-20000−2i2i00−2i2i−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002-200000000000000
χ4422-2-22-2002-2002-20000−2i2i00−2i2i−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-200000000000000
χ4522-2-2-2200-22002-2002i−2i002i−2i002i−2i−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00002-2000000000000
χ4622-2-2-2200-22002-2002i−2i002i−2i002i−2i−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00002-2000000000000
χ4722-2-2-2200-22002-2002i−2i002i−2i00−2i2i2i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000-22000000000000
χ4822-2-2-2200-22002-2002i−2i002i−2i00−2i2i2i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000-22000000000000
χ4922-2-2-2200-22002-200−2i2i00−2i2i002i−2i−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000-22000000000000
χ5022-2-2-2200-22002-200−2i2i00−2i2i002i−2i−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000-22000000000000
χ5122-2-2-2200-22002-200−2i2i00−2i2i00−2i2i2i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00002-2000000000000
χ5222-2-2-2200-22002-200−2i2i00−2i2i00−2i2i2i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00002-2000000000000
χ534444-4-4444444-4-4-4-40000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000
χ5544-4-44-400-4400-4400004i−4i00−4i4i00000000000000000000000000000000000000
χ5644-4-44-400-4400-440000−4i4i004i−4i00000000000000000000000000000000000000
χ5744-4-4-44004-400-44004i−4i00−4i4i0000000000000000000000000000000000000000
χ5844-4-4-44004-400-4400−4i4i004i−4i0000000000000000000000000000000000000000
χ598-88-80000008i−8i00000000000000000000000000000000000000000000000000
χ608-88-8000000−8i8i00000000000000000000000000000000000000000000000000
χ618-8-88008-8000000000000000000000000000000000000000000000000000000
χ628-8-8800-88000000000000000000000000000000000000000000000000000000

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