Finite Group Databasebeta

← Group #141111

Character table — Group #141111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244448888224444448888884444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-111−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-111iiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222-2-22-2-2222222-2-200000000-2-2-2-200000000000000000000
χ1822222222222222-2-2-222-22222-2-2-2-2-2-200000000-2-22200000000000000000000
χ192222222222-2-2-2-2222-2-22-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000
χ202222222222-2-2-2-2-2-2-222-222-2-22222-2-20000000022-2-200000000000000000000
χ21222222-2-2-2-2000022-222-2-2-20000002-20000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222-2-2-2-2000022-222-2-2-20000002-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-2-2-222000000-2222-2-222-2-2000000000000000000000000
χ24222222-2-2-2-2000022-2-2-2-222000000-22-2-222-2-222000000000000000000000000
χ25222222-2-2-2-20000-2-22222-2-2000000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ26222222-2-2-2-20000-2-22222-2-2000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ27222222-2-2-2-20000-2-22-2-22220000002-200000000000022-2-2-2-222000000000000
χ28222222-2-2-2-20000-2-22-2-22220000002-2000000000000-2-22222-2-2000000000000
χ2922-2-22-22-22-222-2-22-2200-2002-222-2-200000000000000000000002−22−22−22−20000
χ3022-2-22-22-22-222-2-22-2200-2002-222-2-20000000000000000000000−22−22−22−220000
χ3122-2-22-22-22-222-2-2-22-2002002-2-2-2220000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ3222-2-22-22-22-222-2-2-22-2002002-2-2-2220000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ3322-2-22-22-22-2-2-2222-2200-200-22-2-22200000000000000000000002−2−222−2−220000
χ3422-2-22-22-22-2-2-2222-2200-200-22-2-2220000000000000000000000−222−2−222−20000
χ3522-2-22-22-22-2-2-222-22-200200-2222-2-20000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ3622-2-22-22-22-2-2-222-22-200200-2222-2-20000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3722-2-2-222-2-2200000002i−2i02i−2i002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-2-2-222-2-2200000002i−2i02i−2i002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-2-2-222-2-2200000002i−2i02i−2i00−2i2i−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4022-2-2-222-2-2200000002i−2i02i−2i00−2i2i−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4122-2-2-222-2-220000000−2i2i0−2i2i002i−2i2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4222-2-2-222-2-220000000−2i2i0−2i2i002i−2i2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4322-2-2-222-2-220000000−2i2i0−2i2i00−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4422-2-2-222-2-220000000−2i2i0−2i2i00−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4522-2-2-22-222-222-2-20002i−2i0−2i2i-220000001−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ4622-2-2-22-222-222-2-20002i−2i0−2i2i-22000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ4722-2-2-22-222-222-2-2000−2i2i02i−2i-220000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ4822-2-2-22-222-222-2-2000−2i2i02i−2i-22000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ4922-2-2-22-222-2-2-2220002i−2i0−2i2i2-20000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ5022-2-2-22-222-2-2-2220002i−2i0−2i2i2-2000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ5122-2-2-22-222-2-2-222000−2i2i02i−2i2-20000001+i−1−i−1−i1+i1−i−1+i−1+i1−i002i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5222-2-2-22-222-2-2-222000−2i2i02i−2i2-2000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i002i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ534444-4-444-4-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ544444-4-444-4-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554444-4-4-4-444444400000000-4-400000000000000000000000000000000000000
χ564444-4-4-4-444-4-4-4-4000000004400000000000000000000000000000000000000
χ5744-4-44-4-44-4400004-4-4004000000000000000000000000000000000000000000
χ5844-4-44-4-44-440000-44400-4000000000000000000000000000000000000000000
χ598-88-80000004i2−4i24i2−4i2000000000000000000000000000000000000000000000000
χ608-88-8000000−4i24i2−4i24i2000000000000000000000000000000000000000000000000
χ618-8-880000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-8-88000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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