Finite Group Databasebeta

← Group #124697

Character table — Group #124697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ21222-22-2-2-22-2-2200002i−2i2i2i−2i−2i2i−2i2-2000000002i−2i002-20000000000000000
χ22222-22-2-2-22-2-2200002i−2i2i2i−2i−2i2i−2i2-200000000−2i2i00-220000000000000000
χ23222-22-2-2-22-2-2200002i−2i−2i−2i2i2i2i−2i-220000002i−2i002-2000000000000000000
χ24222-22-2-2-22-2-2200002i−2i−2i−2i2i2i2i−2i-22000000−2i2i00-22000000000000000000
χ25222-22-2-2-22-2-220000−2i2i2i2i−2i−2i−2i2i-220000002i−2i00-22000000000000000000
χ26222-22-2-2-22-2-220000−2i2i2i2i−2i−2i−2i2i-22000000−2i2i002-2000000000000000000
χ27222-22-2-2-22-2-220000−2i2i−2i−2i2i2i−2i2i2-2000000002i−2i00-220000000000000000
χ28222-22-2-2-22-2-220000−2i2i−2i−2i2i2i−2i2i2-200000000−2i2i002-20000000000000000
χ2922-2-2-22-2222-2-222-2-2002i−2i2i−2i0000002i−2i0000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ3022-2-2-22-2222-2-222-2-2002i−2i2i−2i0000002i−2i000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ3122-2-2-22-2222-2-222-2-200−2i2i−2i2i000000−2i2i0000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ3222-2-2-22-2222-2-222-2-200−2i2i−2i2i000000−2i2i000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ3322-2-2-22-2222-2-2-2-222002i−2i2i−2i000000−2i2i0000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ3422-2-2-22-2222-2-2-2-222002i−2i2i−2i000000−2i2i000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ3522-2-2-22-2222-2-2-2-22200−2i2i−2i2i0000002i−2i0000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ3622-2-2-22-2222-2-2-2-22200−2i2i−2i2i0000002i−2i000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ3722-2-2-22-22-2-2222-22-2220000-2-20000002-200000000i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-2-22-22-2-2222-22-2220000-2-20000002-200000000−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-2-22-22-2-2222-22-2-2-2000022000000-22000000002−22−2−22−2200000000
χ4022-2-2-22-22-2-2222-22-2-2-2000022000000-2200000000−22−222−22−200000000
χ4122-2-2-22-22-2-222-22-22220000-2-2000000-2200000000i2−i2−i2i2i2−i2−i2i200000000
χ4222-2-2-22-22-2-222-22-22220000-2-2000000-2200000000−i2i2i2−i2−i2i2i2−i200000000
χ4322-2-2-22-22-2-222-22-22-2-20000220000002-2000000002−2−22−222−200000000
χ4422-2-2-22-22-2-222-22-22-2-20000220000002-200000000−222−22−2−2200000000
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ47444-44-4-4-4-444-4000000000000004-40000000000000000000000000000
χ48444-44-4-4-4-444-400000000000000-440000000000000000000000000000
χ4944-44-4-44-44-44-40000004-4-440000000000000000000000000000000000
χ5044-44-4-44-44-44-4000000-444-40000000000000000000000000000000000
χ5144-44-4-44-4-44-4400004i−4i0000−4i4i00000000000000000000000000000000
χ5244-44-4-44-4-44-440000−4i4i00004i−4i00000000000000000000000000000000
χ538-888-88-8-8000000000000000000000000000000000000000000000000
χ548-88-8-8-888000000000000000000000000000000000000000000000000
χ558-8-888-8-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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