Finite Group Databasebeta

← Group #98516

Character table — Group #98516

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2220000-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000022000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000022000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-2000022-2-222-2-2000000000022-2-2002-20000000000000000
χ2222222222-2-2-2-222-2-2000022-2-222-2-20000000000-2-22200-220000000000000000
χ2322222222-2-2-2-222-2-20000-2-222-2-222000000000022-2-200-220000000000000000
χ2422222222-2-2-2-222-2-20000-2-222-2-2220000000000-2-222002-20000000000000000
χ2522222222-2-2-2-2-2-222000022-2-2-2-222000022-2-20000002-2000000000000000000
χ2622222222-2-2-2-2-2-222000022-2-2-2-2220000-2-222000000-22000000000000000000
χ2722222222-2-2-2-2-2-2220000-2-22222-2-2000022-2-2000000-22000000000000000000
χ2822222222-2-2-2-2-2-2220000-2-22222-2-20000-2-2220000002-2000000000000000000
χ2922-2-22-22-222-2-2000022-2-200002i−2i2i−2i000000002i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ3022-2-22-22-222-2-2000022-2-200002i−2i2i−2i000000002i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ3122-2-22-22-222-2-2000022-2-20000−2i2i−2i2i00000000−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ3222-2-22-22-222-2-2000022-2-20000−2i2i−2i2i00000000−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ3322-2-22-22-222-2-20000-2-22200002i−2i2i−2i00000000−2i2i000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3422-2-22-22-222-2-20000-2-22200002i−2i2i−2i00000000−2i2i00000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3522-2-22-22-222-2-20000-2-2220000−2i2i−2i2i000000002i−2i000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3622-2-22-22-222-2-20000-2-2220000−2i2i−2i2i000000002i−2i00000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3722-2-2-22-222-22-200002-22-22i−2i2i−2i0000002i−2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ3822-2-2-22-222-22-200002-22-22i−2i2i−2i0000002i−2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ3922-2-2-22-222-22-200002-22-2−2i2i−2i2i000000−2i2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ4022-2-2-22-222-22-200002-22-2−2i2i−2i2i000000−2i2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ4122-2-2-22-222-22-20000-22-222i−2i2i−2i000000−2i2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ4222-2-2-22-222-22-20000-22-222i−2i2i−2i000000−2i2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ4322-2-2-22-222-22-20000-22-22−2i2i−2i2i0000002i−2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ4422-2-2-22-222-22-20000-22-22−2i2i−2i2i0000002i−2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ454444-4-4-4-44-4-4400004-4-44000000000000000000000000000000000000000000
χ464444-4-4-4-44-4-440000-444-4000000000000000000000000000000000000000000
χ474444-4-4-4-4-444-400000000000000004-400000000000000000000000000000000
χ484444-4-4-4-4-444-40000000000000000-4400000000000000000000000000000000
χ4944-4-44-44-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000
χ5044-4-44-44-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000
χ5144-4-4-44-44-44-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ5244-4-4-44-44-44-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ534-44-44-4-440000004-40000000000000000004i−4i00000000000000000000000000
χ544-44-44-4-440000004-4000000000000000000−4i4i00000000000000000000000000
χ554-44-44-4-44000000-4400000000000000004i−4i0000000000000000000000000000
χ564-44-44-4-44000000-440000000000000000−4i4i0000000000000000000000000000
χ574-44-4-444-400004-4000000000000000000000000004i−4i00000000000000000000
χ584-44-4-444-400004-400000000000000000000000000−4i4i00000000000000000000
χ594-44-4-444-40000-440000000000000000000000004i−4i0000000000000000000000
χ604-44-4-444-40000-44000000000000000000000000−4i4i0000000000000000000000
χ618-8-8888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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