Finite Group Databasebeta

← Group #124809

Character table — Group #124809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-200000000000000000000000000000000
χ2122-22-2-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i002-2000000002i2i−2i−2i000022-2-20000000000000000
χ2222-22-2-22-22-22-2000000002i2i−2i−2i2i2i−2i−2i002-200000000−2i−2i2i2i0000-2-2220000000000000000
χ2322-22-2-22-22-22-2000000002i2i−2i−2i−2i−2i2i2i00-22000022-2-200002i2i−2i−2i00000000000000000000
χ2422-22-2-22-22-22-2000000002i2i−2i−2i−2i−2i2i2i00-220000-2-2220000−2i−2i2i2i00000000000000000000
χ2522-22-2-22-22-22-200000000−2i−2i2i2i2i2i−2i−2i00-22000022-2-20000−2i−2i2i2i00000000000000000000
χ2622-22-2-22-22-22-200000000−2i−2i2i2i2i2i−2i−2i00-220000-2-22200002i2i−2i−2i00000000000000000000
χ2722-22-2-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i002-2000000002i2i−2i−2i0000-2-2220000000000000000
χ2822-22-2-22-22-22-200000000−2i−2i2i2i−2i−2i2i2i002-200000000−2i−2i2i2i000022-2-20000000000000000
χ2922-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i2i−2i2i−2i00002-20000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ3022-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i2i−2i2i−2i00002-2000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ3122-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i−2i2i−2i2i0000-220000000000000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i
χ3222-2-22-2-222-2-222i2i2i2i−2i−2i−2i−2i−2i2i−2i2i0000-22000000000000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i
χ3322-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i0000-220000000000000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i
χ3422-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i0000-22000000000000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i
χ3522-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i00002-20000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ3622-2-22-2-222-2-22−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i00002-2000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ3722-2-22-2-22-222-22i2i−2i−2i2i2i−2i−2i00002-22-20000002i−2i0000000000000000i2−i22−2i2−i22−200000000
χ3822-2-22-2-22-222-22i2i−2i−2i2i2i−2i−2i00002-22-20000002i−2i0000000000000000−i2i2−22−i2i2−2200000000
χ3922-2-22-2-22-222-22i2i−2i−2i2i2i−2i−2i0000-22-22000000−2i2i00000000000000002−2−i2i2−22i2−i200000000
χ4022-2-22-2-22-222-22i2i−2i−2i2i2i−2i−2i0000-22-22000000−2i2i0000000000000000−22i2−i22−2−i2i200000000
χ4122-2-22-2-22-222-2−2i−2i2i2i−2i−2i2i2i00002-22-2000000−2i2i0000000000000000i2−i2−22i2−i2−2200000000
χ4222-2-22-2-22-222-2−2i−2i2i2i−2i−2i2i2i00002-22-2000000−2i2i0000000000000000−i2i22−2−i2i22−200000000
χ4322-2-22-2-22-222-2−2i−2i2i2i−2i−2i2i2i0000-22-220000002i−2i00000000000000002−2i2−i2−22−i2i200000000
χ4422-2-22-2-22-222-2−2i−2i2i2i−2i−2i2i2i0000-22-220000002i−2i0000000000000000−22−i2i22−2i2−i200000000
χ4544444444-4-4-4-444-4-4-4-444000000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4-44444-4-4000000000000000000000000000000000000000000000000
χ47444-4-44-4-444-4-4000000004-4-4400000000000000000000000000000000000000000000
χ48444-4-44-4-444-4-400000000-444-400000000000000000000000000000000000000000000
χ49444-4-44-4-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ50444-4-44-4-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ5144-44-4-44-4-44-44000000000000000000004i−4i0000000000000000000000000000000000
χ5244-44-4-44-4-44-4400000000000000000000−4i4i0000000000000000000000000000000000
χ534-444-4-4-440000004i−4i4i−4i0000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ544-444-4-4-440000004i−4i4i−4i000000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ554-444-4-4-44000000−4i4i−4i4i0000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ564-444-4-4-44000000−4i4i−4i4i000000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ574-44-44-44-400004i−4i00004i−4i0000000000000000000000002i−2i2i−2i2-22-20000000000000000
χ584-44-44-44-400004i−4i00004i−4i000000000000000000000000−2i2i−2i2i-22-220000000000000000
χ594-44-44-44-40000−4i4i0000−4i4i0000000000000000000000002i−2i2i−2i-22-220000000000000000
χ604-44-44-44-40000−4i4i0000−4i4i000000000000000000000000−2i2i−2i2i2-22-20000000000000000
χ614-4-4444-4-400004-40000-4400000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ624-4-4444-4-400004-40000-440000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ634-4-4444-4-40000-4400004-400000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ644-4-4444-4-40000-4400004-40000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ654-4-4-4-44440000004-4-44000000000000000000000000002-2-22-222-20000000000000000
χ664-4-4-4-44440000004-4-4400000000000000000000000000-222-22-2-220000000000000000
χ674-4-4-4-4444000000-444-4000000000000000000000000002-2-222-2-220000000000000000
χ684-4-4-4-4444000000-444-400000000000000000000000000-222-2-222-20000000000000000

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