Finite Group Databasebeta

← Group #124696

Character table — Group #124696

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444444444444448888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-22200000000000000000000000000000000
χ1822222222222222222222-2-22222-2-2-2-2-2-222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000
χ212222-2-2-2-22-2-22000000002i−2i2i2i−2i−2i2i−2i2-200000000002i2i−2i−2i000022-2-20000000000000000
χ222222-2-2-2-22-2-22000000002i−2i2i2i−2i−2i2i−2i2-20000000000−2i−2i2i2i0000-2-2220000000000000000
χ232222-2-2-2-22-2-22000000002i−2i−2i−2i2i2i2i−2i-220000002i2i−2i−2i000022-2-200000000000000000000
χ242222-2-2-2-22-2-22000000002i−2i−2i−2i2i2i2i−2i-22000000−2i−2i2i2i0000-2-22200000000000000000000
χ252222-2-2-2-22-2-2200000000−2i2i2i2i−2i−2i−2i2i-220000002i2i−2i−2i0000-2-22200000000000000000000
χ262222-2-2-2-22-2-2200000000−2i2i2i2i−2i−2i−2i2i-22000000−2i−2i2i2i000022-2-200000000000000000000
χ272222-2-2-2-22-2-2200000000−2i2i−2i−2i2i2i−2i2i2-200000000002i2i−2i−2i0000-2-2220000000000000000
χ282222-2-2-2-22-2-2200000000−2i2i−2i−2i2i2i−2i2i2-20000000000−2i−2i2i2i000022-2-20000000000000000
χ2922-2-2-2-22222-2-22222-2-2-2-2002i−2i2i−2i0000002i−2i000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ3022-2-2-2-22222-2-22222-2-2-2-2002i−2i2i−2i0000002i−2i00000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ3122-2-2-2-22222-2-22222-2-2-2-200−2i2i−2i2i000000−2i2i000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ3222-2-2-2-22222-2-22222-2-2-2-200−2i2i−2i2i000000−2i2i00000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ3322-2-2-2-22222-2-2-2-2-2-22222002i−2i2i−2i000000−2i2i000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ3422-2-2-2-22222-2-2-2-2-2-22222002i−2i2i−2i000000−2i2i00000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ3522-2-2-2-22222-2-2-2-2-2-2222200−2i2i−2i2i0000002i−2i000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ3622-2-2-2-22222-2-2-2-2-2-2222200−2i2i−2i2i0000002i−2i00000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ3722-2-2-2-222-2-22222-2-222-2-2220000-2-20000002-20000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ3822-2-2-2-222-2-22222-2-222-2-2220000-2-20000002-20000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ3922-2-2-2-222-2-22222-2-222-2-2-2-2000022000000-2200000000000000002−22−2−22−2200000000
χ4022-2-2-2-222-2-22222-2-222-2-2-2-2000022000000-220000000000000000−22−222−22−200000000
χ4122-2-2-2-222-2-222-2-222-2-222220000-2-2000000-220000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ4222-2-2-2-222-2-222-2-222-2-222220000-2-2000000-220000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ4322-2-2-2-222-2-222-2-222-2-222-2-20000220000002-200000000000000002−2−22−222−200000000
χ4422-2-2-2-222-2-222-2-222-2-222-2-20000220000002-20000000000000000−222−22−2−2200000000
χ4544444444-4-4-4-444-4-4-4-444000000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4-44444-4-4000000000000000000000000000000000000000000000000
χ474444-4-4-4-4-444-40000000000000000004-4000000000000000000000000000000000000
χ484444-4-4-4-4-444-4000000000000000000-44000000000000000000000000000000000000
χ4944-4-444-4-44-44-400000000004-4-44000000000000000000000000000000000000000000
χ5044-4-444-4-44-44-40000000000-444-4000000000000000000000000000000000000000000
χ5144-4-444-4-4-44-44000000004i−4i0000−4i4i0000000000000000000000000000000000000000
χ5244-4-444-4-4-44-4400000000−4i4i00004i−4i0000000000000000000000000000000000000000
χ534-44-44-44-40000004i−4i4i−4i000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ544-44-44-44-40000004i−4i4i−4i00000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ554-44-44-44-4000000−4i4i−4i4i000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ564-44-44-44-4000000−4i4i−4i4i00000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ574-44-4-44-4400004i−4i00004i−4i0000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ584-44-4-44-4400004i−4i00004i−4i000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ594-44-4-44-440000−4i4i0000−4i4i0000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ604-44-4-44-440000−4i4i0000−4i4i000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ614-4-444-4-4400004i−4i0000−4i4i00000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ624-4-444-4-4400004i−4i0000−4i4i0000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ634-4-444-4-440000−4i4i00004i−4i00000000000000002i−2i2i−2i-22-22000000000000000000000000
χ644-4-444-4-440000−4i4i00004i−4i0000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ654-4-44-444-40000004i−4i−4i4i0000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ664-4-44-444-40000004i−4i−4i4i000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ674-4-44-444-4000000−4i4i4i−4i0000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ684-4-44-444-4000000−4i4i4i−4i000000000000000000-222-22i−2i−2i2i000000000000000000000000

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