Finite Group Databasebeta

← Group #124674

Character table — Group #124674

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444448888888888888888
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
χ17222222222222222222-2-2-2-222-2-2-2-222-2-2000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-222-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ212222-2-2-2-222-2-222-2-2220000-2-200002-200000000002−22−22−22−200000000
χ222222-2-2-2-222-2-222-2-2220000-2-200002-20000000000−22−22−22−2200000000
χ232222-2-2-2-222-2-222-2-2-2-20000220000-220000000000i2−i2i2−i2−i2i2−i2i200000000
χ242222-2-2-2-222-2-222-2-2-2-20000220000-220000000000−i2i2−i2i2i2−i2i2−i200000000
χ252222-2-2-2-222-2-2-2-222220000-2-20000-2200000000002−2−222−2−2200000000
χ262222-2-2-2-222-2-2-2-222220000-2-20000-220000000000−222−2−222−200000000
χ272222-2-2-2-222-2-2-2-222-2-200002200002-20000000000i2−i2−i2i2−i2i2i2−i200000000
χ282222-2-2-2-222-2-2-2-222-2-200002200002-20000000000−i2i2i2−i2i2−i2−i2i200000000
χ292222-2-2-2-2-2-2222-22-2002i2i−2i−2i000000002i−2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ302222-2-2-2-2-2-2222-22-2002i2i−2i−2i000000002i−2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ312222-2-2-2-2-2-2222-22-200−2i−2i2i2i00000000−2i2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ322222-2-2-2-2-2-2222-22-200−2i−2i2i2i00000000−2i2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ332222-2-2-2-2-2-222-22-22002i2i−2i−2i00000000−2i2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ342222-2-2-2-2-2-222-22-22002i2i−2i−2i00000000−2i2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ352222-2-2-2-2-2-222-22-2200−2i−2i2i2i000000002i−2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ362222-2-2-2-2-2-222-22-2200−2i−2i2i2i000000002i−2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ3722-2-222-2-22-2-2200002i−2i2i−2i2i−2i2i−2i2-2000000002i−2i002-20000000000000000
χ3822-2-222-2-22-2-2200002i−2i2i−2i2i−2i2i−2i2-200000000−2i2i00-220000000000000000
χ3922-2-222-2-22-2-2200002i−2i−2i2i−2i2i2i−2i-220000002i−2i002-2000000000000000000
χ4022-2-222-2-22-2-2200002i−2i−2i2i−2i2i2i−2i-22000000−2i2i00-22000000000000000000
χ4122-2-222-2-22-2-220000−2i2i2i−2i2i−2i−2i2i-220000002i−2i00-22000000000000000000
χ4222-2-222-2-22-2-220000−2i2i2i−2i2i−2i−2i2i-22000000−2i2i002-2000000000000000000
χ4322-2-222-2-22-2-220000−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i00-220000000000000000
χ4422-2-222-2-22-2-220000−2i2i−2i2i−2i2i−2i2i2-200000000−2i2i002-20000000000000000
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ4744-4-444-4-4-444-4000000000000004-40000000000000000000000000000
χ4844-4-444-4-4-444-400000000000000-440000000000000000000000000000
χ4944-4-4-4-4444-44-400004i−4i0000−4i4i00000000000000000000000000000000
χ5044-4-4-4-4444-44-40000−4i4i00004i−4i00000000000000000000000000000000
χ5144-4-4-4-444-44-440000004-4-440000000000000000000000000000000000
χ5244-4-4-4-444-44-44000000-444-40000000000000000000000000000000000
χ538-88-88-88-8000000000000000000000000000000000000000000000000
χ548-88-8-88-88000000000000000000000000000000000000000000000000
χ558-8-888-8-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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