Finite Group Databasebeta

← Group #124657

Character table — Group #124657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444224444448888888888888888
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
χ2122-2-222-2-222-2-200002i−2i2i2i−2i−2i2i−2i2-2000000002-2002i−2i0000000000000000
χ2222-2-222-2-222-2-200002i−2i2i2i−2i−2i2i−2i2-200000000-2200−2i2i0000000000000000
χ2322-2-222-2-222-2-200002i−2i−2i−2i2i2i2i−2i-220000002-2002i−2i000000000000000000
χ2422-2-222-2-222-2-200002i−2i−2i−2i2i2i2i−2i-22000000-2200−2i2i000000000000000000
χ2522-2-222-2-222-2-20000−2i2i2i2i−2i−2i−2i2i-220000002-200−2i2i000000000000000000
χ2622-2-222-2-222-2-20000−2i2i2i2i−2i−2i−2i2i-22000000-22002i−2i000000000000000000
χ2722-2-222-2-222-2-20000−2i2i−2i−2i2i2i−2i2i2-2000000002-200−2i2i0000000000000000
χ2822-2-222-2-222-2-20000−2i2i−2i−2i2i2i−2i2i2-200000000-22002i−2i0000000000000000
χ292-22-22-22-22-22-222-2-2002i−2i2i−2i000000002i−2i00000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ302-22-22-22-22-22-222-2-2002i−2i2i−2i000000002i−2i0000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ312-22-22-22-22-22-222-2-200−2i2i−2i2i00000000−2i2i00000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ322-22-22-22-22-22-222-2-200−2i2i−2i2i00000000−2i2i0000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ332-22-22-22-22-22-2-2-222002i−2i2i−2i00000000−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ342-22-22-22-22-22-2-2-222002i−2i2i−2i00000000−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ352-22-22-22-22-22-2-2-22200−2i2i−2i2i000000002i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ362-22-22-22-22-22-2-2-22200−2i2i−2i2i000000002i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ372-22-22-22-2-22-222-22-2220000-2-200002-20000000000i2−i2i2−i2i2−i2i2−i200000000
χ382-22-22-22-2-22-222-22-2220000-2-200002-20000000000−i2i2−i2i2−i2i2−i2i200000000
χ392-22-22-22-2-22-222-22-2-2-20000220000-2200000000002−22−2−22−2200000000
χ402-22-22-22-2-22-222-22-2-2-20000220000-220000000000−22−222−22−200000000
χ412-22-22-22-2-22-22-22-22220000-2-20000-220000000000i2−i2−i2i2i2−i2−i2i200000000
χ422-22-22-22-2-22-22-22-22220000-2-20000-220000000000−i2i2i2−i2−i2i2i2−i200000000
χ432-22-22-22-2-22-22-22-22-2-200002200002-200000000002−2−22−222−200000000
χ442-22-22-22-2-22-22-22-22-2-200002200002-20000000000−222−22−2−2200000000
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ4744-4-444-4-4-4-444000000000000004-40000000000000000000000000000
χ4844-4-444-4-4-4-44400000000000000-440000000000000000000000000000
χ494-4-444-4-444-4-440000004-4-440000000000000000000000000000000000
χ504-4-444-4-444-4-44000000-444-40000000000000000000000000000000000
χ514-4-444-4-44-444-400004i−4i0000−4i4i00000000000000000000000000000000
χ524-4-444-4-44-444-40000−4i4i00004i−4i00000000000000000000000000000000
χ538888-8-8-8-8000000000000000000000000000000000000000000000000
χ5488-8-8-8-888000000000000000000000000000000000000000000000000
χ558-88-8-88-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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