Finite Group Databasebeta

← Group #138313

Character table — Group #138313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222444444444444444488888888888888888888881616161616161616161616163232
order12222244442244444444444444444444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ8111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ91111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1-1
χ101111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-11
χ111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii1-1
χ121111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−iii−i−i-11
χ131111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii-11
χ141111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i1-1
χ151111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i-11
χ161111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii1-1
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000000000
χ192222222222-2-22222-2-2-2-22222-2-2-2-2-2-222000000000000000000000000000000
χ202222222222-2-2-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000000000
χ21222222-2-2-2-2220000000022-2-2-2-22-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ22222222-2-2-2-2220000000022-2-2-2-22-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ23222222-2-2-2-22200000000-2-222-2-2-2200002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ24222222-2-2-2-22200000000-2-222-2-2-220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ25222222-2-2-2-2-2-20000000022-2-222-22000022-2-2-2-2220000000000000000000000
χ26222222-2-2-2-2-2-20000000022-2-222-220000-2-22222-2-20000000000000000000000
χ27222222-2-2-2-2-2-200000000-2-222222-200000000000022-2-2-2-22200000000000000
χ28222222-2-2-2-2-2-200000000-2-222222-2000000000000-2-22222-2-200000000000000
χ292-2-222-22-22-20000002i2i−2i−2i2i−2i2i−2i00002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ302-2-222-22-22-20000002i2i−2i−2i2i−2i2i−2i00002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ312-2-222-22-22-20000002i2i−2i−2i−2i2i−2i2i0000-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ322-2-222-22-22-20000002i2i−2i−2i−2i2i−2i2i0000-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ332-2-222-22-22-2000000−2i−2i2i2i2i−2i2i−2i0000-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ342-2-222-22-22-2000000−2i−2i2i2i2i−2i2i−2i0000-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ352-2-222-22-22-2000000−2i−2i2i2i−2i2i−2i2i00002-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ362-2-222-22-22-2000000−2i−2i2i2i−2i2i−2i2i00002-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ372-2-222-2-22-22002i2i−2i−2i00002i−2i−2i2i0000002-21+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000
χ382-2-222-2-22-22002i2i−2i−2i00002i−2i−2i2i0000002-2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000
χ392-2-222-2-22-22002i2i−2i−2i0000−2i2i2i−2i000000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000
χ402-2-222-2-22-22002i2i−2i−2i0000−2i2i2i−2i000000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000
χ412-2-222-2-22-2200−2i−2i2i2i00002i−2i−2i2i000000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000
χ422-2-222-2-22-2200−2i−2i2i2i00002i−2i−2i2i000000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000
χ432-2-222-2-22-2200−2i−2i2i2i0000−2i2i2i−2i0000002-21−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000
χ442-2-222-2-22-2200−2i−2i2i2i0000−2i2i2i−2i0000002-2−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000
χ452-2-22-2222-2-22-22i−2i2i−2i2i−2i2i−2i00002-200000000000000000000000000i2−i2i2−i22−22−200
χ462-2-22-2222-2-22-22i−2i2i−2i2i−2i2i−2i00002-200000000000000000000000000−i2i2−i2i2−22−2200
χ472-2-22-2222-2-22-2−2i2i−2i2i−2i2i−2i2i00002-200000000000000000000000000i2−i2i2−i2−22−2200
χ482-2-22-2222-2-22-2−2i2i−2i2i−2i2i−2i2i00002-200000000000000000000000000−i2i2−i2i22−22−200
χ492-2-22-2222-2-2-222i−2i2i−2i−2i2i−2i2i0000-22000000000000000000000000002−2−22−i2i2i2−i200
χ502-2-22-2222-2-2-222i−2i2i−2i−2i2i−2i2i0000-2200000000000000000000000000−222−2i2−i2−i2i200
χ512-2-22-2222-2-2-22−2i2i−2i2i2i−2i2i−2i0000-22000000000000000000000000002−2−22i2−i2−i2i200
χ522-2-22-2222-2-2-22−2i2i−2i2i2i−2i2i−2i0000-2200000000000000000000000000−222−2−i2i2i2−i200
χ534444-4-44-4-440000004-4-44000000000000000000000000000000000000000000
χ544444-4-44-4-44000000-444-4000000000000000000000000000000000000000000
χ554444-4-4-444-4004-4-440000000000000000000000000000000000000000000000
χ564444-4-4-444-400-444-40000000000000000000000000000000000000000000000
χ574-4-44-44-4-4444-4000000000000-44000000000000000000000000000000000000
χ584-4-44-44-4-444-440000000000004-4000000000000000000000000000000000000
χ5988-8-800000000000000000000000000000000000000000000002i2−2i20000000000
χ6088-8-80000000000000000000000000000000000000000000000−2i22i20000000000
χ618-88-8000000000000000000000000000000000000000000002i2−2i2000000000000
χ628-88-800000000000000000000000000000000000000000000−2i22i2000000000000

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