Finite Group Databasebeta

← Group #124751

Character table — Group #124751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444422444444444444448888888888888888
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
χ51111111111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000000000
χ19222222222222-2-2222222-2-22222-2-2-2-2-2-2000000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ2122-2-2-2-22222-2-22i−2i0022-2-22i−2i000000002i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ2222-2-2-2-22222-2-22i−2i0022-2-22i−2i000000002i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ2322-2-2-2-22222-2-22i−2i00-2-2222i−2i00000000−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ2422-2-2-2-22222-2-22i−2i00-2-2222i−2i00000000−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ2522-2-2-2-22222-2-2−2i2i0022-2-2−2i2i00000000−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ2622-2-2-2-22222-2-2−2i2i0022-2-2−2i2i00000000−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ2722-2-2-2-22222-2-2−2i2i00-2-222−2i2i000000002i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ2822-2-2-2-22222-2-2−2i2i00-2-222−2i2i000000002i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ2922-2-2-2-222-2-22200222-22-200-2-22-200000000000000i2−i2i2−i2i2−i2i2−i200000000
χ3022-2-2-2-222-2-22200222-22-200-2-22-200000000000000−i2i2−i2i2−i2i2−i2i200000000
χ3122-2-2-2-222-2-2220022-22-2200-2-2-2200000000000000i2−i2i2−i2−i2i2−i2i200000000
χ3222-2-2-2-222-2-2220022-22-2200-2-2-2200000000000000−i2i2−i2i2i2−i2i2−i200000000
χ3322-2-2-2-222-2-22200-2-22-22-20022-22000000000000002−2−222−2−2200000000
χ3422-2-2-2-222-2-22200-2-22-22-20022-2200000000000000−222−2−222−200000000
χ3522-2-2-2-222-2-22200-2-2-22-2200222-2000000000000002−2−22−222−200000000
χ3622-2-2-2-222-2-22200-2-2-22-2200222-200000000000000−222−22−2−2200000000
χ372-222-2-22-22-22-22i−2i2i−2i0000−2i2i2i−2i002-20000002i−2i002-20000000000000000
χ382-222-2-22-22-22-22i−2i2i−2i0000−2i2i2i−2i002-2000000−2i2i00-220000000000000000
χ392-222-2-22-22-22-22i−2i−2i2i0000−2i2i−2i2i00-2200002-2002i−2i000000000000000000
χ402-222-2-22-22-22-22i−2i−2i2i0000−2i2i−2i2i00-220000-2200−2i2i000000000000000000
χ412-222-2-22-22-22-2−2i2i2i−2i00002i−2i2i−2i00-2200002-200−2i2i000000000000000000
χ422-222-2-22-22-22-2−2i2i2i−2i00002i−2i2i−2i00-220000-22002i−2i000000000000000000
χ432-222-2-22-22-22-2−2i2i−2i2i00002i−2i−2i2i002-20000002i−2i00-220000000000000000
χ442-222-2-22-22-22-2−2i2i−2i2i00002i−2i−2i2i002-2000000−2i2i002-20000000000000000
χ4544444444-4-4-4-400004-4-44000000000000000000000000000000000000
χ4644444444-4-4-4-40000-444-4000000000000000000000000000000000000
χ474-444-4-44-4-44-4400000000000000004i−4i00000000000000000000000000
χ484-444-4-44-4-44-440000000000000000−4i4i00000000000000000000000000
χ494-4-4-4444-44-4-4444000000-4-40000000000000000000000000000000000
χ504-4-4-4444-44-4-44-4-4000000440000000000000000000000000000000000
χ514-4-4-4444-4-444-4004i−4i000000−4i4i00000000000000000000000000000000
χ524-4-4-4444-4-444-400−4i4i0000004i−4i00000000000000000000000000000000
χ53888-88-8-8-8000000000000000000000000000000000000000000000000
χ5488-88-88-8-8000000000000000000000000000000000000000000000000
χ558-88-8-88-88000000000000000000000000000000000000000000000000
χ568-8-888-8-88000000000000000000000000000000000000000000000000

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