Finite Group Databasebeta

← Group #8623

Character table — Group #8623

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order1222224444444488888888444444444488888888888888888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ10111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ11111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ12111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ13111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111i−i−iii−i−ii
χ14111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−iii−i−iii−i
χ15111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−ii−iii−i
χ16111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−ii−i−ii
χ17222222-2-2-22222-200000000-2-222-2-222-2-200000000000000000000
χ18222222-2-2-22222-200000000-2-2-2-222-2-22200000000000000000000
χ19222222-2-2-2-2-2-2-2-2000000002222-2-2-2-22200000000000000000000
χ20222222-2-2-2-2-2-2-2-20000000022-2-22222-2-200000000000000000000
χ212222-2-222-222-2-2-2000000002-20000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222-2-222-222-2-2-2000000002-2000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ232222-2-222-2-2-222-200000000-220000000000002i2i−2i−2i−2i−2i2i2i00000000
χ242222-2-222-2-2-222-200000000-22000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ252222-2-2-2-2222-2-222222-2-2-2-2-220000000022-2-20000000000000000
χ262222-2-2-2-2222-2-22-2-2-2-22222-2200000000-2-2220000000000000000
χ272222-2-2-2-22-2-22222222-2-2-2-22-200000000-2-2220000000000000000
χ282222-2-2-2-22-2-2222-2-2-2-222222-20000000022-2-20000000000000000
χ292-22-22-20002i−2i2i−2i022−2−222−2−200002i−2i002-2i2−i2i2−i2i2−i2i2−i22−22−200000000
χ302-22-22-20002i−2i2i−2i022−2−222−2−20000−2i2i00-22i2−i2i2−i2−i2i2−i2i2−22−2200000000
χ312-22-22-20002i−2i2i−2i0−2−222−2−22200002i−2i002-2−i2i2−i2i2−i2i2−i2i2−22−2200000000
χ322-22-22-20002i−2i2i−2i0−2−222−2−2220000−2i2i00-22−i2i2−i2i2i2−i2i2−i22−22−200000000
χ332-22-22-2000−2i2i−2i2i022−2−222−2−200002i−2i00-22−i2i2−i2i2i2−i2i2−i2−22−2200000000
χ342-22-22-2000−2i2i−2i2i022−2−222−2−20000−2i2i002-2−i2i2−i2i2−i2i2−i2i22−22−200000000
χ352-22-22-2000−2i2i−2i2i0−2−222−2−22200002i−2i00-22i2−i2i2−i2−i2i2−i2i22−22−200000000
χ362-22-22-2000−2i2i−2i2i0−2−222−2−2220000−2i2i002-2i2−i2i2−i2i2−i2i2−i2−22−2200000000
χ372-22-2-220002i−2i−2i2i022−2−2−2−222002-2002i−2i00i2−i2−i2i22−2−22−i2i2i2−i200000000
χ382-22-2-220002i−2i−2i2i022−2−2−2−22200-2200−2i2i00i2−i2−i2i2−222−2i2−i2−i2i200000000
χ392-22-2-220002i−2i−2i2i0−2−22222−2−2002-2002i−2i00−i2i2i2−i2−222−2i2−i2−i2i200000000
χ402-22-2-220002i−2i−2i2i0−2−22222−2−200-2200−2i2i00−i2i2i2−i22−2−22−i2i2i2−i200000000
χ412-22-2-22000−2i2i2i−2i022−2−2−2−222002-200−2i2i00−i2i2i2−i22−2−22i2−i2−i2i200000000
χ422-22-2-22000−2i2i2i−2i022−2−2−2−22200-22002i−2i00−i2i2i2−i2−222−2−i2i2i2−i200000000
χ432-22-2-22000−2i2i2i−2i0−2−22222−2−2002-200−2i2i00i2−i2−i2i2−222−2−i2i2i2−i200000000
χ442-22-2-22000−2i2i2i−2i0−2−22222−2−200-22002i−2i00i2−i2−i2i22−2−22i2−i2−i2i200000000
χ4544-4-4000040000-400004-44-4000000000000000000000000000000
χ4644-4-4000040000-40000-44-44000000000000000000000000000000
χ4744-4-40000-4000044i−4i4i−4i0000000000000000000000000000000000
χ4844-4-40000-400004−4i4i−4i4i0000000000000000000000000000000000
χ494-4-44004i−4i0000002i2−2i2−2i22i222−22−2222000000000000000000000000000000
χ504-4-44004i−4i000000−2i22i22i2−2i2−222222−22000000000000000000000000000000
χ514-4-4400−4i4i0000002i2−2i2−2i22i2−222222−22000000000000000000000000000000
χ524-4-4400−4i4i000000−2i22i22i2−2i222−22−2222000000000000000000000000000000

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