Finite Group Databasebeta

← Group #313141

Character table — Group #313141

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888824444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ51111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-1-1111-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-11-1
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-111-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111-1-111-1-111-11
χ13111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11-111-1-1-1-111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-111-11
χ15111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11-1-1-1111111-1-11-1
χ17222222222-22-22-22-2-2-2222222000000220000-2-20000000000-2-2000000000000
χ18222222222-22-22-22-2-2-22222-2-2000000-2-20000-2-2000000000022000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-222000000-2-200002200000000002-2000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2-2-2000000220000220000000000-22000000000000
χ2122222222-22-22-22-22-2-20000002222-2-200-2-2-2-200000022000000000000000000
χ2222222222-22-22-22-22-2-200000022-2-22200-2-222000000-2-2000000000000000000
χ2322222222-22-22-22-22-2-2000000-2-222-2-2002222000000-2-2000000000000000000
χ2422222222-22-22-22-22-2-2000000-2-2-2-2220022-2-200000022000000000000000000
χ252-22-2-22-2222-2-222-2-2-222i2i−2i−2i00002i−2i2i−2i0000002i−2i00000000000000002-2000000
χ262-22-2-22-2222-2-222-2-2-222i2i−2i−2i0000−2i2i−2i2i0000002i−2i0000000000000000-22000000
χ272-22-2-22-2222-2-222-2-2-22−2i−2i2i2i00002i−2i2i−2i000000−2i2i0000000000000000-22000000
χ282-22-2-22-2222-2-222-2-2-22−2i−2i2i2i0000−2i2i−2i2i000000−2i2i00000000000000002-2000000
χ292-22-2-22-222-2-222-2-222-22i2i−2i−2i00000000000000−2i2i0000000000002i−2i2-200000000
χ302-22-2-22-222-2-222-2-222-22i2i−2i−2i00000000000000−2i2i000000000000−2i2i-2200000000
χ312-22-2-22-222-2-222-2-222-2−2i−2i2i2i000000000000002i−2i0000000000002i−2i-2200000000
χ322-22-2-22-222-2-222-2-222-2−2i−2i2i2i000000000000002i−2i000000000000−2i2i2-200000000
χ332-22-2-22-22-222-2-222-22-2000000002i−2i−2i2i0000000022-2-2002i2i−2i−2i00000000000000
χ342-22-2-22-22-222-2-222-22-2000000002i−2i−2i2i00000000-2-22200−2i−2i2i2i00000000000000
χ352-22-2-22-22-222-2-222-22-200000000−2i2i2i−2i0000000022-2-200−2i−2i2i2i00000000000000
χ362-22-2-22-22-222-2-222-22-200000000−2i2i2i−2i00000000-2-222002i2i−2i−2i00000000000000
χ372-2-22-222-2-202020-20002-22-22i−2i0000002i−2i00i2−i2000000i2−i2i2−i2i2−i2000000002−22−200
χ382-2-22-222-2-202020-20002-22-22i−2i0000002i−2i00−i2i2000000−i2i2−i2i2−i2i200000000−22−2200
χ392-2-22-222-2-202020-20002-22-2−2i2i000000−2i2i00i2−i2000000i2−i2i2−i2i2−i200000000−22−2200
χ402-2-22-222-2-202020-20002-22-2−2i2i000000−2i2i00−i2i2000000−i2i2−i2i2−i2i2000000002−22−200
χ412-2-22-222-2-202020-2000-22-222i−2i000000−2i2i00i2−i2000000i2−i2−i2i2−i2i200000000−222−200
χ422-2-22-222-2-202020-2000-22-222i−2i000000−2i2i00−i2i2000000−i2i2i2−i2i2−i2000000002−2−2200
χ432-2-22-222-2-202020-2000-22-22−2i2i0000002i−2i00i2−i2000000i2−i2−i2i2−i2i2000000002−2−2200
χ442-2-22-222-2-202020-2000-22-22−2i2i0000002i−2i00−i2i2000000−i2i2i2−i2i2−i200000000−222−200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-44-4-4-44040-40-40400000000000000000000002i2−2i22i2−2i200000000000000000000
χ4744-44-4-4-44040-40-4040000000000000000000000−2i22i2−2i22i200000000000000000000
χ4844-44-4-4-440-404040-4000000004i−4i000000000000000000000000000000000000
χ4944-44-4-4-440-404040-400000000−4i4i000000000000000000000000000000000000
χ5044-4-444-4-44040-40-40000000000000000000000000000022−22−222200000000000000
χ5144-4-444-4-44040-40-400000000000000000000000000000−222222−2200000000000000
χ5244-4-444-4-4-40-404040004i−4i−4i4i0000000000000000000000000000000000000000
χ5344-4-444-4-4-40-40404000−4i4i4i−4i0000000000000000000000000000000000000000
χ544-44-4-44-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ554-4-44-444-440-40-40400000000000000000002i2−2i2000000−2i22i2000000000000000000
χ564-4-44-444-440-40-4040000000000000000000−2i22i20000002i2−2i2000000000000000000
χ574-4-4-44-44404040-40-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-4-4-44-44404040-40-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-4-4-44-4440-40-4040400000000000000004-40000000000000000000000000000
χ604-4-4-44-4440-40-404040000000000000000-440000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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