Finite Group Databasebeta

← Group #112331

Character table — Group #112331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222222444444244444444444444444222444444444888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111
χ911111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-1111111-1-11-1-11ii−i−i−i−iii−i−iiiii−i−i
χ1411111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-1111111-1-11-1-11−i−iiiii−i−iii−i−i−i−iii
χ1511111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-111-111-1ii−i−i−i−iiiii−i−i−i−iii
χ1611111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-111-111-1−i−iiiii−i−i−i−iiiii−i−i
χ172222222222-2-2-2-222-2-22-2-2-2-22000000002-20002-200000000000000000
χ182222222222-2-2-2-222-2-22-2-2-2-2200000000-22000-2200000000000000000
χ1922222222-2-222-2-22-222-22-2-2-2-200000000002-2-20020000000000000000
χ2022222222-2-222-2-22-222-22-2-2-2-20000000000-22200-20000000000000000
χ2122222222-2-2-2-2222-2-2-2-2-2222-222-2-222-2-2000000000000000000000000
χ2222222222-2-2-2-2222-2-2-2-2-2222-2-2-222-2-222000000000000000000000000
χ2322222-2-22222222-22-2-2-22-2-22-2000000002-2000-2200000000000000000
χ2422222-2-22222222-22-2-2-22-2-22-200000000-220002-200000000000000000
χ2522222-2-22-2-222-2-2-2-2-2-22222-2222-2-2-2-222000000000000000000000000
χ2622222-2-22-2-222-2-2-2-2-2-22222-22-2-22222-2-2000000000000000000000000
χ2722222-2-22-2-2-2-222-2-2222-2-2-22200000000002-2200-20000000000000000
χ2822222-2-22-2-2-2-222-2-2222-2-2-2220000000000-22-20020000000000000000
χ292222-222-2222222-2-22-22-22-2-2-20000000000000000000000002-22-20000
χ302222-222-2222222-2-22-22-22-2-2-2000000000000000000000000-22-220000
χ312222-222-222-2-2-2-2-2-2-2222-222-2000000000000000000002i−2i2i−2i00000000
χ322222-222-222-2-2-2-2-2-2-2222-222-200000000000000000000−2i2i−2i2i00000000
χ332222-222-2-2-222-2-2-222-2-2-2-222200000000000000002-22-2000000000000
χ342222-222-2-2-222-2-2-222-2-2-2-22220000000000000000-22-22000000000000
χ352222-222-2-2-2-2-222-22-22-222-2-2200000000000000000000000000002-22-2
χ362222-222-2-2-2-2-222-22-22-222-2-220000000000000000000000000000-22-22
χ372222-2-2-2-22222222-2-22-2-2-22-22000000000000000000002-2-2200000000
χ382222-2-2-2-22222222-2-22-2-2-22-2200000000000000000000-222-200000000
χ392222-2-2-2-222-2-2-2-22-22-2-222-2220000000000000000000000002i−2i−2i2i0000
χ402222-2-2-2-222-2-2-2-22-22-2-222-222000000000000000000000000−2i2i2i−2i0000
χ412222-2-2-2-2-2-222-2-222-222-22-22-200000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-222-2-222-222-22-22-20000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-2-2-222222-222-22-2-200000000000000002i−2i−2i2i000000000000
χ442222-2-2-2-2-2-2-2-222222-222-22-2-20000000000000000−2i2i2i−2i000000000000
χ4544-4-400004-44i−4i4i−4i00000000002-22-22i−2i2i−2i000000000000000000000000
χ4644-4-400004-44i−4i4i−4i0000000000-22-22−2i2i−2i2i000000000000000000000000
χ4744-4-400004-4−4i4i−4i4i00000000002-22-2−2i2i−2i2i000000000000000000000000
χ4844-4-400004-4−4i4i−4i4i0000000000-22-222i−2i2i−2i000000000000000000000000
χ4944-4-40000-444i−4i−4i4i00000000002-2-22−2i2i2i−2i000000000000000000000000
χ5044-4-40000-444i−4i−4i4i0000000000-222-22i−2i−2i2i000000000000000000000000
χ5144-4-40000-44−4i4i4i−4i00000000002-2-222i−2i−2i2i000000000000000000000000
χ5244-4-40000-44−4i4i4i−4i0000000000-222-2−2i2i2i−2i000000000000000000000000
χ538-88-8800-8000000000000000000000000000000000000000000000000
χ548-88-8-8008000000000000000000000000000000000000000000000000
χ558-8-8808-80000000000000000000000000000000000000000000000000
χ568-8-880-880000000000000000000000000000000000000000000000000

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