Finite Group Databasebeta

← Group #112397

Character table — Group #112397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888222244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i111-1-1-11-1ii−i−iii−i−i11-1-1ii−i−i
χ1011111111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-11-1-1-11−i−iiiii−i−i-1-111−i−iii
χ1111111111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11-1111-1−i−iii−i−iii-1-111ii−i−i
χ1211111111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1111-11ii−i−i−i−iii11-1-1−i−iii
χ1311111111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii111-1-1-11-1−i−iii−i−iii11-1-1−i−iii
χ1411111111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-11-1-1-11ii−i−i−i−iii-1-111ii−i−i
χ1511111111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11-1111-1ii−i−iii−i−i-1-111−i−iii
χ1611111111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1111-11−i−iiiii−i−i11-1-1ii−i−i
χ172222222222-2-222-2-2-2-22-2-2-22222-2-222-2-2000000000000000000000000
χ182222222222-2-222-2-2-2-22-2-2-222-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-2-2-222-2-22-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2022222222-2-2-2-2-2-222-2-22-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ21222222-2-222222222-2-2-22-2-2-2-200000000002-200-220000000000000000
χ22222222-2-222222222-2-2-22-2-2-2-20000000000-22002-20000000000000000
χ23222222-2-222-2-222-2-222-2-222-2-200000000000000000000000000002i−2i2i−2i
χ24222222-2-222-2-222-2-222-2-222-2-20000000000000000000000000000−2i2i−2i2i
χ25222222-2-2-2-222-2-2-2-2-2-2-22222200000000002200-2-20000000000000000
χ26222222-2-2-2-222-2-2-2-2-2-2-2222220000000000-2-200220000000000000000
χ27222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000-222-2
χ292222-2-2222222-2-2-222-2-2-22-22-2000000002-2002-2000000000000000000
χ302222-2-2222222-2-2-222-2-2-22-22-200000000-2200-22000000000000000000
χ312222-2-22222-2-2-2-22-2-22-22-222-2000000000000000000002i−2i2i−2i00000000
χ322222-2-22222-2-2-2-22-2-22-22-222-200000000000000000000−2i2i−2i2i00000000
χ332222-2-222-2-222222-22-2-2-2-22-22000000002-200-22000000000000000000
χ342222-2-222-2-222222-22-2-2-2-22-2200000000-22002-2000000000000000000
χ352222-2-222-2-2-2-222-22-22-222-2-22000000000000000000002-2-2200000000
χ362222-2-222-2-2-2-222-22-22-222-2-2200000000000000000000-222-200000000
χ372222-2-2-2-22222-2-2-22-222-2-22-220000000000000000000000002-22-20000
χ382222-2-2-2-22222-2-2-22-222-2-22-22000000000000000000000000-22-220000
χ392222-2-2-2-222-2-2-2-22-22-2222-2-2200000000000000002i−2i2i−2i000000000000
χ402222-2-2-2-222-2-2-2-22-22-2222-2-220000000000000000−2i2i−2i2i000000000000
χ412222-2-2-2-2-2-222222-2-222-22-22-20000000000000000000000002-2-220000
χ422222-2-2-2-2-2-222222-2-222-22-22-2000000000000000000000000-222-20000
χ432222-2-2-2-2-2-2-2-222-222-222-222-200000000000000002-2-22000000000000
χ442222-2-2-2-2-2-2-2-222-222-222-222-20000000000000000-222-2000000000000
χ4544-4-44-4004i−4i004i−4i0000000000002+2i−2−2i002−2i−2+2i000000000000000000000000
χ4644-4-44-4004i−4i004i−4i000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ4744-4-44-400−4i4i00−4i4i0000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ4844-4-44-400−4i4i00−4i4i000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ4944-4-4-44004i−4i00−4i4i00000000002−2i−2+2i002+2i−2−2i00000000000000000000000000
χ5044-4-4-44004i−4i00−4i4i0000000000−2+2i2−2i00−2−2i2+2i00000000000000000000000000
χ5144-4-4-4400−4i4i004i−4i00000000002+2i−2−2i002−2i−2+2i00000000000000000000000000
χ5244-4-4-4400−4i4i004i−4i0000000000−2−2i2+2i00−2+2i2−2i00000000000000000000000000
χ538-88-80000008-800000000000000000000000000000000000000000000
χ548-88-8000000-8800000000000000000000000000000000000000000000
χ558-8-88008-8000000000000000000000000000000000000000000000000
χ568-8-8800-88000000000000000000000000000000000000000000000000

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