Finite Group Databasebeta

← Group #238002

Character table — Group #238002

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-11111-1-1
χ1211111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-1-1-111
χ1311111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ1511111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22-222-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ202222222222-2-2-2-2-2-222-2-22-222-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ212222222222-2-2-2-2-2-222-2-2-22-2-222-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222-2-2-2-2-2-222-2-2-22-2-222-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-2222-2-2-2222-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-222-2-2-2-2-2-2222-2-2-2222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-222-2-2-2-2-2-222-2222-2-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-222-2-2-2-2-2-222-2222-2-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ292222-2-2-2-2222222-2-2-2-2-2-22-22-22-2-22000000000000000000000000000000002-22-20000
χ302222-2-2-2-2222222-2-2-2-2-2-22-22-22-2-2200000000000000000000000000000000-22-220000
χ312222-2-2-2-2222222-2-2-2-2-2-2-22-22-222-200000000000000000000000000002-22-200000000
χ322222-2-2-2-2222222-2-2-2-2-2-2-22-22-222-20000000000000000000000000000-22-2200000000
χ332222-2-2-2-222-2-2-2-222-2-222222-2-22-2-200000000000000000000000022-2-2000000000000
χ342222-2-2-2-222-2-2-2-222-2-222222-2-22-2-2000000000000000000000000-2-222000000000000
χ352222-2-2-2-222-2-2-2-222-2-222-2-2-222-2220000000000000000000000000000000000002i−2i2i−2i
χ362222-2-2-2-222-2-2-2-222-2-222-2-2-222-222000000000000000000000000000000000000−2i2i−2i2i
χ372222-2-2-2-2-2-222-2-22222-2-222-222-2-2-20000000000000000000000002-2-22000000000000
χ382222-2-2-2-2-2-222-2-22222-2-222-222-2-2-2000000000000000000000000-222-2000000000000
χ392222-2-2-2-2-2-222-2-22222-2-2-2-22-2-22220000000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-2-2-222-2-22222-2-2-2-22-2-2222000000000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-2-2-2-222-2-222222-2-22-22-22000000000000000000000000000000002-2-220000
χ422222-2-2-2-2-2-2-2-222-2-222222-2-22-22-2200000000000000000000000000000000-222-20000
χ432222-2-2-2-2-2-2-2-222-2-22222-222-22-22-200000000000000000000000000002-2-2200000000
χ442222-2-2-2-2-2-2-2-222-2-22222-222-22-22-20000000000000000000000000000-222-200000000
χ452-2-2222-2-22-22-22-22-22-22-200000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ462-2-2222-2-22-22-22-22-22-22-200000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ472-2-2222-2-22-22-22-22-22-22-20000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ482-2-2222-2-22-22-22-22-22-22-20000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ492-2-2222-2-22-2-22-22-222-2-22000000002i−2i002i−2i002−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ502-2-2222-2-22-2-22-22-222-2-22000000002i−2i002i−2i00−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ512-2-2222-2-22-2-22-22-222-2-2200000000−2i2i00−2i2i002−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ522-2-2222-2-22-2-22-22-222-2-2200000000−2i2i00−2i2i00−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ532-2-2222-2-2-222-2-22-22-222-2000000002i−2i00−2i2i002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ542-2-2222-2-2-222-2-22-22-222-2000000002i−2i00−2i2i00−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ552-2-2222-2-2-222-2-22-22-222-200000000−2i2i002i−2i002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ562-2-2222-2-2-222-2-22-22-222-200000000−2i2i002i−2i00−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ572-2-2222-2-2-22-222-22-2-22-2200000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ582-2-2222-2-2-22-222-22-2-22-2200000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ592-2-2222-2-2-22-222-22-2-22-220000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ602-2-2222-2-2-22-222-22-2-22-220000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ614-4-44-4-4444-44-44-4-44-44-44000000000000000000000000000000000000000000000000
χ624-4-44-4-4444-4-44-444-4-444-4000000000000000000000000000000000000000000000000
χ634-4-44-4-444-444-4-444-44-4-44000000000000000000000000000000000000000000000000
χ644-4-44-4-444-44-444-4-444-44-4000000000000000000000000000000000000000000000000
χ6588-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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