Finite Group Databasebeta

← Group #235261

Character table — Group #235261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444442222444488888888888888882222444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ911111-1-1-1-11-1-1111-1-1-1-11111-1-11-1111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111-1-1-1-11-1-1111-1-1-1-11111-1-11-1111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ1111111-1-1-1-11-1-1111-1-1-1-11111-1-11-1111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1111-1-1-1-111
χ1211111-1-1-1-11-1-1111-1-1-1-11111-1-11-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-11111-1-1
χ1311111-1-1-1-11-1-1111-1-1-1-11111-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-11-1-11111-1-1
χ1411111-1-1-1-11-1-1111-1-1-1-11111-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-111-1-1-1-111
χ1511111-1-1-1-11-1-1111-1-1-1-11111-1-11-11-1-111-1-111-1-1-1-111111111-1-1-1-11-11-11-11-1-1-111-1-111
χ1611111-1-1-1-11-1-1111-1-1-1-11111-1-11-11-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11-11-1111-1-111-1-1
χ17222222222222-2-2-2-2-2-2-222-2-2-2-222-2000000000000000000000000000000002-22-20000
χ18222222222222-2-2-2-2-2-2-222-2-2-2-222-200000000000000000000000000000000-22-220000
χ192222222222-2-22222222-2-22-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-220000000000000000000000002-200-220000000000
χ222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22000000000000000000000000-22002-20000000000
χ2322222-2-2-2-2222222-2-2-2-2-2-22-222-22-222-2-2-2-22200000000000000000000000000000000
χ2422222-2-2-2-2222222-2-2-2-2-2-22-222-22-2-2-22222-2-200000000000000000000000000000000
χ2522222-2-2-2-2222-2-2-22222-2-2-22-2-2-2220000000000000000000000002200-2-20000000000
χ2622222-2-2-2-2222-2-2-22222-2-2-22-2-2-222000000000000000000000000-2-200220000000000
χ2722222-2-2-2-22-2-2-2-2-2222222-2-2222-2-2000000000000000000000000000000002-2-220000
χ2822222-2-2-2-22-2-2-2-2-2222222-2-2222-2-200000000000000000000000000000000-222-20000
χ292222-222-2-2-22222-222-2-222-2-22-2-2-22000000000000000022-2-222-2-20000000000000000
χ302222-222-2-2-22222-222-2-222-2-22-2-2-220000000000000000-2-222-2-2220000000000000000
χ312222-222-2-2-222-2-22-2-2222222-22-2-2-20000000000000000000000000000000000002-22-2
χ322222-222-2-2-222-2-22-2-2222222-22-2-2-2000000000000000000000000000000000000-22-22
χ332222-222-2-2-2-2-222-222-2-2-2-2-22-2222-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ342222-222-2-2-2-2-222-222-2-2-2-2-22-2222-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ352222-222-2-2-2-2-2-2-22-2-222-2-22-22-2222000000000000000000000000002-200-2200000000
χ362222-222-2-2-2-2-2-2-22-2-222-2-22-22-222200000000000000000000000000-22002-200000000
χ372222-2-2-222-22222-2-2-222-2-2-222-22-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ382222-2-2-222-22222-2-2-222-2-2-222-22-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ392222-2-2-222-222-2-2222-2-2-2-22-2-222-22000000000000000000000000002200-2-200000000
χ402222-2-2-222-222-2-2222-2-2-2-22-2-222-2200000000000000000000000000-2-2002200000000
χ412222-2-2-222-2-2-222-2-2-22222-2-2-22-222000000000000000022-2-2-2-2220000000000000000
χ422222-2-2-222-2-2-222-2-2-22222-2-2-22-2220000000000000000-2-22222-2-20000000000000000
χ432222-2-2-222-2-2-2-2-2222-2-222222-2-22-20000000000000000000000000000000000002-2-22
χ442222-2-2-222-2-2-2-2-2222-2-222222-2-22-2000000000000000000000000000000000000-222-2
χ452-2-2222-22-2-2002-222-22-200-200000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ462-2-2222-22-2-2002-222-22-200-200000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ472-2-2222-22-2-2002-222-22-200-20000000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ482-2-2222-22-2-2002-222-22-200-20000000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ492-2-222-22-22-2002-22-22-2200-200000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ502-2-222-22-22-2002-22-22-2200-200000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ512-2-222-22-22-2002-22-22-2200-20000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ522-2-222-22-22-2002-22-22-2200-20000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ532-2-22-22-2-222002-2-22-2-220020000002-22-200002−2−222−2−222−2−222−2−220000000000000000
χ542-2-22-22-2-222002-2-22-2-220020000002-22-20000−222−2−222−2−222−2−222−20000000000000000
χ552-2-22-22-2-222002-2-22-2-22002000000-22-2200002−2−222−2−22−222−2−222−20000000000000000
χ562-2-22-22-2-222002-2-22-2-22002000000-22-220000−222−2−222−22−2−222−2−220000000000000000
χ572-2-22-2-222-22002-2-2-222-20020000002-2-2200002−2−22−222−22−2−22−222−20000000000000000
χ582-2-22-2-222-22002-2-2-222-20020000002-2-220000−222−22−2−22−222−22−2−220000000000000000
χ592-2-22-2-222-22002-2-2-222-2002000000-222-200002−2−22−222−2−222−22−2−220000000000000000
χ602-2-22-2-222-22002-2-2-222-2002000000-222-20000−222−22−2−222−2−22−222−20000000000000000
χ614-4-4444-44-4-400-44-4-44-440040000000000000000000000000000000000000000000000
χ624-4-444-44-44-400-44-44-44-40040000000000000000000000000000000000000000000000
χ634-4-44-44-4-44400-444-444-400-40000000000000000000000000000000000000000000000
χ644-4-44-4-444-4400-4444-4-4400-40000000000000000000000000000000000000000000000
χ6588-8-80000000000000008i−8i00000000000000000000000000000000000000000000000
χ6688-8-8000000000000000−8i8i00000000000000000000000000000000000000000000000
χ678-88-80000008-800000000000000000000000000000000000000000000000000000000
χ688-88-8000000-8800000000000000000000000000000000000000000000000000000000

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