Finite Group Databasebeta

← Group #237180

Character table — Group #237180

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111
χ911111111111111-1-11-1-1-1-1-1-111111-1-1-1-11-111111-1-1-1-1-111-1-111-1-111-1-1
χ1011111111111111-1-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-11-11111-1-111-1-11111-1-1
χ1111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-111111-11-1-1-1-1-1-111-1-111-1-111
χ1211111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-11-1-1-1-1-11111111-1-111-1-1-1-111
χ1311111111111111-1-11-1-1-1-1-1-11-1-1-1-111111-111-1-11-1-1-11111-1-1-1-111-1-111
χ1411111111111111-1-11-1-1-1-1-1-11-1-1-1-111111-1-1-1111-111-1-1-1-11111-1-1-1-111
χ1511111111111111-1-11-1-1-1-1-1-11-1-1-1-11111-1111-1-1-11-1-111-1-11111-1-111-1-1
χ1611111111111111-1-11-1-1-1-1-1-11-1-1-1-11111-11-1-111-1111-1-111-1-1-1-11111-1-1
χ1722222222-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000002i−2i2i−2i
χ1822222222-2-2-2-2-2-222222-2-2-2-2-20000000000000000000000000000−2i2i−2i2i
χ1922222222-2-2-2-2-2-2-2-22-2-22222-200000000000000000000000000002i−2i−2i2i
χ2022222222-2-2-2-2-2-2-2-22-2-22222-20000000000000000000000000000−2i2i2i−2i
χ21222222-2-22-2-222222-2-2-2-2-222-20000000000000000000000002-22-20000
χ22222222-2-22-2-222222-2-2-2-2-222-2000000000000000000000000-22-220000
χ23222222-2-22-2-2222-2-2-22222-2-2-20000000000000000000000002-2-220000
χ24222222-2-22-2-2222-2-2-22222-2-2-2000000000000000000000000-222-20000
χ25222222-2-2-222-2-2-222-2-2-222-2-2200000000002-200002-200000000000000
χ26222222-2-2-222-2-2-222-2-2-222-2-220000000000-220000-2200000000000000
χ27222222-2-2-222-2-2-2-2-2-222-2-222200000000002-20000-2200000000000000
χ28222222-2-2-222-2-2-2-2-2-222-2-22220000000000-2200002-200000000000000
χ292222-2-2222-2-2-2-222-2-22-22-22-2222-2-222-2-2000000000000000000000000
χ302222-2-2222-2-2-2-222-2-22-22-22-22-2-222-2-222000000000000000000000000
χ312222-2-2222-2-2-2-22-22-2-22-22-22222-2-2-2-222000000000000000000000000
χ322222-2-2222-2-2-2-22-22-2-22-22-222-2-22222-2-2000000000000000000000000
χ332222-2-222-22222-22-2-22-2-22-22-200000000220000-2-20000000000000000
χ342222-2-222-22222-22-2-22-2-22-22-200000000-2-20000220000000000000000
χ352222-2-222-22222-2-22-2-222-22-2-2000000002-20000-220000000000000000
χ362222-2-222-22222-2-22-2-222-22-2-200000000-2200002-20000000000000000
χ372222-2-2-2-2222-2-222-22-22-222-2-2000000000000000000002-22-200000000
χ382222-2-2-2-2222-2-222-22-22-222-2-200000000000000000000-22-2200000000
χ392222-2-2-2-2222-2-22-2222-22-2-22-2000000000000000000002-2-2200000000
χ402222-2-2-2-2222-2-22-2222-22-2-22-200000000000000000000-222-200000000
χ412222-2-2-2-2-2-2-222-22-22-222-2-2220000000000002-200002-2000000000000
χ422222-2-2-2-2-2-2-222-22-22-222-2-222000000000000-220000-22000000000000
χ432222-2-2-2-2-2-2-222-2-2222-2-222-220000000000002-20000-22000000000000
χ442222-2-2-2-2-2-2-222-2-2222-2-222-22000000000000-2200002-2000000000000
χ454-4-444-4004004-4-4000000000000002i2−2i22i2−2i2000000000000000000000000
χ464-4-444-4004004-4-400000000000000−2i22i2−2i22i2000000000000000000000000
χ474-4-444-400-400-444000000000022−2222−220000000000000000000000000000
χ484-4-444-400-400-4440000000000−2222−22220000000000000000000000000000
χ494-4-44-4400400-44-4000000000000002i2−2i2−2i22i2000000000000000000000000
χ504-4-44-4400400-44-400000000000000−2i22i22i2−2i2000000000000000000000000
χ514-4-44-4400-4004-44000000000022−22−22220000000000000000000000000000
χ524-4-44-4400-4004-440000000000−222222−220000000000000000000000000000
χ5388-8-8000008-8000000000000000000000000000000000000000000000
χ5488-8-800000-88000000000000000000000000000000000000000000000
χ558-88-8008-8000000000000000000000000000000000000000000000000
χ568-88-800-88000000000000000000000000000000000000000000000000

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