Finite Group Databasebeta

← Group #233849

Character table — Group #233849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222222444444244444444488888888222444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-11111-111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1
χ911111-1-11-1-11111-11-11-1-1-1-1111111-1-1-1-11-11-1-1111-11-1-111-1-111-1-111-1-1
χ1011111-1-11-1-11111-11-11-1-1-1-1111111-1-1-1-11-1-111-1-11-1-11111-1-1-1-111-1-111
χ1111111-1-11-1-11111-11-11-1-1-1-1111111-1-1-1-1-111-1-111-111-1-1-1-111-1-111-1-111
χ1211111-1-11-1-11111-11-11-1-1-1-1111111-1-1-1-1-11-111-1-1-11-111-1-11111-1-111-1-1
χ1311111-1-11-1-11111-11-11-1-1-1-111-1-1-1-111111-11-1-1-1-11-1111-1-11111-1-1-1-111
χ1411111-1-11-1-11111-11-11-1-1-1-111-1-1-1-111111-1-111111-1-1-1-1-1-111-1-11111-1-1
χ1511111-1-11-1-11111-11-11-1-1-1-111-1-1-1-11111-111-1-1-1-1-1111111-1-1-1-11111-1-1
χ1611111-1-11-1-11111-11-11-1-1-1-111-1-1-1-11111-11-11111-11-1-1-111-1-111-1-1-1-111
χ172222222222-2-2-2-2222-2-2-2-2-22-222-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-2222-2-2-2-2-22-2-2-222-2-222000000000000000000000000
χ1922222222-2-222222-2-2-2-2-222-2-20000000000000000000000002-22-20000
χ2022222222-2-222222-2-2-2-2-222-2-2000000000000000000000000-22-220000
χ2122222222-2-2-2-2-2-22-2-2222-2-2-2200000000000000000000000000002-22-2
χ2222222222-2-2-2-2-2-22-2-2222-2-2-220000000000000000000000000000-22-22
χ2322222-2-22222222-2-22-222-2-2-2-20000000000000000000000002-2-220000
χ2422222-2-22222222-2-22-222-2-2-2-2000000000000000000000000-222-20000
χ2522222-2-2222-2-2-2-2-2-222-2-222-2200000000000000000000000000002-2-22
χ2622222-2-2222-2-2-2-2-2-222-2-222-220000000000000000000000000000-222-2
χ2722222-2-22-2-2-2-2-2-2-22-2-222222-222-2-2-2-222000000000000000000000000
χ2822222-2-22-2-2-2-2-2-2-22-2-222222-2-2-22222-2-2000000000000000000000000
χ292222-222-22222-2-2-2-2-2-22-22-22200000000000002-20002-2000000000000
χ302222-222-22222-2-2-2-2-2-22-22-2220000000000000-22000-22000000000000
χ312222-222-222-2-222-2-2-22-22-222-2000000000022-20000-200000000000000
χ322222-222-222-2-222-2-2-22-22-222-20000000000-2-220000200000000000000
χ332222-222-2-2-222-2-2-2222-222-2-2-2000000000000000000002i−2i2i−2i00000000
χ342222-222-2-2-222-2-2-2222-222-2-2-200000000000000000000−2i2i−2i2i00000000
χ352222-222-2-2-2-2-222-222-22-2-22-22000000002200000-2-2000000000000000
χ362222-222-2-2-2-2-222-222-22-2-22-2200000000-2-20000022000000000000000
χ372222-2-2-2-22222-2-222-222-2-22-2-2000000000000000000002i−2i−2i2i00000000
χ382222-2-2-2-22222-2-222-222-2-22-2-200000000000000000000−2i2i2i−2i00000000
χ392222-2-2-2-222-2-22222-2-2-222-2-22000000002-200000-22000000000000000
χ402222-2-2-2-222-2-22222-2-2-222-2-2200000000-22000002-2000000000000000
χ412222-2-2-2-2-2-222-2-22-22-2-22-222200000000000002-2000-22000000000000
χ422222-2-2-2-2-2-222-2-22-22-2-22-22220000000000000-220002-2000000000000
χ432222-2-2-2-2-2-2-2-2222-2222-22-22-200000000002-220000-200000000000000
χ442222-2-2-2-2-2-2-2-2222-2222-22-22-20000000000-22-20000200000000000000
χ454-4-44400-4004-44-400000000002i2−2i22i2−2i20000000000000000000000000000
χ464-4-44400-4004-44-40000000000−2i22i2−2i22i20000000000000000000000000000
χ474-4-44400-400-44-4400000000002i2−2i2−2i22i20000000000000000000000000000
χ484-4-44400-400-44-440000000000−2i22i22i2−2i20000000000000000000000000000
χ494-4-44-4004004-4-440000000000000022−2222−22000000000000000000000000
χ504-4-44-4004004-4-4400000000000000−2222−2222000000000000000000000000
χ514-4-44-400400-444-40000000000000022−22−2222000000000000000000000000
χ524-4-44-400400-444-400000000000000−222222−22000000000000000000000000
χ5388-8-808-80000000000000000000000000000000000000000000000000
χ5488-8-80-880000000000000000000000000000000000000000000000000
χ558-88-800008i−8i0000000000000000000000000000000000000000000000
χ568-88-80000−8i8i0000000000000000000000000000000000000000000000

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