Finite Group Databasebeta

← Group #397011

Character table — Group #397011

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222244444444444444448888222244444444444444448888888888244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-111-1-111-1-111
χ1722222222-2-2-2-222-22-2-2-222222-2-2-2-200000000000000000000000000000022-2-22-20000000000
χ1822222222-2-2-2-222-22-2-2-222222-2-2-2-2000000000000000000000000000000-2-222-220000000000
χ1922222222-2-2-2-222-22-2-2-22-2-2-2-2222200000000000000000000000000000022-2-2-220000000000
χ2022222222-2-2-2-222-22-2-2-22-2-2-2-22222000000000000000000000000000000-2-2222-20000000000
χ2122222222-2-2-2-2-2-22-2222-2000000002222000022-2-222-2-200000000-2-200000000000000000000
χ2222222222-2-2-2-2-2-22-2222-20000000022220000-2-222-2-22200000000-2-200000000000000000000
χ2322222222-2-2-2-2-2-22-2222-200000000-2-2-2-2000022-2-2-2-222000000002200000000000000000000
χ2422222222-2-2-2-2-2-22-2222-200000000-2-2-2-20000-2-22222-2-2000000002200000000000000000000
χ252222-2-2-2-222-2-22-2-2-222-222i2i−2i−2i2i2i−2i−2i000022-2-200002i−2i2i−2i000000000000000000000000000000
χ262222-2-2-2-222-2-22-2-2-222-222i2i−2i−2i2i2i−2i−2i0000-2-2220000−2i2i−2i2i000000000000000000000000000000
χ272222-2-2-2-222-2-22-2-2-222-22−2i−2i2i2i−2i−2i2i2i000022-2-20000−2i2i−2i2i000000000000000000000000000000
χ282222-2-2-2-222-2-22-2-2-222-22−2i−2i2i2i−2i−2i2i2i0000-2-22200002i−2i2i−2i000000000000000000000000000000
χ292222-2-2-2-2-2-2222-22-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000002i−2i00002-2
χ302222-2-2-2-2-2-2222-22-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000−2i2i0000-22
χ312222-2-2-2-2-2-2222-22-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000002i−2i0000-22
χ322222-2-2-2-2-2-2222-22-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000−2i2i00002-2
χ332222-2-2-2-2-2-222-22-2222-2-2000000000000000000002i−2i−2i2i2i2i−2i−2i00000022-2-20000000000000000
χ342222-2-2-2-2-2-222-22-2222-2-2000000000000000000002i−2i−2i2i−2i−2i2i2i000000-2-2220000000000000000
χ352222-2-2-2-2-2-222-22-2222-2-200000000000000000000−2i2i2i−2i2i2i−2i−2i000000-2-2220000000000000000
χ362222-2-2-2-2-2-222-22-2222-2-200000000000000000000−2i2i2i−2i−2i−2i2i2i00000022-2-20000000000000000
χ372-2-2222-2-22-22-22-2-222-22-22-22-22-22-20000000000000000000000000000000000002i−2i00002i−2i00
χ382-2-2222-2-22-22-22-2-222-22-22-22-22-22-2000000000000000000000000000000000000−2i2i0000−2i2i00
χ392-2-2222-2-22-22-22-2-222-22-2-22-22-22-220000000000000000000000000000000000002i−2i0000−2i2i00
χ402-2-2222-2-22-22-22-2-222-22-2-22-22-22-22000000000000000000000000000000000000−2i2i00002i−2i00
χ412-2-2222-2-22-22-2-222-2-22-220000000000002-22-22i−2i2i−2i000000000000002i−2i2i−2i0000000000000000
χ422-2-2222-2-22-22-2-222-2-22-220000000000002-22-2−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000
χ432-2-2222-2-22-22-2-222-2-22-22000000000000-22-222i−2i2i−2i00000000000000−2i2i−2i2i0000000000000000
χ442-2-2222-2-22-22-2-222-2-22-22000000000000-22-22−2i2i−2i2i000000000000002i−2i2i−2i0000000000000000
χ452-2-2222-2-2-22-222-222-22-2-22-22-2-22-22000000002i−2i−2i2i00002i−2i2i−2i00000000000000000000000000
χ462-2-2222-2-2-22-222-222-22-2-22-22-2-22-2200000000−2i2i2i−2i0000−2i2i−2i2i00000000000000000000000000
χ472-2-2222-2-2-22-222-222-22-2-2-22-222-22-2000000002i−2i−2i2i0000−2i2i−2i2i00000000000000000000000000
χ482-2-2222-2-2-22-222-222-22-2-2-22-222-22-200000000−2i2i2i−2i00002i−2i2i−2i00000000000000000000000000
χ492-2-22-2-2222-2-22222-22-2-2-22i−2i−2i2i2i−2i−2i2i0000000000000000000022-2-200000000000000002i−2i0000
χ502-2-22-2-2222-2-22222-22-2-2-22i−2i−2i2i2i−2i−2i2i00000000000000000000-2-2220000000000000000−2i2i0000
χ512-2-22-2-2222-2-22222-22-2-2-2−2i2i2i−2i−2i2i2i−2i0000000000000000000022-2-20000000000000000−2i2i0000
χ522-2-22-2-2222-2-22222-22-2-2-2−2i2i2i−2i−2i2i2i−2i00000000000000000000-2-22200000000000000002i−2i0000
χ532-2-22-2-2222-2-22-2-2-22-22220000000022-2-22-2-22000000002-2-2200002-200000000000000000000
χ542-2-22-2-2222-2-22-2-2-22-22220000000022-2-2-222-200000000-222-200002-200000000000000000000
χ552-2-22-2-2222-2-22-2-2-22-222200000000-2-2222-2-2200000000-222-20000-2200000000000000000000
χ562-2-22-2-2222-2-22-2-2-22-222200000000-2-222-222-2000000002-2-220000-2200000000000000000000
χ572-2-22-2-222-222-222-2-2-222-22i−2i−2i2i−2i2i2i−2i22-2-200000000000000000000-22−2i2i2i−2i0000000000000000
χ582-2-22-2-222-222-222-2-2-222-22i−2i−2i2i−2i2i2i−2i-2-222000000000000000000002-22i−2i−2i2i0000000000000000
χ592-2-22-2-222-222-222-2-2-222-2−2i2i2i−2i2i−2i−2i2i22-2-200000000000000000000-222i−2i−2i2i0000000000000000
χ602-2-22-2-222-222-222-2-2-222-2−2i2i2i−2i2i−2i−2i2i-2-222000000000000000000002-2−2i2i2i−2i0000000000000000
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000000000
χ6344-4-44-44-40000000000000000000022−2222−2200000000000000002i−2i2i−2i000000002i2−2i2000000000000
χ6444-4-44-44-40000000000000000000022−2222−220000000000000000−2i2i−2i2i00000000−2i22i2000000000000
χ6544-4-44-44-400000000000000000000−2222−222200000000000000002i−2i2i−2i00000000−2i22i2000000000000
χ6644-4-44-44-400000000000000000000−2222−22220000000000000000−2i2i−2i2i000000002i2−2i2000000000000
χ674-44-4-444-40000000000000000000022−22−222200000000000000002i−2i−2i2i0000002i2−2i200000000000000
χ684-44-4-444-40000000000000000000022−22−22220000000000000000−2i2i2i−2i000000−2i22i200000000000000
χ694-44-4-444-400000000000000000000−222222−2200000000000000002i−2i−2i2i000000−2i22i200000000000000
χ704-44-4-444-400000000000000000000−222222−220000000000000000−2i2i2i−2i0000002i2−2i200000000000000
χ714-4-4444-4-4-44-44-44-4-44-444000000000000000000000000000000000000000000000000000000
χ724-4-44-4-444-444-4-4-4444-4-44000000000000000000000000000000000000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000

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