Finite Group Databasebeta

← Group #401621

Character table — Group #401621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111112222222222224444444444444444444488888888888888888816161616161616161616161616161616
order12222222222244444444222222444444888888882224448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ5111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-111-1-1-1-111111111111-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-111-1-1-1-111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-20000220000-2-200000000200-200002i2i−2i−2i002i2i−2i−2i0000000000000000
χ18222222222222-2-2-2-2-2-2-2-20000220000-2-200000000200-20000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000-2-200002200000000-200200002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000-2-200002200000000-20020000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2122222222-2-2-2-222-2-2-222-200002200002222222222-200-200-2-20000-2-200000000000000000000
χ2222222222-2-2-2-222-2-2-222-2000022000022-2-2-2-2-2-2-2-2-200-2002200002200000000000000000000
χ2322222222-2-2-2-222-2-2-222-20000-2-20000-2-22222-2-2-2-2200200-2-200002200000000000000000000
χ2422222222-2-2-2-222-2-2-222-20000-2-20000-2-2-2-2-2-22222200200220000-2-200000000000000000000
χ2522222222-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-200000000-2222-2-20000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-222000000002-2-2-2220000000000000000000000000000
χ2722222222-2-2-2-2-2-2222-2-22-2-2-2-2222222-2-200000000-2-2-22220000000000000000000000000000
χ2822222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-222222200000000222-2-2-20000000000000000000000000000
χ2922-22-2-2-2222-2-22-222-22-2-222-2-20022-2-200000000000000000000000000000000002i−2i0000002i−2i
χ3022-22-2-2-2222-2-22-222-22-2-222-2-20022-2-20000000000000000000000000000000000−2i2i000000−2i2i
χ3122-22-2-2-2222-2-22-222-22-2-2-2-22200-2-22200000000000000000000000000000000002i−2i000000−2i2i
χ3222-22-2-2-2222-2-22-222-22-2-2-2-22200-2-2220000000000000000000000000000000000−2i2i0000002i−2i
χ3322-22-2-2-22-2-222-2222-2-22-222-2-200-2-222000000000000000000000000000000002i−2i00002i−2i0000
χ3422-22-2-2-22-2-222-2222-2-22-222-2-200-2-22200000000000000000000000000000000−2i2i0000−2i2i0000
χ3522-22-2-2-22-2-222-2222-2-22-2-2-2220022-2-2000000000000000000000000000000002i−2i0000−2i2i0000
χ3622-22-2-2-22-2-222-2222-2-22-2-2-2220022-2-200000000000000000000000000000000−2i2i00002i−2i0000
χ372-22-22-2-222-22-22-22-22-22-22-22-2002-22-200000000000000000000000000002i−2i0000002i−2i000000
χ382-22-22-2-222-22-22-22-22-22-22-22-2002-22-20000000000000000000000000000−2i2i000000−2i2i000000
χ392-22-22-2-222-22-22-22-22-22-2-22-2200-22-2200000000000000000000000000002i−2i000000−2i2i000000
χ402-22-22-2-222-22-22-22-22-22-2-22-2200-22-220000000000000000000000000000−2i2i0000002i−2i000000
χ412-22-22-2-22-22-22-222-222-2-22-22-200-22-220000000000000000000000000000002i−2i000000002i−2i00
χ422-22-22-2-22-22-22-222-222-2-22-22-200-22-22000000000000000000000000000000−2i2i00000000−2i2i00
χ432-22-22-2-22-22-22-222-222-2-2-22-22002-22-20000000000000000000000000000002i−2i00000000−2i2i00
χ442-22-22-2-22-22-22-222-222-2-2-22-22002-22-2000000000000000000000000000000−2i2i000000002i−2i00
χ452-2-2-2-22222-2-22222-2-2-2-222-2-22002-2-220000002i2i−2i−2i0000000000002i−2i2i−2i2i−2i0000000000000000
χ462-2-2-2-22222-2-22222-2-2-2-222-2-22002-2-22000000−2i−2i2i2i000000000000−2i2i−2i2i−2i2i0000000000000000
χ472-2-2-2-22222-2-22222-2-2-2-22-222-200-222-20000002i2i−2i−2i0000000000002i−2i−2i2i−2i2i0000000000000000
χ482-2-2-2-22222-2-22222-2-2-2-22-222-200-222-2000000−2i−2i2i2i000000000000−2i2i2i−2i2i−2i0000000000000000
χ492-2-2-2-22222-2-22-2-2-22222-200000000000022-2-2000002-202-22-20000002-2-220000000000000000
χ502-2-2-2-22222-2-22-2-2-22222-200000000000022-2-200000-220-222-2000000-222-20000000000000000
χ512-2-2-2-22222-2-22-2-2-22222-2000000000000-2-222000002-202-2-22000000-222-20000000000000000
χ522-2-2-2-22222-2-22-2-2-22222-2000000000000-2-22200000-220-22-220000002-2-220000000000000000
χ532-2-2-2-2222-222-222-222-2-2-200000000000000002i2i−2i−2i02-20-22002i−2i2i−2i−2i2i00000000000000000000
χ542-2-2-2-2222-222-222-222-2-2-200000000000000002i2i−2i−2i0-2202-200−2i2i−2i2i−2i2i00000000000000000000
χ552-2-2-2-2222-222-222-222-2-2-20000000000000000−2i−2i2i2i02-20-2200−2i2i−2i2i2i−2i00000000000000000000
χ562-2-2-2-2222-222-222-222-2-2-20000000000000000−2i−2i2i2i0-2202-2002i−2i2i−2i2i−2i00000000000000000000
χ572-2-2-2-2222-222-2-2-22-2-22222-2-2200-222-20022-2-20000000000-222-2-220000000000000000000000
χ582-2-2-2-2222-222-2-2-22-2-22222-2-2200-222-200-2-22200000000002-2-222-20000000000000000000000
χ592-2-2-2-2222-222-2-2-22-2-2222-222-2002-2-220022-2-20000000000-22-222-20000000000000000000000
χ602-2-2-2-2222-222-2-2-22-2-2222-222-2002-2-2200-2-22200000000002-22-2-220000000000000000000000
χ6144-44-4-4-4444-4-4-44-4-44-444000000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44-4-4444-4-4-444-44000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-400000000000000000000004i−4i2i2−2i22i2−2i222−2222−220000000000000000000000000000000000
χ6444-4-444-4-400000000000000000000004i−4i−2i22i2−2i22i2−2222−22220000000000000000000000000000000000
χ6544-4-444-4-40000000000000000000000−4i4i2i2−2i22i2−2i2−2222−22220000000000000000000000000000000000
χ6644-4-444-4-40000000000000000000000−4i4i−2i22i2−2i22i222−2222−220000000000000000000000000000000000
χ674-444-44-4-400000000000000004-40000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ684-444-44-4-400000000000000004-4000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ694-444-44-4-40000000000000000-440000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ704-444-44-4-40000000000000000-44000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ714-44-44-4-444-44-4-44-44-44-44000000000000000000000000000000000000000000000000000000
χ724-44-44-4-44-44-444-4-44-4-444000000000000000000000000000000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000

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