Finite Group Databasebeta

← Group #396597

Character table — Group #396597

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111112222222222224444444444444444444488888888888888888816161616161616161616161616161616
order12222222222244444444222244444444888888884444448888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-20000000022-2-2000000002-20000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ18222222222222-2-2-2-2-2-2-2-20000000022-2-2000000002-2000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2-2-2-2-200000000-2-22200000000-220000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-200000000-2-22200000000-22000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2122222222-2-2-2-222-2-2-222-200000000222222222222-2-20000-2-20000-2-200000000000000000000
χ2222222222-2-2-2-222-2-2-222-2000000002222-2-2-2-2-2-2-2-2-2-200002200002200000000000000000000
χ2322222222-2-2-2-222-2-2-222-200000000-2-2-2-22222-2-2-2-2220000-2-200002200000000000000000000
χ2422222222-2-2-2-222-2-2-222-200000000-2-2-2-2-2-2-2-22222220000220000-2-200000000000000000000
χ2522222222-2-2-2-2-2-2222-2-222222-2-2-2-222-2-200000000-2222-2-20000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-222222-2-2-2-2-2-222000000002-2-2-2220000000000000000000000000000
χ2722222222-2-2-2-2-2-2222-2-22-2-2-2-2222222-2-200000000-22-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2222-2-22-2-2-2-22222-2-222000000002-222-2-20000000000000000000000000000
χ2922-222-2-2-222-2-22-22-2-22-2200000000000000002i2i−2i−2i002i−2i2i−2i002-22-22i−2i00000000000000000000
χ3022-222-2-2-222-2-22-22-2-22-2200000000000000002i2i−2i−2i00−2i2i−2i2i00-22-222i−2i00000000000000000000
χ3122-222-2-2-222-2-22-22-2-22-220000000000000000−2i−2i2i2i002i−2i2i−2i00-22-22−2i2i00000000000000000000
χ3222-222-2-2-222-2-22-22-2-22-220000000000000000−2i−2i2i2i00−2i2i−2i2i002-22-2−2i2i00000000000000000000
χ3322-222-2-2-222-2-2-22-222-22-222-2-222-2-200002i2i−2i−2i00000000002i−2i2i−2i−2i2i0000000000000000000000
χ3422-222-2-2-222-2-2-22-222-22-222-2-222-2-20000−2i−2i2i2i0000000000−2i2i−2i2i2i−2i0000000000000000000000
χ3522-222-2-2-222-2-2-22-222-22-2-2-222-2-22200002i2i−2i−2i00000000002i−2i−2i2i2i−2i0000000000000000000000
χ3622-222-2-2-222-2-2-22-222-22-2-2-222-2-2220000−2i−2i2i2i0000000000−2i2i2i−2i−2i2i0000000000000000000000
χ3722-222-2-2-2-2-2222-2-2222-2-222-2-2-2-222000000002i2i−2i−2i000000000000−2i2i2i−2i2i−2i0000000000000000
χ3822-222-2-2-2-2-2222-2-2222-2-222-2-2-2-22200000000−2i−2i2i2i0000000000002i−2i−2i2i−2i2i0000000000000000
χ3922-222-2-2-2-2-2222-2-2222-2-2-2-22222-2-2000000002i2i−2i−2i000000000000−2i2i−2i2i−2i2i0000000000000000
χ4022-222-2-2-2-2-2222-2-2222-2-2-2-22222-2-200000000−2i−2i2i2i0000000000002i−2i2i−2i2i−2i0000000000000000
χ4122-222-2-2-2-2-222-222-2-2-2220000000000002i2i−2i−2i0000002i−2i−2i2i−2i2i000000-222-20000000000000000
χ4222-222-2-2-2-2-222-222-2-2-2220000000000002i2i−2i−2i000000−2i2i2i−2i−2i2i0000002-2-220000000000000000
χ4322-222-2-2-2-2-222-222-2-2-222000000000000−2i−2i2i2i0000002i−2i−2i2i2i−2i0000002-2-220000000000000000
χ4422-222-2-2-2-2-222-222-2-2-222000000000000−2i−2i2i2i000000−2i2i2i−2i2i−2i000000-222-20000000000000000
χ452-222-2-2-222-22-222-22-2-2-222-22-22-22-2000000000000000000000000000000002i−2i0000002i−2i0000
χ462-222-2-2-222-22-222-22-2-2-222-22-22-22-200000000000000000000000000000000−2i2i000000−2i2i0000
χ472-222-2-2-222-22-222-22-2-2-22-22-22-22-22000000000000000000000000000000002i−2i000000−2i2i0000
χ482-222-2-2-222-22-222-22-2-2-22-22-22-22-2200000000000000000000000000000000−2i2i0000002i−2i0000
χ492-222-2-2-22-22-22-2-2-22-22222-22-2-22-220000000000000000000000000000002-20000002-2000000
χ502-222-2-2-22-22-22-2-2-22-22222-22-2-22-22000000000000000000000000000000-22000000-22000000
χ512-222-2-2-22-22-22-2-2-22-2222-22-222-22-20000000000000000000000000000002-2000000-22000000
χ522-222-2-2-22-22-22-2-2-22-2222-22-222-22-2000000000000000000000000000000-220000002-2000000
χ532-2-22-222-22-2-22-2222-22-2-22-2-222-2-220000000000000000000000000000000000002i−2i0000002i−2i
χ542-2-22-222-22-2-22-2222-22-2-22-2-222-2-22000000000000000000000000000000000000−2i2i000000−2i2i
χ552-2-22-222-22-2-22-2222-22-2-2-222-2-222-20000000000000000000000000000000000002i−2i000000−2i2i
χ562-2-22-222-22-2-22-2222-22-2-2-222-2-222-2000000000000000000000000000000000000−2i2i0000002i−2i
χ572-2-22-222-2-222-22-222-2-22-22-2-22-222-200000000000000000000000000000000002i−2i0000002i−2i00
χ582-2-22-222-2-222-22-222-2-22-22-2-22-222-20000000000000000000000000000000000−2i2i000000−2i2i00
χ592-2-22-222-2-222-22-222-2-22-2-222-22-2-2200000000000000000000000000000000002i−2i000000−2i2i00
χ602-2-22-222-2-222-22-222-2-22-2-222-22-2-220000000000000000000000000000000000−2i2i0000002i−2i00
χ614-444-4-4-444-44-4-4-44-4444-4000000000000000000000000000000000000000000000000000000
χ624-444-4-4-44-44-44444-44-4-4-4000000000000000000000000000000000000000000000000000000
χ634-44-444-4-400000000000000000000004-42i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000
χ644-44-444-4-400000000000000000000004-4−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000
χ654-44-444-4-40000000000000000000000-442i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ664-44-444-4-40000000000000000000000-44−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ674-4-44-444-44-4-444-4-4-44-444000000000000000000000000000000000000000000000000000000
χ684-4-44-444-4-444-4-44-4-444-44000000000000000000000000000000000000000000000000000000
χ694-4-4-44-444000000000000000000004-40022−22−222222−22−22220000000000000000000000000000000000
χ704-4-4-44-444000000000000000000004-400−222222−22−222222−220000000000000000000000000000000000
χ714-4-4-44-44400000000000000000000-440022−22−2222−222222−220000000000000000000000000000000000
χ724-4-4-44-44400000000000000000000-4400−222222−2222−22−22220000000000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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