Finite Group Databasebeta

← Group #400690

Character table — Group #400690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888822224444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2122222222-2-2-2-222-2-22-2-222222222222-2-222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ2222222222-2-2-2-222-2-22-2-2222222222-2-222-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2322222222-2-2-2-222-2-22-2-22-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-22-2-22-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-222-20000000022-2-2-2-2220000000000002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-222-222-20000000022-2-2-2-222000000000000-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-2-2-222-222-200000000-2-22222-2-200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-222-222-200000000-2-22222-2-2000000000000-2-22222-2-2000000000000000000000000
χ2922-2-22-2-2222-2-22-222-2-2-222222-2-2-2-2000000000000000022-2-200000000000000002i−2i002i−2i0000000000
χ3022-2-22-2-2222-2-22-222-2-2-222222-2-2-2-2000000000000000022-2-20000000000000000−2i2i00−2i2i0000000000
χ3122-2-22-2-2222-2-22-222-2-2-22-2-2-2-222220000000000000000-2-22200000000000000002i−2i00−2i2i0000000000
χ3222-2-22-2-2222-2-22-222-2-2-22-2-2-2-222220000000000000000-2-2220000000000000000−2i2i002i−2i0000000000
χ3322-2-22-2-22-2-2222-2-2-2-22222222-2-2-2-20000000000000000-2-2220000000000000000002-2002-200000000
χ3422-2-22-2-22-2-2222-2-2-2-22222222-2-2-2-20000000000000000-2-222000000000000000000-2200-2200000000
χ3522-2-22-2-22-2-2222-2-2-2-2222-2-2-2-22222000000000000000022-2-20000000000000000002-200-2200000000
χ3622-2-22-2-22-2-2222-2-2-2-2222-2-2-2-22222000000000000000022-2-2000000000000000000-22002-200000000
χ372-22-2-22-222-22-22-22-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i00000000000000000000000000002-22i−2i
χ382-22-2-22-222-22-22-22-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i0000000000000000000000000000-22−2i2i
χ392-22-2-22-222-22-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i00000000000000000000000000002-2−2i2i
χ402-22-2-22-222-22-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i0000000000000000000000000000-222i−2i
χ412-22-2-22-22-22-222-2-222-22-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i0000000000000000000000002-22i−2i0000
χ422-22-2-22-22-22-222-2-222-22-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i000000000000000000000000-22−2i2i0000
χ432-22-2-22-22-22-222-2-222-22-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i0000000000000000000000002-2−2i2i0000
χ442-22-2-22-22-22-222-2-222-22-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i000000000000000000000000-222i−2i0000
χ452-2-22-2-2222-2-22222-2-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i002-2002-200002i−2i2i−2i0000000000000000
χ462-2-22-2-2222-2-22222-2-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00-2200-220000−2i2i−2i2i0000000000000000
χ472-2-22-2-2222-2-22222-2-2-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i002-2002-20000−2i2i−2i2i0000000000000000
χ482-2-22-2-2222-2-22222-2-2-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00-2200-2200002i−2i2i−2i0000000000000000
χ492-2-22-2-2222-2-22-2-2-2222-22000000000000000022-2-222-2-200002-2002-20000002-2-220000000000000000
χ502-2-22-2-2222-2-22-2-2-2222-22000000000000000022-2-222-2-20000-2200-22000000-222-20000000000000000
χ512-2-22-2-2222-2-22-2-2-2222-220000000000000000-2-222-2-22200002-2002-2000000-222-20000000000000000
χ522-2-22-2-2222-2-22-2-2-2222-220000000000000000-2-222-2-2220000-2200-220000002-2-220000000000000000
χ532-2-22-2-222-222-222-22-22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i2-200-22002i−2i2i−2i00000000000000000000
χ542-2-22-2-222-222-222-22-22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i-22002-200−2i2i−2i2i00000000000000000000
χ552-2-22-2-222-222-222-22-22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i2-200-2200−2i2i−2i2i00000000000000000000
χ562-2-22-2-222-222-222-22-22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i-22002-2002i−2i2i−2i00000000000000000000
χ572-2-22-2-222-222-2-2-22-22-222000000000000000022-2-2-2-2220000002-200-222-2-2200000000000000000000
χ582-2-22-2-222-222-2-2-22-22-222000000000000000022-2-2-2-222000000-22002-2-222-200000000000000000000
χ592-2-22-2-222-222-2-2-22-22-2220000000000000000-2-22222-2-20000002-200-22-222-200000000000000000000
χ602-2-22-2-222-222-2-2-22-22-2220000000000000000-2-22222-2-2000000-22002-22-2-2200000000000000000000
χ614444-4-4-4-400000000000022−2222−2222−2222−224-400000022−2222−220000000000000000000000000000000000000000
χ624444-4-4-4-400000000000022−2222−2222−2222−22-44000000−2222−22220000000000000000000000000000000000000000
χ634444-4-4-4-4000000000000−2222−2222−2222−22224-4000000−2222−22220000000000000000000000000000000000000000
χ644444-4-4-4-4000000000000−2222−2222−2222−2222-4400000022−2222−220000000000000000000000000000000000000000
χ6544-4-44-4-4444-4-4-44-4-4444-4000000000000000000000000000000000000000000000000000000000000
χ6644-4-44-4-44-4-444-44444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6744-4-4-444-400000000000022−2222−22−2222−2222004i−4i000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ6844-4-4-444-400000000000022−2222−22−2222−222200−4i4i00000000−2i22i2−2i22i2000000000000000000000000000000000000
χ6944-4-4-444-4000000000000−2222−222222−2222−22004i−4i00000000−2i22i2−2i22i2000000000000000000000000000000000000
χ7044-4-4-444-4000000000000−2222−222222−2222−2200−4i4i000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ714-44-44-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i20000004-400002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-44-44-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000-440000−2i22i22i2−2i2000000000000000000000000000000000000
χ734-44-44-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i20000004-40000−2i22i22i2−2i2000000000000000000000000000000000000
χ744-44-44-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000-4400002i2−2i2−2i22i2000000000000000000000000000000000000
χ754-44-4-44-444-44-4-44-44-4-444000000000000000000000000000000000000000000000000000000000000
χ764-44-4-44-44-44-44-444-4-44-44000000000000000000000000000000000000000000000000000000000000
χ774-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200004i−4i0022−22−22220000000000000000000000000000000000000000
χ784-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000−4i4i00−222222−220000000000000000000000000000000000000000
χ794-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200004i−4i00−222222−220000000000000000000000000000000000000000
χ804-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000−4i4i0022−22−22220000000000000000000000000000000000000000

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