Finite Group Databasebeta

← Group #408530

Character table — Group #408530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1-1-1-1-11111
χ9111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-111
χ10111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-111-1-111111-1-1
χ11111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-1-1-111-1-111
χ12111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1111-1-111-1-1
χ13111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1111-1-1-1-1-11111-1-1
χ14111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-1-1-111111-1-1-1-111
χ15111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-1-111111-1-1-111-1-1
χ16111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1111-1-111
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i
χ20222222222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i
χ2122222222-2-2-2-222222-2-2-2-222-2-2-2-22-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-2-2-222222-2-2-2-222-2-2-2-22-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-22222-22222-2-22222-2-2-2-2-2000000000000000000000000000000002200-20000-2000000
χ2422222222-2-2-2-22222-22222-2-22222-2-2-2-2-200000000000000000000000000000000-2-200200002000000
χ2522222222-2-2-2-2-2-2-2-22222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-22222000000000000000000000000000000002-200-200002000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2222200000000000000000000000000000000-220020000-2000000
χ2922-22-22-2-222-2-20000-200002-222-2-2200002i2i−2i−2i2i2i−2i−2i0000000000002i2i−2i−2i000022-2-20000000000000000
χ3022-22-22-2-222-2-20000-200002-222-2-2200002i2i−2i−2i2i2i−2i−2i000000000000−2i−2i2i2i0000-2-2220000000000000000
χ3122-22-22-2-222-2-20000-200002-222-2-220000−2i−2i2i2i−2i−2i2i2i0000000000002i2i−2i−2i0000-2-2220000000000000000
χ3222-22-22-2-222-2-20000-200002-222-2-220000−2i−2i2i2i−2i−2i2i2i000000000000−2i−2i2i2i000022-2-20000000000000000
χ3322-22-22-2-2-2-2220000-200002-2-2-222200002i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i000022-2-200000000000000000000
χ3422-22-22-2-2-2-2220000-200002-2-2-222200002i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i0000-2-22200000000000000000000
χ3522-22-22-2-2-2-2220000-200002-2-2-22220000−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i0000-2-22200000000000000000000
χ3622-22-22-2-2-2-2220000-200002-2-2-22220000−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i000022-2-200000000000000000000
χ372-22-2-222-22-22-22i2i−2i−2i22i2i−2i−2i-2-22-22-222i−2i2i−2i0000000000000000000000000000000000000002-202i−2i0000
χ382-22-2-222-22-22-22i2i−2i−2i22i2i−2i−2i-2-22-22-222i−2i2i−2i000000000000000000000000000000000000000-220−2i2i0000
χ392-22-2-222-22-22-22i2i−2i−2i-2−2i−2i2i2i22-22-22-22i−2i−2i2i00000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ402-22-2-222-22-22-22i2i−2i−2i-2−2i−2i2i2i22-22-22-22i−2i−2i2i0000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ412-22-2-222-22-22-2−2i−2i2i2i2−2i−2i2i2i-2-22-22-22−2i2i−2i2i0000000000000000000000000000000000000002-20−2i2i0000
χ422-22-2-222-22-22-2−2i−2i2i2i2−2i−2i2i2i-2-22-22-22−2i2i−2i2i000000000000000000000000000000000000000-2202i−2i0000
χ432-22-2-222-22-22-2−2i−2i2i2i-22i2i−2i−2i22-22-22-2−2i2i2i−2i00000000000000002i−2i2i−2i-22-22000000000000000000000000
χ442-22-2-222-22-22-2−2i−2i2i2i-22i2i−2i−2i22-22-22-2−2i2i2i−2i0000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ452-22-2-222-2-22-222i2i−2i−2i2−2i−2i2i2i-2-2-22-222−2i2i2i−2i00000000000000000000000000000000002i−2i02-2000000000
χ462-22-2-222-2-22-222i2i−2i−2i2−2i−2i2i2i-2-2-22-222−2i2i2i−2i0000000000000000000000000000000000−2i2i0-22000000000
χ472-22-2-222-2-22-222i2i−2i−2i-22i2i−2i−2i222-22-2-2−2i2i−2i2i0000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ482-22-2-222-2-22-222i2i−2i−2i-22i2i−2i−2i222-22-2-2−2i2i−2i2i000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ492-22-2-222-2-22-22−2i−2i2i2i22i2i−2i−2i-2-2-22-2222i−2i−2i2i00000000000000000000000000000000002i−2i0-22000000000
χ502-22-2-222-2-22-22−2i−2i2i2i22i2i−2i−2i-2-2-22-2222i−2i−2i2i0000000000000000000000000000000000−2i2i02-2000000000
χ512-22-2-222-2-22-22−2i−2i2i2i-2−2i−2i2i2i222-22-2-22i−2i2i−2i0000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ522-22-2-222-2-22-22−2i−2i2i2i-2−2i−2i2i2i222-22-2-22i−2i2i−2i000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ532-2-2-222-222-2-220000200002-2-222-2-20000000000002i2i−2i−2i2i2i−2i−2i00002i−2i−2i2i2-2-2200000000000000000000
χ542-2-2-222-222-2-220000200002-2-222-2-20000000000002i2i−2i−2i2i2i−2i−2i0000−2i2i2i−2i-222-200000000000000000000
χ552-2-2-222-222-2-220000200002-2-222-2-2000000000000−2i−2i2i2i−2i−2i2i2i00002i−2i−2i2i-222-200000000000000000000
χ562-2-2-222-222-2-220000200002-2-222-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000−2i2i2i−2i2-2-2200000000000000000000
χ572-2-2-222-22-222-20000200002-22-2-22-20000000000002i2i−2i−2i−2i−2i2i2i2-2-22000000002i−2i−2i2i0000000000000000
χ582-2-2-222-22-222-20000200002-22-2-22-20000000000002i2i−2i−2i−2i−2i2i2i-222-200000000−2i2i2i−2i0000000000000000
χ592-2-2-222-22-222-20000200002-22-2-22-2000000000000−2i−2i2i2i2i2i−2i−2i2-2-2200000000−2i2i2i−2i0000000000000000
χ602-2-2-222-22-222-20000200002-22-2-22-2000000000000−2i−2i2i2i2i2i−2i−2i-222-2000000002i−2i−2i2i0000000000000000
χ61444-44-4-4-400004-44-40000000000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ62444-44-4-4-400004-44-400000000000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ63444-44-4-4-40000-44-440000000000000000000022−2222−220000−2222−222200000000000000000000000000000000
χ64444-44-4-4-40000-44-4400000000000000000000−2222−2222000022−2222−2200000000000000000000000000000000
χ6544-44-44-4-444-4-4000040000-44-4-444-40000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-4-444000040000-4444-4-4-40000000000000000000000000000000000000000000000000000
χ6744-4-4-4-4440000000004-44-40000000000000002i2−2i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ6844-4-4-4-4440000000004-44-4000000000000000−2i22i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ6944-4-4-4-444000000000-44-440000000000000002i2−2i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ7044-4-4-4-444000000000-44-44000000000000000−2i22i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ714-444-4-4-4400004i−4i−4i4i00000000000000002i2−2i22i2−2i2000022−22−2222000000000000000000000000000000000000
χ724-444-4-4-4400004i−4i−4i4i0000000000000000−2i22i2−2i22i20000−222222−22000000000000000000000000000000000000
χ734-444-4-4-440000−4i4i4i−4i00000000000000002i2−2i22i2−2i20000−222222−22000000000000000000000000000000000000
χ744-444-4-4-440000−4i4i4i−4i0000000000000000−2i22i2−2i22i2000022−22−2222000000000000000000000000000000000000
χ754-4-444-44-40000000004i−4i−4i4i0000000000022−22−222200000000−2i22i22i2−2i200000000000000000000000000000000
χ764-4-444-44-40000000004i−4i−4i4i00000000000−222222−22000000002i2−2i2−2i22i200000000000000000000000000000000
χ774-4-444-44-4000000000−4i4i4i−4i0000000000022−22−2222000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-4-444-44-4000000000−4i4i4i−4i00000000000−222222−2200000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-4-444-444-4-440000-40000-444-4-4440000000000000000000000000000000000000000000000000000
χ804-4-4-444-44-444-40000-40000-44-444-440000000000000000000000000000000000000000000000000000

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