Finite Group Databasebeta

← Group #242124

Character table — Group #242124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888822444444888888882444444444448888
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
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-111111-1-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1111-1-111
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-1-11111-1-1
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111111-1-1-1-111
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1111-1-1-111-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1111-1-111-1-1-1-1-111
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1-1-111-1-111111-1-1
χ1722222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000002-200-200002000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000-220020000-2000000
χ192222222222-2-2-2-2-2-22222222222-2-2-2-2-2-2000000000000000000000000000000002200-20000-2000000
χ202222222222-2-2-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000000000-2-200200002000000
χ2122222222-2-2222222-2-2-2-22222-2-222-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2222222222-2-2222222-2-2-2-22222-2-222-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2322222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000002-202-2000000000
χ2422222222-2-22222-2-22222-2-2-2-2-2-2-2-2-2-2220000000000000000000000000000000000-220-22000000000
χ2522222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-20000000000000000-2-222-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000002-20-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000-2202-2000000000
χ2922-2-2-222-2002i2i−2i−2i2-200002i2i−2i−2i002-200002222−2−2−2−2i2i2i2i2−i2−i2−i2−i22-200002i−2i22−2−2i2i2−i2−i20000000000000000
χ3022-2-2-222-2002i2i−2i−2i2-200002i2i−2i−2i002-200002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2-220000−2i2i−2−222−i2−i2i2i20000000000000000
χ3122-2-2-222-2002i2i−2i−2i2-200002i2i−2i−2i002-20000−2−2−2−22222−i2−i2−i2−i2i2i2i2i22-200002i−2i−2−222−i2−i2i2i20000000000000000
χ3222-2-2-222-2002i2i−2i−2i2-200002i2i−2i−2i002-20000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2-220000−2i2i22−2−2i2i2−i2−i20000000000000000
χ3322-2-2-222-200−2i−2i2i2i2-20000−2i−2i2i2i002-200002222−2−2−2−2−i2−i2−i2−i2i2i2i2i22-20000−2i2i22−2−2−i2−i2i2i20000000000000000
χ3422-2-2-222-200−2i−2i2i2i2-20000−2i−2i2i2i002-200002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2-2200002i−2i−2−222i2i2−i2−i20000000000000000
χ3522-2-2-222-200−2i−2i2i2i2-20000−2i−2i2i2i002-20000−2−2−2−22222i2i2i2i2−i2−i2−i2−i22-20000−2i2i−2−222i2i2−i2−i20000000000000000
χ3622-2-2-222-200−2i−2i2i2i2-20000−2i−2i2i2i002-20000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2-2200002i−2i22−2−2−i2−i2i2i20000000000000000
χ372-22-222-2-22-22i−2i2i−2i2-22i2i−2i−2i2i−2i2i−2i2-2-222i−2i2-20000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ382-22-222-2-22-22i−2i2i−2i2-22i2i−2i−2i2i−2i2i−2i2-2-222i−2i2-2000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ392-22-222-2-22-22i−2i2i−2i-22−2i−2i2i2i−2i2i−2i2i2-22-22i−2i-220000000000000000000000000000000000000002-202i−2i0000
χ402-22-222-2-22-22i−2i2i−2i-22−2i−2i2i2i−2i2i−2i2i2-22-22i−2i-22000000000000000000000000000000000000000-220−2i2i0000
χ412-22-222-2-22-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i−2i2i2-2-22−2i2i2-20000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ422-22-222-2-22-2−2i2i−2i2i2-2−2i−2i2i2i−2i2i−2i2i2-2-22−2i2i2-2000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ432-22-222-2-22-2−2i2i−2i2i-222i2i−2i−2i2i−2i2i−2i2-22-2−2i2i-220000000000000000000000000000000000000002-20−2i2i0000
χ442-22-222-2-22-2−2i2i−2i2i-222i2i−2i−2i2i−2i2i−2i2-22-2−2i2i-22000000000000000000000000000000000000000-2202i−2i0000
χ452-22-222-2-2-222i−2i2i−2i2-2−2i−2i2i2i2i−2i2i−2i-22-22−2i2i-222i2i−2i−2i2i2i−2i−2i22-2-222-2-200000000000000000000000000000000
χ462-22-222-2-2-222i−2i2i−2i2-2−2i−2i2i2i2i−2i2i−2i-22-22−2i2i-22−2i−2i2i2i−2i−2i2i2i-2-222-2-22200000000000000000000000000000000
χ472-22-222-2-2-222i−2i2i−2i-222i2i−2i−2i−2i2i−2i2i-222-2−2i2i2-2000000000000000000000000000000000000000000002-22i−2i
χ482-22-222-2-2-222i−2i2i−2i-222i2i−2i−2i−2i2i−2i2i-222-2−2i2i2-200000000000000000000000000000000000000000000-22−2i2i
χ492-22-222-2-2-22−2i2i−2i2i2-22i2i−2i−2i−2i2i−2i2i-22-222i−2i-222i2i−2i−2i2i2i−2i−2i-2-222-2-22200000000000000000000000000000000
χ502-22-222-2-2-22−2i2i−2i2i2-22i2i−2i−2i−2i2i−2i2i-22-222i−2i-22−2i−2i2i2i−2i−2i2i2i22-2-222-2-200000000000000000000000000000000
χ512-22-222-2-2-22−2i2i−2i2i-22−2i−2i2i2i2i−2i2i−2i-222-22i−2i2-2000000000000000000000000000000000000000000002-2−2i2i
χ522-22-222-2-2-22−2i2i−2i2i-22−2i−2i2i2i2i−2i2i−2i-222-22i−2i2-200000000000000000000000000000000000000000000-222i−2i
χ532-2-22-22-22002-2-222200002-2-2200-2-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2002i−2i2i−2i002−2−222−2−220000000000000000
χ542-2-22-22-22002-2-222200002-2-2200-2-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200−2i2i−2i2i00−222−2−222−20000000000000000
χ552-2-22-22-22002-2-222200002-2-2200-2-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2002i−2i2i−2i00−222−2−222−20000000000000000
χ562-2-22-22-22002-2-222200002-2-2200-2-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200−2i2i−2i2i002−2−222−2−220000000000000000
χ572-2-22-22-2200-222-2220000-222-200-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2002i−2i−2i2i002−2−22−222−20000000000000000
χ582-2-22-22-2200-222-2220000-222-200-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200−2i2i2i−2i00−222−22−2−220000000000000000
χ592-2-22-22-2200-222-2220000-222-200-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2002i−2i−2i2i00−222−22−2−220000000000000000
χ602-2-22-22-2200-222-2220000-222-200-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200−2i2i2i−2i002−2−22−222−20000000000000000
χ614444-4-4-4-44-400000000000000-440000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ624444-4-4-4-44-400000000000000-4400000000000000−2222−2222−2222−222200000000000000000000000000000000
χ634444-4-4-4-4-44000000000000004-400000022−2222−2222−2222−220000000000000000000000000000000000000000
χ644444-4-4-4-4-44000000000000004-4000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ6544-4-44-4-44000000004i−4i4i−4i0000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6644-4-44-4-44000000004i−4i4i−4i000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-44-4-4400000000−4i4i−4i4i0000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6844-4-44-4-4400000000−4i4i−4i4i000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6944-4-4-444-4004i4i−4i−4i-440000−4i−4i4i4i00-440000000000000000000000000000000000000000000000000000
χ7044-4-4-444-400−4i−4i4i4i-4400004i4i−4i−4i00-440000000000000000000000000000000000000000000000000000
χ714-44-4-4-4444400000000000000-4-40000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ724-44-4-4-4444400000000000000-4-4000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ734-44-4-4-444-4-400000000000000440000000000000022−22−222222−22−222200000000000000000000000000000000
χ744-44-4-4-444-4-4000000000000004400000000000000−222222−22−222222−2200000000000000000000000000000000
χ754-4-444-44-4000000004-4-440000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ764-4-444-44-4000000004-4-44000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ774-4-444-44-400000000-444-40000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ784-4-444-44-400000000-444-4000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ794-4-44-44-44004-4-44-4-40000-444-400440000000000000000000000000000000000000000000000000000
χ804-4-44-44-4400-444-4-4-400004-4-4400440000000000000000000000000000000000000000000000000000

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