Finite Group Databasebeta

← Group #307355

Character table — Group #307355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ172222222222-2-222-2-2222222220000-2-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ182222222222-2-222-2-2222222220000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000022-2-200000000-220000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000-2-222000000002-20000000000
χ2122222222-2-222-2-222000000002222-2-200002222-2-2-2-200000000-2-222-2-2000000000000000000000000
χ2222222222-2-222-2-222000000002222-2-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ2322222222-2-222-2-22200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-222000000000000000000000000
χ2422222222-2-222-2-22200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ2522-2-22-22-2002-2002-2i2i2i2i2−i2−i2−i2−i222-2-200i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i200002-20000i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-2-22-22-2002-2002-2i2i2i2i2−i2−i2−i2−i222-2-200i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i20000-220000i2i2−i2−i2−i2−i2i2i2000000000000
χ2722-2-22-22-2002-2002-2i2i2i2i2−i2−i2−i2−i2-2-22200i2i2−i2−i2000022-2-2i2i2i2i2−i2−i2−i2−i20000-220000−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-22-22-2002-2002-2i2i2i2i2−i2−i2−i2−i2-2-22200i2i2−i2−i20000-2-222−i2−i2−i2−i2i2i2i2i200002-20000−i2−i2i2i2i2i2−i2−i2000000000000
χ2922-2-22-22-2002-2002-2−i2−i2−i2−i2i2i2i2i222-2-200−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i200002-20000−i2−i2i2i2−i2−i2i2i2000000000000
χ3022-2-22-22-2002-2002-2−i2−i2−i2−i2i2i2i2i222-2-200−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i20000-220000−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-2-22-22-2002-2002-2−i2−i2−i2−i2i2i2i2i2-2-22200−i2−i2i2i2000022-2-2−i2−i2−i2−i2i2i2i2i20000-220000i2i2−i2−i2i2i2−i2−i2000000000000
χ3222-2-22-22-2002-2002-2−i2−i2−i2−i2i2i2i2i2-2-22200−i2−i2i2i20000-2-222i2i2i2i2−i2−i2−i2−i200002-20000i2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-2-222-2002-200-22i2i2−i2−i2i2i2−i2−i22i−2i2i−2i00i2−i2i2−i22i2i−2i−2i000022−2−222−2−2002-20000002−22−2i2−i2i2−i2000000000000
χ342-22-2-222-2002-200-22i2i2−i2−i2i2i2−i2−i22i−2i2i−2i00i2−i2i2−i2−2i−2i2i2i0000−2−222−2−22200-220000002−22−2−i2i2−i2i2000000000000
χ352-22-2-222-2002-200-22i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00i2−i2i2−i22i2i−2i−2i000022−2−222−2−200-22000000−22−22−i2i2−i2i2000000000000
χ362-22-2-222-2002-200-22i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00i2−i2i2−i2−2i−2i2i2i0000−2−222−2−222002-2000000−22−22i2−i2i2−i2000000000000
χ372-22-2-222-2002-200-22−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00−i2i2−i2i22i2i−2i−2i0000−2−222−2−222002-2000000−22−22−i2i2−i2i2000000000000
χ382-22-2-222-2002-200-22−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00−i2i2−i2i2−2i−2i2i2i000022−2−222−2−200-22000000−22−22i2−i2i2−i2000000000000
χ392-22-2-222-2002-200-22−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i00−i2i2−i2i22i2i−2i−2i0000−2−222−2−22200-220000002−22−2i2−i2i2−i2000000000000
χ402-22-2-222-2002-200-22−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i00−i2i2−i2i2−2i−2i2i2i000022−2−222−2−2002-20000002−22−2−i2i2−i2i2000000000000
χ412-2-2222-2-22-2002-2002-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002i−2i2i−2i000000000000002−22−200
χ422-2-2222-2-22-2002-2002-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000−2i2i−2i2i00000000000000−22−2200
χ432-2-2222-2-22-2002-2002-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002i−2i2i−2i00000000000000−22−2200
χ442-2-2222-2-22-2002-2002-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000−2i2i−2i2i000000000000002−22−200
χ452-2-2222-2-22-2002-200-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002i−2i−2i2i000000000000002−2−2200
χ462-2-2222-2-22-2002-200-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000−2i2i2i−2i00000000000000−222−200
χ472-2-2222-2-22-2002-200-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000002i−2i−2i2i00000000000000−222−200
χ482-2-2222-2-22-2002-200-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000−2i2i2i−2i000000000000002−2−2200
χ492-2-22-2-2222222-2-2-2-222-2-2-2-2222i−2i−2i2i-222-2-2200000000000000002i−2i00000000−2i2i2i−2i0000000000000000
χ502-2-22-2-2222222-2-2-2-222-2-2-2-222−2i2i2i−2i-222-2-220000000000000000−2i2i000000002i−2i−2i2i0000000000000000
χ512-2-22-2-2222222-2-2-2-2-2-22222-2-22i−2i−2i2i-22-222-200000000000000002i−2i000000002i−2i−2i2i0000000000000000
χ522-2-22-2-2222222-2-2-2-2-2-22222-2-2−2i2i2i−2i-22-222-20000000000000000−2i2i00000000−2i2i2i−2i0000000000000000
χ532-2-22-2-22222-2-2-2-22222-2-2-2-22200002-2-222-20000000000000000000000000000000000002i−2i2i−2i000000
χ542-2-22-2-22222-2-2-2-22222-2-2-2-22200002-2-222-2000000000000000000000000000000000000−2i2i−2i2i000000
χ552-2-22-2-22222-2-2-2-222-2-22222-2-200002-22-2-220000000000000000000000000000000000002i−2i−2i2i000000
χ562-2-22-2-22222-2-2-2-222-2-22222-2-200002-22-2-22000000000000000000000000000000000000−2i2i2i−2i000000
χ572-2-22-2-222-2-22222-2-2000000002i−2i−2i2i2-20000000000002i2i−2i−2i−2i−2i2i2i−2i2i000000000000-222-2000000000000
χ582-2-22-2-222-2-22222-2-2000000002i−2i−2i2i2-2000000000000−2i−2i2i2i2i2i−2i−2i−2i2i0000000000002-2-22000000000000
χ592-2-22-2-222-2-22222-2-200000000−2i2i2i−2i2-20000000000002i2i−2i−2i−2i−2i2i2i2i−2i0000000000002-2-22000000000000
χ602-2-22-2-222-2-22222-2-200000000−2i2i2i−2i2-2000000000000−2i−2i2i2i2i2i−2i−2i2i−2i000000000000-222-2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-400-44004-4-44-444-400000000000000000000000000000000000000000000000000000000
χ634444-4-4-4-44-400-4400-444-44-4-4400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-44004-4000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ654444-4-4-4-4-44004-40000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6644-4-44-44-400-4400-442i22i22i22i2−2i2−2i2−2i2−2i2000000−2i2−2i22i22i20000000000000000000000000000000000000000000000
χ6744-4-44-44-400-4400-44−2i2−2i2−2i2−2i22i22i22i22i20000002i22i2−2i2−2i20000000000000000000000000000000000000000000000
χ6844-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000022−22−22220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6944-4-4-44-44000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000−222222−2200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ7044-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000022−22−222200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ7144-4-4-44-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000−222222−220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000002i2−2i2−2i22i2-22-222-22-2000000000000000000000000000000
χ734-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000−2i22i22i2−2i22-22-2-22-22000000000000000000000000000000
χ744-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000002i2−2i2−2i22i22-22-2-22-22000000000000000000000000000000
χ754-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000−2i22i22i2−2i2-22-222-22-2000000000000000000000000000000
χ764-44-4-444-400-44004-42i22i2−2i2−2i22i22i2−2i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ774-44-4-444-400-44004-4−2i2−2i22i22i2−2i2−2i22i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ784-4-4444-4-4-4400-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ794-4-4444-4-4-4400-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ804-4-44-4-444-4-4-4-44444000000000000-4400000000000000000000000000000000000000000000000000

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