Finite Group Databasebeta

← Group #296673

Character table — Group #296673

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ91111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11-1-111-1-111-11
χ111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111-1-1-11111-1-1-11
χ141111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1111-1-1-1-1111-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ17222222222222222222-2-2-222-20000-2-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ18222222222222222222-2-2-222-20000-2-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-222-200002222-2-2000000000000000000000022-2-200000000-220000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-222-200002222-2-20000000000000000000000-2-222000000002-20000000000
χ2122222222-2-22222-2-2-2-2222-2-22222222-2-2-2-2000000000000000022-2-2-2-2000000000000000000000000
χ2222222222-2-22222-2-2-2-2222-2-22-2-2-2-222-2-2-2-20000000000000000-2-22222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-20000-2-222220000000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-22222222-2-222222-2-222-2-20000000000000000-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-22222222-2-22-2-2-2-2-2-222-2-200000000000000002222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-2000022-2-2220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-2000022-2-222000000000000000000000000000000000000-222-2000000
χ29222-2-22-2-22-2000000002-2-22-222i2i−2i−2i00002-2000000002222-2-2-2-2002i−2i00000000002i2i−2i−2i000000000000
χ30222-2-22-2-22-2000000002-2-22-222i2i−2i−2i00002-200000000-2-2-2-22222002i−2i0000000000−2i−2i2i2i000000000000
χ31222-2-22-2-22-2000000002-2-22-22−2i−2i2i2i00002-2000000002222-2-2-2-200−2i2i0000000000−2i−2i2i2i000000000000
χ32222-2-22-2-22-2000000002-2-22-22−2i−2i2i2i00002-200000000-2-2-2-2222200−2i2i00000000002i2i−2i−2i000000000000
χ33222-2-22-2-2-22000000002-2-2-2222i2i−2i−2i0000-222222-2-2-2-20000000000−2i2i0000002i2i−2i−2i0000000000000000
χ34222-2-22-2-2-22000000002-2-2-2222i2i−2i−2i0000-22-2-2-2-222220000000000−2i2i000000−2i−2i2i2i0000000000000000
χ35222-2-22-2-2-22000000002-2-2-222−2i−2i2i2i0000-222222-2-2-2-200000000002i−2i000000−2i−2i2i2i0000000000000000
χ36222-2-22-2-2-22000000002-2-2-222−2i−2i2i2i0000-22-2-2-2-2222200000000002i−2i0000002i2i−2i−2i0000000000000000
χ372-2222-2-2-2-2-222-2-222-2-2000220000000000022−2−222−2−222−2−222−2−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ382-2222-2-2-2-2-222-2-222-2-2000220000000000022−2−222−2−222−2−222−2−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ392-2222-2-2-2-2-222-2-222-2-20002200000000000−2−222−2−222−2−222−2−2220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ402-2222-2-2-2-2-222-2-222-2-20002200000000000−2−222−2−222−2−222−2−222000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ412-2222-2-2-2-2-2-2-222-2-222000220000000000022−2−222−2−2−2−222−2−2220000002i−2i−2i2i00000000000000i2−i2−i2i200
χ422-2222-2-2-2-2-2-2-222-2-222000220000000000022−2−222−2−2−2−222−2−222000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ432-2222-2-2-2-2-2-2-222-2-2220002200000000000−2−222−2−22222−2−222−2−20000002i−2i−2i2i00000000000000−i2i2i2−i200
χ442-2222-2-2-2-2-2-2-222-2-2220002200000000000−2−222−2−22222−2−222−2−2000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ452-2-22-222-20000002-22-222-200-22i−2i2i−2i002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−22−22−2000000000000
χ462-2-22-222-20000002-22-222-200-22i−2i2i−2i002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−22−22−22000000000000
χ472-2-22-222-20000002-22-222-200-2−2i2i−2i2i002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−22−22−22000000000000
χ482-2-22-222-20000002-22-222-200-2−2i2i−2i2i002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−22−22−2000000000000
χ492-2-22-222-2000000-22-2222-200-22i−2i2i−2i00-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−2−22−22000000000000
χ502-2-22-222-2000000-22-2222-200-22i−2i2i−2i00-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−222−22−2000000000000
χ512-2-22-222-2000000-22-2222-200-2−2i2i−2i2i00-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−222−22−2000000000000
χ522-2-22-222-2000000-22-2222-200-2−2i2i−2i2i00-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−2−22−22000000000000
χ532-2-2-222-22002-22-200002-2200-22-2-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22-200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ542-2-2-222-22002-22-200002-2200-22-2-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22-200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ552-2-2-222-22002-22-200002-2200-2-222-22-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2-2200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ562-2-2-222-22002-22-200002-2200-2-222-22-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2-2200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ572-2-2-222-2200-22-2200002-2200-22-2-22-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2-2200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ582-2-2-222-2200-22-2200002-2200-22-2-22-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2-2200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ592-2-2-222-2200-22-2200002-2200-2-222-2-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22-200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ602-2-2-222-2200-22-2200002-2200-2-222-2-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22-200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ61444-4-44-4-44-400000000-4444-4-400000000-440000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4400000000-444-44-4000000004-40000000000000000000000000000000000000000000000
χ6344-44-4-4-440000004-4-4400000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6444-44-4-4-440000004-4-440000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6544-44-4-4-44000000-444-400000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6644-44-4-4-44000000-444-40000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ6744-4-44-44-4004-4-44000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ6844-4-44-44-4004-4-4400000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ6944-4-44-44-400-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ7044-4-44-44-400-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ714-4444-4-4-44444-4-4-4-444000-4-4000000000000000000000000000000000000000000000000000000000
χ724-4444-4-4-444-4-44444-4-4000-4-4000000000000000000000000000000000000000000000000000000000
χ734-44-4-4-4444-400000000000-44000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ744-44-4-4-4444-400000000000-4400000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ754-44-4-4-444-44000000000004-400000000000000000002222−22−22−22−222222000000000000000000000000000000
χ764-44-4-4-444-44000000000004-40000000000000000000−22−2222222222−22−22000000000000000000000000000000
χ774-4-44-444-40000004-44-4-4-44004000000-44000000000000000000000000000000000000000000000000
χ784-4-44-444-4000000-44-44-4-440040000004-4000000000000000000000000000000000000000000000000
χ794-4-4-444-44004-44-40000-44-40040000-4400000000000000000000000000000000000000000000000000
χ804-4-4-444-4400-44-440000-44-400400004-400000000000000000000000000000000000000000000000000

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