Finite Group Databasebeta

← Group #398906

Character table — Group #398906

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ511111111111111111111111111111111-1-11111-1-1-1-111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000022-2-200000000-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000-2-22200000000220000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2-22200000000-2-20000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000022-2-200000000220000000000000000000000000000
χ21222222-2-2-2-222-2-2-2-2222-2-22-2-2000000000022-2-2000022-2-2000000000022-2-200000000000000000000
χ22222222-2-2-2-222-2-2-2-2222-2-22-2-2000000000022-2-20000-2-2220000000000-2-22200000000000000000000
χ23222222-2-2-2-222-2-2-2-2222-2-22-2-20000000000-2-222000022-2-20000000000-2-22200000000000000000000
χ24222222-2-2-2-222-2-2-2-2222-2-22-2-20000000000-2-2220000-2-222000000000022-2-200000000000000000000
χ25222-2-2-2222-2-222-2-2-222-222-2-2-222-2-222-2-200000000002-22-222-2-2000000000000000000000000000000
χ26222-2-2-2222-2-222-2-2-222-222-2-2-222-2-222-2-20000000000-22-22-2-222000000000000000000000000000000
χ27222-2-2-2222-2-222-2-2-222-222-2-2-2-2-222-2-22200000000002-22-2-2-222000000000000000000000000000000
χ28222-2-2-2222-2-222-2-2-222-222-2-2-2-2-222-2-2220000000000-22-2222-2-2000000000000000000000000000000
χ29222-2-2-2222-2-222-2-2-2-2-22-2-222222-2-2-2-2220000000000000000000000000000000000000000002i−2i002i−2i
χ30222-2-2-2222-2-222-2-2-2-2-22-2-222222-2-2-2-222000000000000000000000000000000000000000000−2i2i00−2i2i
χ31222-2-2-2222-2-222-2-2-2-2-22-2-2222-2-22222-2-20000000000000000000000000000000000000000002i−2i00−2i2i
χ32222-2-2-2222-2-222-2-2-2-2-22-2-2222-2-22222-2-2000000000000000000000000000000000000000000−2i2i002i−2i
χ33222-2-2-2-2-2-22-22-222222-2-2-2-2220000000000000000002-2-2200000022-2-20000000022-2-2000000000000
χ34222-2-2-2-2-2-22-22-222222-2-2-2-2220000000000000000002-2-22000000-2-22200000000-2-222000000000000
χ35222-2-2-2-2-2-22-22-222222-2-2-2-222000000000000000000-222-200000022-2-200000000-2-222000000000000
χ36222-2-2-2-2-2-22-22-222222-2-2-2-222000000000000000000-222-2000000-2-2220000000022-2-2000000000000
χ372-2-222-222-22-22-2-2-222-222-2-2-222i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2i−2i00002-22-2000000000000
χ382-2-222-222-22-22-2-2-222-222-2-2-222i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i−2i2i0000-22-22000000000000
χ392-2-222-222-22-22-2-2-222-222-2-2-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i2i−2i0000-22-22000000000000
χ402-2-222-222-22-22-2-2-222-222-2-2-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i−2i2i00002-22-2000000000000
χ412-2-222-222-22-22-2-2-22-22-2-2222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000022-2-200002i2i−2i−2i00000000
χ422-2-222-222-22-22-2-2-22-22-2-2222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000-2-2220000−2i−2i2i2i00000000
χ432-2-222-222-22-22-2-2-22-22-2-2222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000022-2-20000−2i−2i2i2i00000000
χ442-2-222-222-22-22-2-2-22-22-2-2222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000-2-22200002i2i−2i−2i00000000
χ452-2-222-2-2-22-2-22222-22-22-22-22-200000000000000000000002-22-2002i−2i2i−2i2i−2i−2i2i00000000000000000000
χ462-2-222-2-2-22-2-22222-22-22-22-22-200000000000000000000002-22-200−2i2i−2i2i−2i2i2i−2i00000000000000000000
χ472-2-222-2-2-22-2-22222-22-22-22-22-20000000000000000000000-22-22002i−2i2i−2i−2i2i2i−2i00000000000000000000
χ482-2-222-2-2-22-2-22222-22-22-22-22-20000000000000000000000-22-2200−2i2i−2i2i2i−2i−2i2i00000000000000000000
χ492-2-2-2-2222-2-222-222-22-2-22-222-22i−2i−2i2i2i−2i−2i2i002-22-2000000000000002i−2i−2i2i000000000000000000000000
χ502-2-2-2-2222-2-222-222-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00-22-2200000000000000−2i2i2i−2i000000000000000000000000
χ512-2-2-2-2222-2-222-222-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i002-22-200000000000000−2i2i2i−2i000000000000000000000000
χ522-2-2-2-2222-2-222-222-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00-22-22000000000000002i−2i−2i2i000000000000000000000000
χ532-2-2-2-2222-2-222-222-2-222-22-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002-2002i−2i00
χ542-2-2-2-2222-2-222-222-2-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000-2200−2i2i00
χ552-2-2-2-2222-2-222-222-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002-200−2i2i00
χ562-2-2-2-2222-2-222-222-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000-22002i−2i00
χ572-2-2-2-22-2-222222-2-222-2-2-222-2200000000002-2-22000000002-2-2200000000000000-222-2000000000000
χ582-2-2-2-22-2-222222-2-222-2-2-222-2200000000002-2-2200000000-222-2000000000000002-2-22000000000000
χ592-2-2-2-22-2-222222-2-222-2-2-222-220000000000-222-2000000002-2-22000000000000002-2-22000000000000
χ602-2-2-2-22-2-222222-2-222-2-2-222-220000000000-222-200000000-222-200000000000000-222-2000000000000
χ61444444-4-4-4-444-4-4-4-4-4-4-444-44400000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-4-4-44-44-4444-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ6344-44-444-44-4-4-4-44-4400000000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ6444-44-444-44-4-4-4-44-440000000000000000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ6544-44-44-44-44-4-44-44-40000000000000000000000004-400000000000000000000000000000000000000
χ6644-44-44-44-44-4-44-44-4000000000000000000000000-4400000000000000000000000000000000000000
χ6744-4-44-44-4444-4-4-44-40000000000000000000000000000000000000000000022−2222−220000000000000000
χ6844-4-44-44-4444-4-4-44-400000000000000000000000000000000000000000000−2222−22220000000000000000
χ6944-4-44-4-44-4-44-444-4400000000000000000000000000000000004-40000000000000000000000000000
χ7044-4-44-4-44-4-44-444-440000000000000000000000000000000000-440000000000000000000000000000
χ714-444-4-44-4-4-44-44-444000000000000000000000000000000000000000000000000000022−22−222200000000
χ724-444-4-44-4-4-44-44-4440000000000000000000000000000000000000000000000000000−222222−2200000000
χ734-444-4-4-44444-4-44-4-400000000000000000000004-40000000000000000000000000000000000000000
χ744-444-4-4-44444-4-44-4-40000000000000000000000-440000000000000000000000000000000000000000
χ754-44-4444-4-44-4-444-4-40000000000000000000000000000000000000000000022−22−22220000000000000000
χ764-44-4444-4-44-4-444-4-400000000000000000000000000000000000000000000−222222−220000000000000000
χ774-44-444-444-4-4-4-4-44400000000000000004i−4i0000000000000000000000000000000000000000000000
χ784-44-444-444-4-4-4-4-4440000000000000000−4i4i0000000000000000000000000000000000000000000000
χ794-4-444-4-4-44-4-44444-4-44-44-44-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-4-44-4-444444-4-44-4444-4-44-400000000000000000000000000000000000000000000000000000000

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