Finite Group Databasebeta

← Group #405721

Character table — Group #405721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444488888888888888888888888888881616161616161616161616161616
order12222222224444444444444444224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-111-1-111-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-111-1-111
χ11111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ12111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111111-1-11-1-1-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-111-1-1
χ172222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-222000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22222-2-2000000000000000000
χ21222222-2-2-2-222-2-222-2-200000000002200-2-200002i2i−2i−2i2i−2i2i−2i0000000000000000000000
χ22222222-2-2-2-222-2-222-2-200000000002200-2-20000−2i−2i2i2i−2i2i−2i2i0000000000000000000000
χ23222222-2-2-2-222-2-222-2-20000000000-2-2002200002i2i−2i−2i−2i2i−2i2i0000000000000000000000
χ24222222-2-2-2-222-2-222-2-20000000000-2-200220000−2i−2i2i2i2i−2i2i−2i0000000000000000000000
χ25222222-2-2-2-2-2-222-2-222000000002200-2-2002i2i−2i−2i00002i−2i−2i2i0000000000000000000000
χ26222222-2-2-2-2-2-222-2-222000000002200-2-200−2i−2i2i2i0000−2i2i2i−2i0000000000000000000000
χ27222222-2-2-2-2-2-222-2-22200000000-2-20022002i2i−2i−2i0000−2i2i2i−2i0000000000000000000000
χ28222222-2-2-2-2-2-222-2-22200000000-2-2002200−2i−2i2i2i00002i−2i−2i2i0000000000000000000000
χ292222-2-2-2-2222-22-22-22-222-2-222-2-20000000000000000000000000000200-22-200000000
χ302222-2-2-2-2222-22-22-22-222-2-222-2-20000000000000000000000000000-2002-2200000000
χ312222-2-2-2-2222-22-22-22-2-2-222-2-2220000000000000000000000000000200-2-2200000000
χ322222-2-2-2-2222-22-22-22-2-2-222-2-2220000000000000000000000000000-20022-200000000
χ332222-2-2-2-222-22-22-22-2222-2-2-2-22200000000000000000000000022-2-202-200000000000
χ342222-2-2-2-222-22-22-22-2222-2-2-2-222000000000000000000000000-2-2220-2200000000000
χ352222-2-2-2-222-22-22-22-22-2-22222-2-200000000000000000000000022-2-20-2200000000000
χ362222-2-2-2-222-22-22-22-22-2-22222-2-2000000000000000000000000-2-22202-200000000000
χ372-22-22-22-22-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002i−2i2-20000
χ382-22-22-22-22-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−2i2i-220000
χ392-22-22-22-22-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002i−2i-220000
χ402-22-22-22-22-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−2i2i2-20000
χ412-22-22-22-22-2-2-22222-2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000002i−2i2-2
χ422-22-22-22-22-2-2-22222-2-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000−2i2i-22
χ432-22-22-22-22-2-2-22222-2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000002i−2i-22
χ442-22-22-22-22-2-2-22222-2-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000−2i2i2-2
χ452-22-2-222-2-222-22-2-22-22000000002-2002-20000002i−2i2i−2i00002i−2i2i−2i000000000000000000
χ462-22-2-222-2-222-22-2-22-22000000002-2002-2000000−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ472-22-2-222-2-222-22-2-22-2200000000-2200-220000002i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ482-22-2-222-2-222-22-2-22-2200000000-2200-22000000−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ492-22-2-222-2-22-22-222-22-200000000002i−2i002i−2i2-22-2000000002i−2i−2i2i000000000000000000
χ502-22-2-222-2-22-22-222-22-200000000002i−2i002i−2i-22-2200000000−2i2i2i−2i000000000000000000
χ512-22-2-222-2-22-22-222-22-20000000000−2i2i00−2i2i2-22-200000000−2i2i2i−2i000000000000000000
χ522-22-2-222-2-22-22-222-22-20000000000−2i2i00−2i2i-22-22000000002i−2i−2i2i000000000000000000
χ532-22-2-22-222-22-2-22-222-22i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i2-2-2200000000000000000000000000
χ542-22-2-22-222-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i-222-200000000000000000000000000
χ552-22-2-22-222-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i-222-200000000000000000000000000
χ562-22-2-22-222-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i2-2-2200000000000000000000000000
χ572-22-2-22-222-2-222-22-2-222i−2i−2i2i−2i2i2i−2i2-2−2i2i-222i−2i0000000000000000000000000000000000
χ582-22-2-22-222-2-222-22-2-222i−2i−2i2i−2i2i2i−2i-222i−2i2-2−2i2i0000000000000000000000000000000000
χ592-22-2-22-222-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i2-22i−2i-22−2i2i0000000000000000000000000000000000
χ602-22-2-22-222-2-222-22-2-22−2i2i2i−2i2i−2i−2i2i-22−2i2i2-22i−2i0000000000000000000000000000000000
χ614444-4-444-4-44-4-444-4-4400000000000000000000000000000000000000000000000000
χ624444-4-444-4-4-444-4-444-400000000000000000000000000000000000000000000000000
χ634-44-44-4-44-444444-4-4-4-400000000000000000000000000000000000000000000000000
χ644-44-44-4-44-44-4-4-4-4444400000000000000000000000000000000000000000000000000
χ6588-8-80000000000000000000000000000000000000000000000004-400000000000000
χ6688-8-8000000000000000000000000000000000000000000000000-4400000000000000
χ678-8-8800000000000000000000000000000000000000000000004i−4i0000000000000000
χ688-8-880000000000000000000000000000000000000000000000−4i4i0000000000000000

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