Finite Group Databasebeta

← Group #409986

Character table — Group #409986

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222222244444444442224444444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ9111111-1-1111111111-1-1111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1111111111-1-1111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1111111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111-1-1111111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111-1-1111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ14111111-1-1111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ15111111-1-1111111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ16111111-1-1111111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ17222222222222-2-2-2-2-2-2-2-2-2-2222-2-2-200000000000000000000000000002-22-200000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2222-2-2-20000000000000000000000000000-22-2200000000
χ1922222222-2-2-2-22222-222-2-2-22-2-22-2-2000000000000000000000000000000002i−2i2i−2i0000
χ2022222222-2-2-2-22222-222-2-2-22-2-22-2-200000000000000000000000000000000−2i2i−2i2i0000
χ2122222222-2-2-2-2-2-2-2-22-2-22222-2-2-222000022220000-2-2-2-2000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-22-2-22222-2-2-2220000-2-2-2-200002222000000000000000000000000
χ23222222-2-22222-2-2-2-2-222-2-2-2-2-2-222200000000000000000000000000002-2-2200000000
χ24222222-2-22222-2-2-2-2-222-2-2-2-2-2-22220000000000000000000000000000-222-200000000
χ25222222-2-2-2-2-2-22222-2-2-2-2-2-2-222-222000000000000000000000000000000002i−2i−2i2i0000
χ26222222-2-2-2-2-2-22222-2-2-2-2-2-2-222-22200000000000000000000000000000000−2i2i2i−2i0000
χ27222222-2-2-2-2-2-2-2-2-2-2222222-2222-2-2000022-2-20000-2-222000000000000000000000000
χ28222222-2-2-2-2-2-2-2-2-2-2222222-2222-2-20000-2-222000022-2-2000000000000000000000000
χ292222-2-22222-2-222-2-2222-2-22-22-2-22-2000000000000000022-2-222-2-20000000000000000
χ302222-2-22222-2-222-2-2222-2-22-22-2-22-20000000000000000-2-222-2-2220000000000000000
χ312222-2-22222-2-2-2-222-2-2-222-2-22-22-220000000000000000000000000000000000002-22-2
χ322222-2-22222-2-2-2-222-2-2-222-2-22-22-22000000000000000000000000000000000000-22-22
χ332222-2-222-2-22222-2-2-22222-2-2-22-2-220000000000000000000000002-22-2000000000000
χ342222-2-222-2-22222-2-2-22222-2-2-22-2-22000000000000000000000000-22-22000000000000
χ352222-2-222-2-222-2-2222-2-2-2-22-2-2222-222220000-2-2-2-20000000000000000000000000000
χ362222-2-222-2-222-2-2222-2-2-2-22-2-2222-2-2-2-2-2000022220000000000000000000000000000
χ372222-2-2-2-222-2-222-2-22-2-2-2-222-222-22000000000000000022-2-2-2-2220000000000000000
χ382222-2-2-2-222-2-222-2-22-2-2-2-222-222-220000000000000000-2-22222-2-20000000000000000
χ392222-2-2-2-222-2-2-2-222-22222-22-22-22-20000000000000000000000000000000000002-2-22
χ402222-2-2-2-222-2-2-2-222-22222-22-22-22-2000000000000000000000000000000000000-222-2
χ412222-2-2-2-2-2-22222-2-2-2-2-222-222-222-20000000000000000000000002-2-22000000000000
χ422222-2-2-2-2-2-22222-2-2-2-2-222-222-222-2000000000000000000000000-222-2000000000000
χ432222-2-2-2-2-2-222-2-222222-2-2222-2-2-2222-2-20000-2-2220000000000000000000000000000
χ442222-2-2-2-2-2-222-2-222222-2-2222-2-2-22-2-222000022-2-20000000000000000000000000000
χ4522-2-22-2002-22-22-22-2-2002-22000000002i−2i002i−2i002i−2i002i−2i2-22-200000000000000000000
χ4622-2-22-2002-22-22-22-2-2002-22000000002i−2i00−2i2i002i−2i00−2i2i-22-2200000000000000000000
χ4722-2-22-2002-22-22-22-2-2002-2200000000−2i2i002i−2i00−2i2i002i−2i-22-2200000000000000000000
χ4822-2-22-2002-22-22-22-2-2002-2200000000−2i2i00−2i2i00−2i2i00−2i2i2-22-200000000000000000000
χ4922-2-22-200-22-22-22-22-2002-220000002i−2i00002i−2i2i−2i0000−2i2i00002-22-20000000000000000
χ5022-2-22-200-22-22-22-22-2002-220000002i−2i0000−2i2i2i−2i00002i−2i0000-22-220000000000000000
χ5122-2-22-200-22-22-22-22-2002-22000000−2i2i00002i−2i−2i2i0000−2i2i0000-22-220000000000000000
χ5222-2-22-200-22-22-22-22-2002-22000000−2i2i0000−2i2i−2i2i00002i−2i00002-22-20000000000000000
χ5322-2-2-22002-2-222-2-22-200-2220000002i−2i002i−2i00−2i2i002i−2i002-2-2200000000000000000000
χ5422-2-2-22002-2-222-2-22-200-2220000002i−2i00−2i2i00−2i2i00−2i2i00-222-200000000000000000000
χ5522-2-2-22002-2-222-2-22-200-222000000−2i2i002i−2i002i−2i002i−2i00-222-200000000000000000000
χ5622-2-2-22002-2-222-2-22-200-222000000−2i2i00−2i2i002i−2i00−2i2i002-2-2200000000000000000000
χ5722-2-2-2200-222-2-222-2-200-222000000002i−2i2i−2i0000−2i2i−2i2i0000002-2-220000000000000000
χ5822-2-2-2200-222-2-222-2-200-222000000002i−2i−2i2i0000−2i2i2i−2i000000-222-20000000000000000
χ5922-2-2-2200-222-2-222-2-200-22200000000−2i2i2i−2i00002i−2i−2i2i000000-222-20000000000000000
χ6022-2-2-2200-222-2-222-2-200-22200000000−2i2i−2i2i00002i−2i2i−2i0000002-2-220000000000000000
χ6144-4-44-4004-44-4-44-44400-44-40000000000000000000000000000000000000000000000
χ6244-4-44-400-44-444-44-4400-44-40000000000000000000000000000000000000000000000
χ6344-4-4-44004-4-44-444-44004-4-40000000000000000000000000000000000000000000000
χ6444-4-4-4400-444-44-4-444004-4-40000000000000000000000000000000000000000000000
χ658-88-8008-8000000000000000000000000000000000000000000000000000000000000
χ668-88-800-88000000000000000000000000000000000000000000000000000000000000
χ678-8-8800000000000008i−8i0000000000000000000000000000000000000000000000000
χ688-8-880000000000000−8i8i0000000000000000000000000000000000000000000000000

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