Finite Group Databasebeta

← Group #404102

Character table — Group #404102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12222222224444444444444444888822444444888888888888882222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ172222222222-2-2-2-2-2-2-2-20000000000002-22-20000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ182222222222-2-2-2-2-2-2-2-20000000000002-22-2000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ192222222222-2-2-2-2-2-2-2-2000000000000-22-220000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ202222222222-2-2-2-2-2-2-2-2000000000000-22-22000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ21222222-2-2-2-2222-2-22-2-22222-2-2-2-20000000000000000002i2i−2i−2i2i−2i2i−2i0000000000000000
χ22222222-2-2-2-2222-2-22-2-22222-2-2-2-2000000000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000
χ23222222-2-2-2-2222-2-22-2-2-2-2-2-222220000000000000000002i2i−2i−2i−2i2i−2i2i0000000000000000
χ24222222-2-2-2-2222-2-22-2-2-2-2-2-22222000000000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000
χ25222222-2-2-2-2-2-2-222-222000000002222000022-2-2-2-2000000002-2-220000000000000000
χ26222222-2-2-2-2-2-2-222-2220000000022220000-2-222-2-200000000-222-20000000000000000
χ27222222-2-2-2-2-2-2-222-22200000000-2-2-2-2000022-2-22200000000-222-20000000000000000
χ28222222-2-2-2-2-2-2-222-22200000000-2-2-2-20000-2-22222000000002-2-220000000000000000
χ292222-2-222-2-222-222-2-2-200000000000000002-22-2002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ302222-2-222-2-222-222-2-2-200000000000000002-22-200−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ312222-2-222-2-222-222-2-2-20000000000000000-22-22002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ322222-2-222-2-222-222-2-2-20000000000000000-22-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ332222-2-222-2-2-2-22-2-222222-2-222-2-222-2-2000000002-22-2-22000000000000000000000000
χ342222-2-222-2-2-2-22-2-222222-2-222-2-2-2-22200000000-22-222-2000000000000000000000000
χ352222-2-222-2-2-2-22-2-2222-2-222-2-22222-2-2000000002-2-222-2000000000000000000000000
χ362222-2-222-2-2-2-22-2-2222-2-222-2-222-2-22200000000-222-2-22000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2220000000022-2-22-2-220000-2200002-2-2200000000000000000000
χ382222-2-2-2-22222-2-2-2-2220000000022-2-2-222-20000-220000-222-200000000000000000000
χ392222-2-2-2-22222-2-2-2-22200000000-2-2222-2-2200002-20000-222-200000000000000000000
χ402222-2-2-2-22222-2-2-2-22200000000-2-222-222-200002-200002-2-2200000000000000000000
χ412222-2-2-2-222-2-22222-2-222-2-2-2-222000022-2-22-2-22000000000000000000000000000000
χ422222-2-2-2-222-2-22222-2-222-2-2-2-2220000-2-222-222-2000000000000000000000000000000
χ432222-2-2-2-222-2-22222-2-2-2-22222-2-2000022-2-2-222-2000000000000000000000000000000
χ442222-2-2-2-222-2-22222-2-2-2-22222-2-20000-2-2222-2-22000000000000000000000000000000
χ4522-2-22-22-22-22-222-2-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000002-200000000002i−2i
χ4622-2-22-22-22-22-222-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000-220000000000−2i2i
χ4722-2-22-22-22-22-222-2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002-20000000000−2i2i
χ4822-2-22-22-22-22-222-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000-2200000000002i−2i
χ4922-2-22-2-22-222-22-22-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000002-2002i−2i000000
χ5022-2-22-2-22-222-22-22-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000-2200−2i2i000000
χ5122-2-22-2-22-222-22-22-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000002-200−2i2i000000
χ5222-2-22-2-22-222-22-22-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000-22002i−2i000000
χ5322-2-2-222-2-22-222-22-22-22i−2i−2i2i2i−2i−2i2i000000000000000000000000002-200000000002i−2i00
χ5422-2-2-222-2-22-222-22-22-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000-220000000000−2i2i00
χ5522-2-2-222-2-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000002-20000000000−2i2i00
χ5622-2-2-222-2-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000-2200000000002i−2i00
χ5722-2-2-22-222-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000002-2002i−2i0000
χ5822-2-2-22-222-2-2222-2-2-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000-2200−2i2i0000
χ5922-2-2-22-222-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000002-200−2i2i0000
χ6022-2-2-22-222-2-2222-2-2-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000-22002i−2i0000
χ6144-4-44-44-44-4-44-4-444-4400000000000000000000000000000000000000000000000000
χ6244-4-44-4-44-44-44-44-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-444-4-44-44-4400000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-44-4-4-4444-400000000000000000000000000000000000000000000000000
χ658-88-800000000000000000000000042−4200000000000000000000000000000000000000
χ668-88-8000000000000000000000000−424200000000000000000000000000000000000000
χ678-8-88000000000000000000000042−420000000000000000000000000000000000000000
χ688-8-880000000000000000000000−42420000000000000000000000000000000000000000

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