Finite Group Databasebeta

← Group #116844

Character table — Group #116844

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444444444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i11-1-1
χ10111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii-1-111
χ11111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii-1-111
χ12111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i11-1-1
χ13111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i-1-111
χ14111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii11-1-1
χ15111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii11-1-1
χ16111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i-1-111
χ1722222222222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-22-2-222-200000000000000000000000000002-22-200000000
χ202222222222-2-2-2-2-2-2-222-2-2-22-2-222-20000000000000000000000000000-22-2200000000
χ212222222222-2-2-2-2-2-2-2-2-222-2-222-2-220000000000000000000000002-22-2000000000000
χ222222222222-2-2-2-2-2-2-2-2-222-2-222-2-22000000000000000000000000-22-22000000000000
χ23222222-2-2-2-2222-2-2-2-2-2-2222-2-2-22222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ24222222-2-2-2-2222-2-2-2-2-2-2222-2-2-2222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ25222222-2-2-2-2-2-2-222222222-22-2-2-2-2200000000000000000000000000002i−2i−2i2i00000000
χ26222222-2-2-2-2-2-2-222222222-22-2-2-2-220000000000000000000000000000−2i2i2i−2i00000000
χ27222222-2-2-2-2-2-2-22222-2-2-2-2-2-22222-20000000000000000000000002-2-22000000000000
χ28222222-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2000000000000000000000000-222-2000000000000
χ292222-2-22-22-222-222-2-222-2-2-2-22-22-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-22-22-222-222-2-222-2-2-2-22-22-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-22-22-222-222-2-2-2-222-22-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ322222-2-22-22-222-222-2-2-2-222-22-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ332222-2-22-22-2-2-22-2-22222222-2-222-2-20000000000000000000000000000000000002-22-2
χ342222-2-22-22-2-2-22-2-22222222-2-222-2-2000000000000000000000000000000000000-22-22
χ352222-2-22-22-2-2-22-2-222-2-2-2-2222-2-222000000000000000000000000000000002i−2i2i−2i0000
χ362222-2-22-22-2-2-22-2-222-2-2-2-2222-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ372222-2-2-22-2222-2-2-2222222-2-22-2-22-20000000022-2-2-2-222000000000000000000000000
χ382222-2-2-22-2222-2-2-2222222-2-22-2-22-200000000-2-22222-2-2000000000000000000000000
χ392222-2-2-22-2222-2-2-222-2-2-2-2-22-222-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-22-2222-2-2-222-2-2-2-2-22-222-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-22-22-2-2222-2-222-2-22-2-22-2220000000000000000000000000000000000002-2-22
χ422222-2-2-22-22-2-2222-2-222-2-22-2-22-222000000000000000000000000000000000000-222-2
χ432222-2-2-22-22-2-2222-2-2-2-222222-22-2-2000000000000000000000000000000002-2-220000
χ442222-2-2-22-22-2-2222-2-2-2-222222-22-2-200000000000000000000000000000000-222-20000
χ4522-2-22-222-2-22-222-22-20000-20000002-22-200002−22−22−22−22−22−22−22−20000000000000000
χ4622-2-22-222-2-22-222-22-20000-20000002-22-20000−22−22−22−22−22−22−22−220000000000000000
χ4722-2-22-222-2-22-222-22-20000-2000000-22-2200002−22−22−22−2−22−22−22−220000000000000000
χ4822-2-22-222-2-22-222-22-20000-2000000-22-220000−22−22−22−222−22−22−22−20000000000000000
χ4922-2-22-2-2-2222-22-22-220000-20000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ5022-2-22-2-2-2222-22-22-220000-20000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ5122-2-22-2-2-2222-22-22-220000-2000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ5222-2-22-2-2-2222-22-22-220000-2000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ5322-2-2-222-2-222-2-22-2-220000200000000002-22-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5422-2-2-222-2-222-2-22-2-220000200000000002-22-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5522-2-2-222-2-222-2-22-2-22000020000000000-22-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5622-2-2-222-2-222-2-22-2-22000020000000000-22-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5722-2-2-22-222-22-2-2-222-20000200000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5822-2-2-22-222-22-2-2-222-20000200000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ5922-2-2-22-222-22-2-2-222-2000020000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ6022-2-2-22-222-22-2-2-222-2000020000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ6144-4-44-444-4-4-44-4-44-44000040000000000000000000000000000000000000000000000
χ6244-4-44-4-4-444-44-44-44-4000040000000000000000000000000000000000000000000000
χ6344-4-4-444-4-44-444-444-40000-40000000000000000000000000000000000000000000000
χ6444-4-4-44-444-4-4444-4-440000-40000000000000000000000000000000000000000000000
χ658-88-80000000000000008i−8i00000000000000000000000000000000000000000000000
χ668-88-8000000000000000−8i8i00000000000000000000000000000000000000000000000
χ678-8-8800000000000008i−8i0000000000000000000000000000000000000000000000000
χ688-8-880000000000000−8i8i0000000000000000000000000000000000000000000000000

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