Finite Group Databasebeta

← Group #235271

Character table — Group #235271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222222224444444444444444442244444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ911111-1-1-1-11111-1-1-1-1-1-111111-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ1011111-1-1-1-11111-1-1-1-1-1-111111-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ1111111-1-1-1-11111-1-1-1-1-1-111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ1211111-1-1-1-11111-1-1-1-1-1-111111-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ1311111-1-1-1-11111-1-1-1-1-1-111111-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1
χ1411111-1-1-1-11111-1-1-1-1-1-111111-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1-1-111
χ1511111-1-1-1-11111-1-1-1-1-1-111111-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-111-1-1-1-111-1-111
χ1611111-1-1-1-11111-1-1-1-1-1-111111-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11-1-11111-1-111-1-1
χ1722222222222222222-2-2-2-22-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-22-22-2-220000000000000000000000002-2-22000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-22-22-2-22000000000000000000000000-222-2000000000000
χ212222222222-2-2-2-2-2-2-2-2-222-2-22-222-2000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-2-2-2-2-2-222-2-22-222-200000000000000000000000000000000-22-220000
χ2322222-2-2-2-22222-2-2-2-222-2-22-2-2222-222-2-2-2-22200000000000000000000000000000000
χ2422222-2-2-2-22222-2-2-2-222-2-22-2-2222-2-2-22222-2-200000000000000000000000000000000
χ2522222-2-2-2-22-2-2-222222222-2-222-2-2-2000000000000000000000000000000002-2-220000
χ2622222-2-2-2-22-2-2-222222222-2-222-2-2-200000000000000000000000000000000-222-20000
χ2722222-2-2-2-22-2-2-22222-2-2-2-2-22-2-222200000000000000000000000022-2-2000000000000
χ2822222-2-2-2-22-2-2-22222-2-2-2-2-22-2-2222000000000000000000000000-2-222000000000000
χ292222-222-2-2-222-222-2-22222-2-2-2-22-22000000000000000022-2-222-2-20000000000000000
χ302222-222-2-2-222-222-2-22222-2-2-2-22-220000000000000000-2-222-2-2220000000000000000
χ312222-222-2-2-222-222-2-2-2-2-2-2-2222-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ322222-222-2-2-222-222-2-2-2-2-2-2-2222-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ332222-222-2-2-2-2-22-2-22222-2-22-22-2-22200000000000000000000000000002-22-200000000
χ342222-222-2-2-2-2-22-2-22222-2-22-22-2-2220000000000000000000000000000-22-2200000000
χ352222-222-2-2-2-2-22-2-222-2-22222-222-2-20000000000000000000000000000000000002-22-2
χ362222-222-2-2-2-2-22-2-222-2-22222-222-2-2000000000000000000000000000000000000-22-22
χ372222-2-2-222-222-2-2-22222-2-2-222-22-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ382222-2-2-222-222-2-2-22222-2-2-222-22-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ392222-2-2-222-222-2-2-222-2-222-2-2-22-222000000000000000022-2-2-2-2220000000000000000
χ402222-2-2-222-222-2-2-222-2-222-2-2-22-2220000000000000000-2-22222-2-20000000000000000
χ412222-2-2-222-2-2-2222-2-2222222-2-2-22-20000000000000000000000000000000000002-2-22
χ422222-2-2-222-2-2-2222-2-2222222-2-2-22-2000000000000000000000000000000000000-222-2
χ432222-2-2-222-2-2-2222-2-2-2-2-2-22-2222-2200000000000000000000000000002-2-2200000000
χ442222-2-2-222-2-2-2222-2-2-2-2-2-22-2222-220000000000000000000000000000-222-200000000
χ4522-2-222-22-2-22-2-22-22-200002000000002i−2i002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4622-2-222-22-2-22-2-22-22-200002000000002i−2i002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ4722-2-222-22-2-22-2-22-22-20000200000000−2i2i00−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4822-2-222-22-2-22-2-22-22-20000200000000−2i2i00−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4922-2-22-22-22-22-2-2-22-2200002000000002i−2i00−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ5022-2-22-22-22-22-2-2-22-2200002000000002i−2i00−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5122-2-22-22-22-22-2-2-22-220000200000000−2i2i002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ5222-2-22-22-22-22-2-2-22-220000200000000−2i2i002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-2-2-22-2-2222-222-2-220000-20000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5422-2-2-22-2-2222-222-2-220000-20000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5522-2-2-22-2-2222-222-2-220000-2000000-2200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5622-2-2-22-2-2222-222-2-220000-2000000-2200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5722-2-2-2-222-222-22-222-20000-20000002-200-2200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5822-2-2-2-222-222-22-222-20000-20000002-200-2200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5922-2-2-2-222-222-22-222-20000-2000000-22002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ6022-2-2-2-222-222-22-222-20000-2000000-22002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ6144-4-444-44-4-4-444-44-440000-40000000000000000000000000000000000000000000000
χ6244-4-44-44-44-4-4444-44-40000-40000000000000000000000000000000000000000000000
χ6344-4-4-44-4-444-44-4-444-4000040000000000000000000000000000000000000000000000
χ6444-4-4-4-444-44-44-44-4-44000040000000000000000000000000000000000000000000000
χ658-88-80000000000000008i−8i00000000000000000000000000000000000000000000000
χ668-88-8000000000000000−8i8i00000000000000000000000000000000000000000000000
χ678-8-8800000000000008i−8i0000000000000000000000000000000000000000000000000
χ688-8-880000000000000−8i8i0000000000000000000000000000000000000000000000000

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