Finite Group Databasebeta

← Group #263621

Character table — Group #263621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order12222244444488884444444888888222444888888888888888822244444444488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-11111-1-1
χ611111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-111
χ711111111111111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-111
χ811111111111111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-111111-1-1
χ9111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1111-1-11-1
χ10111111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111-11
χ11111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-1-111-11
χ12111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111-111-111-1-11-1
χ13111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-11
χ14111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1
χ15111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1111-1
χ16111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-11
χ172222222222-2-20000-222-222-2000000-222-2-2-222-2-200000000000000000000000000
χ182222222222-2-20000-222-222-2000000-2-2-2-222-2-22200000000000000000000000000
χ192222222222-2-20000-2-2-2-2-2-2-20000002222-2-2-2-22200000000000000000000000000
χ202222222222-2-20000-2-2-2-2-2-2-20000002-2-222222-2-200000000000000000000000000
χ21222222-2-2-2-2222222200-200-2-2-2-2-22200000000000000000000002-20002-20000000
χ22222222-2-2-2-2222222200-200-2-2-2-2-2220000000000000000000000-22000-220000000
χ23222222-2-2-2-222-2-2-2-2200-200-22222-2-200000000000000000000002-2000-220000000
χ24222222-2-2-2-222-2-2-2-2200-200-22222-2-20000000000000000000000-220002-20000000
χ252222-2-222-2-2222222-222-2-2-2222-2-2-2-2200-2000000-2-2220000000000000000000000
χ262222-2-222-2-2222222-2-2-2-222222-2-2-2-2-200200000022-2-20000000000000000000000
χ272222-2-222-2-222-2-2-2-2-222-2-2-22-2-22222200-200000022-2-20000000000000000000000
χ282222-2-222-2-222-2-2-2-2-2-2-2-2222-2-22222-2002000000-2-2220000000000000000000000
χ292222-2-222-2-2-2-200002222-2-2-2000000-200200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ302222-2-222-2-2-2-200002222-2-2-2000000-20020000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ312222-2-222-2-2-2-200002-2-2222-2000000200-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ322222-2-222-2-2-2-200002-2-2222-2000000200-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ332222-2-2-2-222222222-200200-2-2-222-2-20000000000000000000000002-2-2002000000
χ342222-2-2-2-222222222-200200-2-2-222-2-2000000000000000000000000-22200-2000000
χ352222-2-2-2-22222-2-2-2-2-200200-222-2-2220000000000000000000000002-2200-2000000
χ362222-2-2-2-22222-2-2-2-2-200200-222-2-222000000000000000000000000-22-2002000000
χ3722-2-22-22-22-200i2i2−i2−i202i−2i02i−2i0i2−i2i2−i2i2−i200002i−2i002-22−22−22−22−2i2−i2i2−i200000000000000
χ3822-2-22-22-22-200i2i2−i2−i202i−2i02i−2i0i2−i2i2−i2i2−i20000−2i2i00-222−22−2−22−22−i2i2−i2i200000000000000
χ3922-2-22-22-22-200i2i2−i2−i20−2i2i0−2i2i0i2−i2i2−i2i2−i200002i−2i00-22−22−222−22−2−i2i2−i2i200000000000000
χ4022-2-22-22-22-200i2i2−i2−i20−2i2i0−2i2i0i2−i2i2−i2i2−i20000−2i2i002-2−22−22−22−22i2−i2i2−i200000000000000
χ4122-2-22-22-22-200−i2−i2i2i202i−2i02i−2i0−i2i2−i2i2−i2i200002i−2i002-2−22−22−22−22−i2i2−i2i200000000000000
χ4222-2-22-22-22-200−i2−i2i2i202i−2i02i−2i0−i2i2−i2i2−i2i20000−2i2i00-22−22−222−22−2i2−i2i2−i200000000000000
χ4322-2-22-22-22-200−i2−i2i2i20−2i2i0−2i2i0−i2i2−i2i2−i2i200002i−2i00-222−22−2−22−22i2−i2i2−i200000000000000
χ4422-2-22-22-22-200−i2−i2i2i20−2i2i0−2i2i0−i2i2−i2i2−i2i20000−2i2i002-22−22−22−22−2−i2i2−i2i200000000000000
χ4522-2-2-222-2-2200i2i2−i2−i202i−2i0−2i2i0i2−i2−i2i2−i2i202-20002i−2i00−222−2i2−i2−i2i2−222−200000000000000
χ4622-2-2-222-2-2200i2i2−i2−i202i−2i0−2i2i0i2−i2−i2i2−i2i20-22000−2i2i00−222−2−i2i2i2−i22−2−2200000000000000
χ4722-2-2-222-2-2200i2i2−i2−i20−2i2i02i−2i0i2−i2−i2i2−i2i202-2000−2i2i002−2−22i2−i2−i2i22−2−2200000000000000
χ4822-2-2-222-2-2200i2i2−i2−i20−2i2i02i−2i0i2−i2−i2i2−i2i20-220002i−2i002−2−22−i2i2i2−i2−222−200000000000000
χ4922-2-2-222-2-2200−i2−i2i2i202i−2i0−2i2i0−i2i2i2−i2i2−i202-20002i−2i002−2−22−i2i2i2−i22−2−2200000000000000
χ5022-2-2-222-2-2200−i2−i2i2i202i−2i0−2i2i0−i2i2i2−i2i2−i20-22000−2i2i002−2−22i2−i2−i2i2−222−200000000000000
χ5122-2-2-222-2-2200−i2−i2i2i20−2i2i02i−2i0−i2i2i2−i2i2−i202-2000−2i2i00−222−2−i2i2i2−i2−222−200000000000000
χ5222-2-2-222-2-2200−i2−i2i2i20−2i2i02i−2i0−i2i2i2−i2i2−i20-220002i−2i00−222−2i2−i2−i2i22−2−2200000000000000
χ53444444-4-4-4-4-4-40000-4004004000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-40000400-4004000000000000000000000000000000000000000000
χ5544-4-44-4-44-44002i22i2−2i2−2i20000000−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ5644-4-44-4-44-4400−2i2−2i22i22i200000002i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ5744-4-4-44-444-4002i22i2−2i2−2i20000000−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ5844-4-4-44-444-400−2i2−2i22i22i200000002i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ594-44-40000004-44i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i00
χ604-44-40000004-44i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i00
χ614-44-40000004-4−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i00
χ624-44-40000004-4−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i00
χ638-88-8000000-8800000000000000000000000000000000000000000000000000000
χ648-8-880000000042−42−42420000000000000000000000000000000000000000000000000
χ658-8-8800000000−424242−420000000000000000000000000000000000000000000000000

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