Finite Group Databasebeta

← Group #314176

Character table — Group #314176

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ3111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11111-1-1111111-1-11111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111111-1-1-1-1111-1-111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-11111-111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-1-111-1-11-1-1-1-111-11
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-11111-111-1-1111-1-1-1-11-1
χ11111111111111111111-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-11-1-111-111-1-1-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111111-1-111-1-1-1-1-111-11
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-111111-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-11111-1-1-11
χ17222222222-22-22-22-2-2-22222002200002200-2-2000000000000-20000-200000000
χ18222222222-22-22-22-2-2-2222200-2-20000-2-200-2-200000000000020000200000000
χ19222222222-22-22-22-2-2-2-2-2-2-200220000-2-2002200000000000020000-200000000
χ20222222222-22-22-22-2-2-2-2-2-2-200-2-20000220022000000000000-20000200000000
χ2122222222-22-22-22-22-2-20000220022-2-200-2-200-2-2000022000000000000000000
χ2222222222-22-22-22-22-2-200002200-2-2-2-2002200220000-2-2000000000000000000
χ2322222222-22-22-22-22-2-20000-2-200222200-2-200220000-2-2000000000000000000
χ2422222222-22-22-22-22-2-20000-2-200-2-222002200-2-2000022000000000000000000
χ2522-2-22-22-222-2-222-2-2-222i2i−2i−2i2-200002-200002i−2i000000000000000000002i−2i0000
χ2622-2-22-22-222-2-222-2-2-222i2i−2i−2i-220000-2200002i−2i00000000000000000000−2i2i0000
χ2722-2-22-22-222-2-222-2-2-22−2i−2i2i2i2-200002-20000−2i2i00000000000000000000−2i2i0000
χ2822-2-22-22-222-2-222-2-2-22−2i−2i2i2i-220000-220000−2i2i000000000000000000002i−2i0000
χ2922-2-22-22-22-2-222-2-222-22i2i−2i−2i000000000000−2i2i00000000000002i−2i2-2000000000
χ3022-2-22-22-22-2-222-2-222-22i2i−2i−2i000000000000−2i2i0000000000000−2i2i-22000000000
χ3122-2-22-22-22-2-222-2-222-2−2i−2i2i2i0000000000002i−2i00000000000002i−2i-22000000000
χ3222-2-22-22-22-2-222-2-222-2−2i−2i2i2i0000000000002i−2i0000000000000−2i2i2-2000000000
χ3322-2-22-22-2-222-2-222-22-200002-20000-22000000002i2i−2i−2i002i2i−2i−2i00000000000000
χ3422-2-22-22-2-222-2-222-22-200002-20000-2200000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ3522-2-22-22-2-222-2-222-22-20000-2200002-2000000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ3622-2-22-22-2-222-2-222-22-20000-2200002-200000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ372-22-222-2-2-202020-20002i−2i2i−2i002-200002i−2i0000i2−i20000i2−i22−22−20000002−200i2−i200
χ382-22-222-2-2-202020-20002i−2i2i−2i002-200002i−2i0000−i2i20000−i2i2−22−22000000−2200−i2i200
χ392-22-222-2-2-202020-20002i−2i2i−2i00-220000−2i2i0000i2−i20000i2−i22−22−2000000−2200−i2i200
χ402-22-222-2-2-202020-20002i−2i2i−2i00-220000−2i2i0000−i2i20000−i2i2−22−220000002−200i2−i200
χ412-22-222-2-2-202020-2000−2i2i−2i2i002-20000−2i2i0000i2−i20000i2−i2−22−22000000−2200i2−i200
χ422-22-222-2-2-202020-2000−2i2i−2i2i002-20000−2i2i0000−i2i20000−i2i22−22−20000002−200−i2i200
χ432-22-222-2-2-202020-2000−2i2i−2i2i00-2200002i−2i0000i2−i20000i2−i2−22−220000002−200−i2i200
χ442-22-222-2-2-202020-2000−2i2i−2i2i00-2200002i−2i0000−i2i20000−i2i22−22−2000000−2200i2−i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-4-44-44-4-4-444-4-444-4400000000000000000000000000000000000000000000
χ474-44-444-4-440-40-4040000000000000000000002i2−2i20000−2i22i2000000000000000000
χ484-44-444-4-440-40-404000000000000000000000−2i22i200002i2−2i2000000000000000000
χ494-44-4-4-444040-40-404000000000000000000000022−2222−2200000000000000000000
χ504-44-4-4-444040-40-4040000000000000000000000−2222−222200000000000000000000
χ514-44-4-4-4440-404040-400000000000000004-40000000000000000000000000000
χ524-44-4-4-4440-404040-40000000000000000-440000000000000000000000000000
χ534-4-444-4-444040-40-4000000000000000000000000000002i2−2i2−2i22i200000000000000
χ544-4-444-4-444040-40-400000000000000000000000000000−2i22i22i2−2i200000000000000
χ554-4-444-4-44-40-404040004-4-440000000000000000000000000000000000000000
χ564-4-444-4-44-40-40404000-444-40000000000000000000000000000000000000000
χ574-4-44-444-404040-40-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-4-44-444-404040-40-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-4-44-444-40-40-4040400000000004-40000000000000000000000000000000000
χ604-4-44-444-40-40-404040000000000-440000000000000000000000000000000000
χ618888-8-8-8-8000000000000000000000000000000000000000000000000000000
χ6288-8-8-88-88000000000000000000000000000000000000000000000000000000

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