Finite Group Databasebeta

← Group #314158

Character table — Group #314158

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888824444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-1111-1
χ10111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-11-1-1-11111-1-1-1-1-11
χ11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1111-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1-111-1-1-1-1111-1
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1111111-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-11111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-111-1-11111-1-11-1
χ17222222222-22-22-22-2-2-22222000000002222-2-2000000000000-2-2000000000000
χ18222222222-22-22-22-2-2-2222200000000-2-2-2-2-2-200000000000022000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000000022-2-2220000000000002-2000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200000000-2-22222000000000000-22000000000000
χ2122222222-22-22-22-22-2-200002222-2-2-2-2000000-2-2000022000000000000000000
χ2222222222-22-22-22-22-2-2000022-2-2-2-222000000220000-2-2000000000000000000
χ2322222222-22-22-22-22-2-20000-2-22222-2-2000000220000-2-2000000000000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-22222000000-2-2000022000000000000000000
χ2522-22-2-2-2222-2-222-2-2-222i2i−2i−2i2-2002-20000002i−2i000000000000000000002i−2i0000
χ2622-22-2-2-2222-2-222-2-2-222i2i−2i−2i-2200-220000002i−2i00000000000000000000−2i2i0000
χ2722-22-2-2-2222-2-222-2-2-22−2i−2i2i2i2-2002-2000000−2i2i00000000000000000000−2i2i0000
χ2822-22-2-2-2222-2-222-2-2-22−2i−2i2i2i-2200-22000000−2i2i000000000000000000002i−2i0000
χ2922-22-2-2-222-2-222-2-222-22i2i−2i−2i000000000000−2i2i000000000000002i−2i2-200000000
χ3022-22-2-2-222-2-222-2-222-22i2i−2i−2i000000000000−2i2i00000000000000−2i2i-2200000000
χ3122-22-2-2-222-2-222-2-222-2−2i−2i2i2i0000000000002i−2i000000000000002i−2i-2200000000
χ3222-22-2-2-222-2-222-2-222-2−2i−2i2i2i0000000000002i−2i00000000000000−2i2i2-200000000
χ3322-22-2-2-22-222-2-222-22-200002-200-2200000000002i2i−2i−2i002i2i−2i−2i00000000000000
χ3422-22-2-2-22-222-2-222-22-200002-200-220000000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ3522-22-2-2-22-222-2-222-22-20000-22002-200000000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ3622-22-2-2-22-222-2-222-22-20000-22002-20000000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ372-2222-2-2-2-20-202020002-22-2000000002i−2i2i−2i002−200002−22−22−2000000i2−i200i2−i200
χ382-2222-2-2-2-20-202020002-22-2000000002i−2i2i−2i00−220000−22−22−22000000−i2i200−i2i200
χ392-2222-2-2-2-20-202020002-22-200000000−2i2i−2i2i002−200002−22−22−2000000−i2i200−i2i200
χ402-2222-2-2-2-20-202020002-22-200000000−2i2i−2i2i00−220000−22−22−22000000i2−i200i2−i200
χ412-2222-2-2-2-20-20202000-22-22000000002i−2i−2i2i002−200002−2−22−22000000−i2i200i2−i200
χ422-2222-2-2-2-20-20202000-22-22000000002i−2i−2i2i00−220000−222−22−2000000i2−i200−i2i200
χ432-2222-2-2-2-20-20202000-22-2200000000−2i2i2i−2i002−200002−2−22−22000000i2−i200−i2i200
χ442-2222-2-2-2-20-20202000-22-2200000000−2i2i2i−2i00−220000−222−22−2000000−i2i200i2−i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-44-4-4-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ474-4444-4-4-44040-40-400000000000000000000022−220000−2222000000000000000000
χ484-4444-4-4-44040-40-4000000000000000000000−2222000022−22000000000000000000
χ494-44-4-44-4404040-40-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ504-44-4-44-4404040-40-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ514-44-4-44-440-40-40404000000004-4000000000000000000000000000000000000
χ524-44-4-44-440-40-4040400000000-44000000000000000000000000000000000000
χ534-4-44-444-440-40-404000000000000000000000000000002i2−2i2−2i22i200000000000000
χ544-4-44-444-440-40-40400000000000000000000000000000−2i22i22i2−2i200000000000000
χ554-4-44-444-4-404040-40004i−4i−4i4i0000000000000000000000000000000000000000
χ564-4-44-444-4-404040-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ574-4-4-44-444040-40-404000000000000000000000022−22−222200000000000000000000
χ584-4-4-44-444040-40-4040000000000000000000000−222222−2200000000000000000000
χ594-4-4-44-4440-404040-40000000000004-400000000000000000000000000000000
χ604-4-4-44-4440-404040-4000000000000-4400000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-888-8-8000000000000000000000000000000000000000000000000000000

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