Finite Group Databasebeta

← Group #337749

Character table — Group #337749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888824448888224
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-111111111-1-1-1-11111-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ9111111111111111111-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-11
χ10111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-11-1-111-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-2000022222222000000-2-2-2-200000000000000-20000000000
χ18222222222-22-22-22-2-2-200002222-2-2-2-200000022-2-20000000000000020000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-222-2-2000000-2-2220000000000000020000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-222000000222200000000000000-20000000000
χ2122222222-22-22-22-22-2-222220000000022-2-22200000000-2-2000000000-2000000000
χ2222222222-22-22-22-22-2-2222200000000-2-222-2-200000000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000022-2-2-2-200000000220000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000-2-222220000000022000000000-2000000000
χ25222-22-2-2-20-202020-20022-2-2i2i2−i2−i200002i−2i002i−2i00i2−i222−2−2000000i2i2−i2−i20000002−2000
χ26222-22-2-2-20-202020-20022-2-2i2i2−i2−i20000−2i2i00−2i2i00i2−i2−2−222000000i2i2−i2−i2000000−22000
χ27222-22-2-2-20-202020-20022-2-2−i2−i2i2i200002i−2i002i−2i00−i2i2−2−222000000−i2−i2i2i2000000−22000
χ28222-22-2-2-20-202020-20022-2-2−i2−i2i2i20000−2i2i00−2i2i00−i2i222−2−2000000−i2−i2i2i20000002−2000
χ29222-22-2-2-20-202020-200-2-222i2i2−i2−i200002i−2i00−2i2i00i2−i222−2−2000000−i2−i2i2i2000000−22000
χ30222-22-2-2-20-202020-200-2-222i2i2−i2−i20000−2i2i002i−2i00i2−i2−2−222000000−i2−i2i2i20000002−2000
χ31222-22-2-2-20-202020-200-2-222−i2−i2i2i200002i−2i00−2i2i00−i2i2−2−222000000i2i2−i2−i20000002−2000
χ32222-22-2-2-20-202020-200-2-222−i2−i2i2i20000−2i2i002i−2i00−i2i222−2−2000000i2i2−i2−i2000000−22000
χ332-222-2-2-2222-2-222-2-22-200000000000000000000002-22-2002i2i−2i−2i0000002i−2i0000000
χ342-222-2-2-2222-2-222-2-22-200000000000000000000002-22-200−2i−2i2i2i000000−2i2i0000000
χ352-222-2-2-2222-2-222-2-22-20000000000000000000000-22-22002i2i−2i−2i000000−2i2i0000000
χ362-222-2-2-2222-2-222-2-22-20000000000000000000000-22-2200−2i−2i2i2i0000002i−2i0000000
χ372-2-2222-2-22020-20-20002−22−22i−2i2i−2i2-22i−2i000000000000002−22−22−2i2−i2i2−i20000i2−i200000
χ382-2-2222-2-22020-20-20002−22−22i−2i2i−2i-22−2i2i000000000000002−2−22−22i2−i2i2−i20000−i2i200000
χ392-2-2222-2-22020-20-20002−22−2−2i2i−2i2i2-2−2i2i000000000000002−22−22−2−i2i2−i2i20000−i2i200000
χ402-2-2222-2-22020-20-20002−22−2−2i2i−2i2i-222i−2i000000000000002−2−22−22−i2i2−i2i20000i2−i200000
χ412-2-2222-2-22020-20-2000−22−222i−2i2i−2i2-22i−2i00000000000000−22−22−22−i2i2−i2i20000−i2i200000
χ422-2-2222-2-22020-20-2000−22−222i−2i2i−2i-22−2i2i00000000000000−222−22−2−i2i2−i2i20000i2−i200000
χ432-2-2222-2-22020-20-2000−22−22−2i2i−2i2i2-2−2i2i00000000000000−22−22−22i2−i2i2−i20000i2−i200000
χ442-2-2222-2-22020-20-2000−22−22−2i2i−2i2i-222i−2i00000000000000−222−22−2i2−i2i2−i20000−i2i200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-44-4-4-4040-40-4040000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ47444-44-4-4-4040-40-404000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ4844-44-4-44-440-40-40400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ4944-44-4-44-440-40-4040000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5044-44-4-44-4-404040-40000000000000000000004i−4i000000000000000000000000000
χ5144-44-4-44-4-404040-4000000000000000000000−4i4i000000000000000000000000000
χ524-444-4-4-444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ534-444-4-4-44-444-4-444-4-4400000000000000000000000000000000000000000000000
χ544-444-4-4-44-4-444-4-4444-400000000000000000000000000000000000000000000000
χ554-44-4-444-404040-40-400000000000000004i−4i0000000000000000000000000000000
χ564-44-4-444-404040-40-40000000000000000−4i4i0000000000000000000000000000000
χ574-44-4-444-40-40-4040400000000000000000000000022−22−2222000000000000000000000
χ584-44-4-444-40-40-40404000000000000000000000000−222222−22000000000000000000000
χ594-4-4444-4-4-40-4040400022−2222−220000000000000000000000−22220000000000000000000
χ604-4-4444-4-4-40-40404000−2222−2222000000000000000000000022−220000000000000000000
χ614-4-4-44-444000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ624-4-4-44-444000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ634-4-4-44-4440000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ644-4-4-44-4440000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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