Finite Group Databasebeta

← Group #343522

Character table — Group #343522

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-111-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-11-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-111111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-11111-1-111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-111111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11-1-111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1111-1111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111-11-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-20000000022000022000-2-20000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-200000000-2-20000-2-2000220000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-20000222200000000220000-2-2000-220000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-20000222200000000-2-20000220002-20000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-200000000000000222200-20000-2000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-200000000000000-2-2-2-200200002000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022220000000000000022-2-200-200002000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000222200000000000000-2-2220020000-2000000000000
χ25222-22-2-2-2-2-222-2-222-2200000000000000002222-2-2-2-20000000002i−2i0002i−2i0000000000
χ26222-22-2-2-2-2-222-2-222-2200000000000000002222-2-2-2-2000000000−2i2i000−2i2i0000000000
χ27222-22-2-2-2-2-222-2-222-220000000000000000-2-2-2-222220000000002i−2i000−2i2i0000000000
χ28222-22-2-2-2-2-222-2-222-220000000000000000-2-2-2-22222000000000−2i2i0002i−2i0000000000
χ2922-22-22-2-20-20-20202002i2i−2i−2i22−2−2000022−2−2i2i2−i2−i2i2i2−i2−i2002i−2i2-2000000000000i2−i2002−200
χ3022-22-22-2-20-20-20202002i2i−2i−2i22−2−2000022−2−2i2i2−i2−i2i2i2−i2−i200−2i2i-22000000000000−i2i200−2200
χ3122-22-22-2-20-20-20202002i2i−2i−2i−2−2220000−2−222−i2−i2i2i2−i2−i2i2i2002i−2i2-2000000000000−i2i200−2200
χ3222-22-22-2-20-20-20202002i2i−2i−2i−2−2220000−2−222−i2−i2i2i2−i2−i2i2i200−2i2i-22000000000000i2−i2002−200
χ3322-22-22-2-20-20-2020200−2i−2i2i2i22−2−2000022−2−2−i2−i2i2i2−i2−i2i2i2002i−2i-22000000000000i2−i200−2200
χ3422-22-22-2-20-20-2020200−2i−2i2i2i22−2−2000022−2−2−i2−i2i2i2−i2−i2i2i200−2i2i2-2000000000000−i2i2002−200
χ3522-22-22-2-20-20-2020200−2i−2i2i2i−2−2220000−2−222i2i2−i2−i2i2i2−i2−i2002i−2i-22000000000000−i2i2002−200
χ3622-22-22-2-20-20-2020200−2i−2i2i2i−2−2220000−2−222i2i2−i2−i2i2i2−i2−i200−2i2i2-2000000000000i2−i200−2200
χ372-222-2-22-2-20-202020002−22−22i−2i2i−2i22−2−20000i2−i2i2−i2i2−i2i2−i22-200002i−2i000000002−200i2−i20000
χ382-222-2-22-2-20-202020002−22−22i−2i2i−2i22−2−20000i2−i2i2−i2i2−i2i2−i2-220000−2i2i00000000−2200−i2i20000
χ392-222-2-22-2-20-202020002−22−2−2i2i−2i2i22−2−20000−i2i2−i2i2−i2i2−i2i22-20000−2i2i000000002−200−i2i20000
χ402-222-2-22-2-20-202020002−22−2−2i2i−2i2i22−2−20000−i2i2−i2i2−i2i2−i2i2-2200002i−2i00000000−2200i2−i20000
χ412-222-2-22-2-20-20202000−22−222i−2i2i−2i−2−2220000−i2i2−i2i2−i2i2−i2i22-200002i−2i00000000−2200−i2i20000
χ422-222-2-22-2-20-20202000−22−222i−2i2i−2i−2−2220000−i2i2−i2i2−i2i2−i2i2-220000−2i2i000000002−200i2−i20000
χ432-222-2-22-2-20-20202000−22−22−2i2i−2i2i−2−2220000i2−i2i2−i2i2−i2i2−i22-20000−2i2i00000000−2200i2−i20000
χ442-222-2-22-2-20-20202000−22−22−2i2i−2i2i−2−2220000i2−i2i2−i2i2−i2i2−i2-2200002i−2i000000002−200−i2i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ47444-44-4-4-44-4-444-4-444-400000000000000000000000000000000000000000000000000
χ48444-44-4-4-4-444-4-444-44-400000000000000000000000000000000000000000000000000
χ4944-44-44-4-404040-40-40000002222−22−220000−22−2222220000000000000000000000000000000000
χ5044-44-44-4-404040-40-4000000−22−22222200002222−22−220000000000000000000000000000000000
χ5144-4-4-4-444040-40-4040000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5244-4-4-4-444040-40-404000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5344-4-4-4-4440-404040-400000000004i−4i4i−4i00000000000000000000000000000000000000
χ5444-4-4-4-4440-404040-40000000000−4i4i−4i4i00000000000000000000000000000000000000
χ554-444-4-44-44040-40-400022−2222−220000−22−22222200000000000000000000000000000000000000
χ564-444-4-44-44040-40-4000−2222−222200002222−22−2200000000000000000000000000000000000000
χ574-44-4-44-4440-40-40400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ584-44-4-44-4440-40-4040000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ594-44-4-44-44-404040-40000000000000004i−4i4i−4i0000000000000000000000000000000000
χ604-44-4-44-44-404040-4000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ614-4-444-4-4400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000-222-2-222-200000000000000000000000000
χ624-4-444-4-4400000000002i2−2i2−2i22i2−2i22i22i2−2i2000000002-2-222-2-2200000000000000000000000000
χ634-4-444-4-440000000000−2i22i22i2−2i22i2−2i2−2i22i2000000002-2-222-2-2200000000000000000000000000
χ644-4-444-4-440000000000−2i22i22i2−2i2−2i22i22i2−2i200000000-222-2-222-200000000000000000000000000
χ654-4-4-4444-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i22-2-22-222-200000000000000000000000000
χ664-4-4-4444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2-222-22-2-2200000000000000000000000000
χ674-4-4-4444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2-222-22-2-2200000000000000000000000000
χ684-4-4-4444-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i22-2-22-222-200000000000000000000000000

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