Finite Group Databasebeta

← Group #343545

Character table — Group #343545

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-111-1-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-11-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111-1-1111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-111-11111-1-111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1-1111-1-1-1-111-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1-111-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-11111-1-11-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-111111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-111111-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-1-1-111111-1-1-1-111
χ17222222222-22-22-22-2-2-222220000-2-2-2-200000000000000222200-2000000-20000000000
χ18222222222-22-22-22-2-2-222220000-2-2-2-200000000000000-2-2-2-200200000020000000000
χ19222222222-22-22-22-2-2-2-2-2-2-2000022220000000000000022-2-200-200000020000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000222200000000000000-2-222002000000-20000000000
χ2122222222-22-22-22-22-2-2000022220000-2-2-2-200000000220000-2-20-22000000000000000
χ2222222222-22-22-22-22-2-2000022220000-2-2-2-200000000-2-200002202-2000000000000000
χ2322222222-22-22-22-22-2-20000-2-2-2-20000222200000000220000220-2-2000000000000000
χ2422222222-22-22-22-22-2-20000-2-2-2-20000222200000000-2-20000-2-2022000000000000000
χ25222-22-2-2-2-2-222-2-222-2200000000000000002222-2-2-2-2000000000002i−2i2i−2i00000000000
χ26222-22-2-2-2-2-222-2-222-2200000000000000002222-2-2-2-200000000000−2i2i−2i2i00000000000
χ27222-22-2-2-2-2-222-2-222-220000000000000000-2-2-2-22222000000000002i−2i−2i2i00000000000
χ28222-22-2-2-2-2-222-2-222-220000000000000000-2-2-2-2222200000000000−2i2i2i−2i00000000000
χ2922-22-22-2-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2−i2−i2i2i2−i2−i2002i−2i2-2000000000000i2−i2002−200
χ3022-22-22-2-2-20-202020002i2i−2i−2i22−2−2000022−2−2i2i2−i2−i2i2i2−i2−i200−2i2i-22000000000000−i2i200−2200
χ3122-22-22-2-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2i2i2−i2−i2i2i2002i−2i2-2000000000000−i2i200−2200
χ3222-22-22-2-2-20-202020002i2i−2i−2i−2−2220000−2−222−i2−i2i2i2−i2−i2i2i200−2i2i-22000000000000i2−i2002−200
χ3322-22-22-2-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2i2i2−i2−i2i2i2002i−2i-22000000000000i2−i200−2200
χ3422-22-22-2-2-20-20202000−2i−2i2i2i22−2−2000022−2−2−i2−i2i2i2−i2−i2i2i200−2i2i2-2000000000000−i2i2002−200
χ3522-22-22-2-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2−i2−i2i2i2−i2−i2002i−2i-22000000000000−i2i2002−200
χ3622-22-22-2-2-20-20202000−2i−2i2i2i−2−2220000−2−222i2i2−i2−i2i2i2−i2−i200−2i2i2-2000000000000i2−i200−2200
χ372-2-2-222-2202020-20-2002−22−2000022−2−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i22i−2i00002-200000000i2−i2002−20000
χ382-2-2-222-2202020-20-2002−22−2000022−2−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2−2i2i0000-2200000000−i2i200−220000
χ392-2-2-222-2202020-20-2002−22−2000022−2−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22i−2i0000-2200000000i2−i200−220000
χ402-2-2-222-2202020-20-2002−22−2000022−2−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2−2i2i00002-200000000−i2i2002−20000
χ412-2-2-222-2202020-20-200−22−220000−2−2222i−2i2i−2i−i2i2−i2i2−i2i2−i2i22i−2i00002-200000000−i2i200−220000
χ422-2-2-222-2202020-20-200−22−220000−2−2222i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−2i2i0000-2200000000i2−i2002−20000
χ432-2-2-222-2202020-20-200−22−220000−2−222−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22i−2i0000-2200000000−i2i2002−20000
χ442-2-2-222-2202020-20-200−22−220000−2−222−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−2i2i00002-200000000i2−i200−220000
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
χ4944-44-44-4-44040-40-400000002222−22−220000−22−2222220000000000000000000000000000000000
χ5044-44-44-4-44040-40-40000000−22−22222200002222−22−220000000000000000000000000000000000
χ5144-4-4-4-44440-40-40400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5244-4-4-4-44440-40-4040000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5344-4-4-4-444-404040-4000000000004i−4i4i−4i00000000000000000000000000000000000000
χ5444-4-4-4-444-404040-400000000000−4i4i−4i4i00000000000000000000000000000000000000
χ554-444-4-4-44000000000000002i2−2i22i2−2i22i2−2i2−2i22i200002-2-22-222-200000000000000000000000000
χ564-444-4-4-44000000000000002i2−2i22i2−2i2−2i22i22i2−2i20000-222-22-2-2200000000000000000000000000
χ574-444-4-4-4400000000000000−2i22i2−2i22i22i2−2i2−2i22i20000-222-22-2-2200000000000000000000000000
χ584-444-4-4-4400000000000000−2i22i2−2i22i2−2i22i22i2−2i200002-2-22-222-200000000000000000000000000
χ594-44-4-444-400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i2-222-2-222-200000000000000000000000000
χ604-44-4-444-400000000002i2−2i2−2i22i200000000−2i22i22i2−2i22-2-222-2-2200000000000000000000000000
χ614-44-4-444-40000000000−2i22i22i2−2i2000000002i2−2i2−2i22i22-2-222-2-2200000000000000000000000000
χ624-44-4-444-40000000000−2i22i22i2−2i200000000−2i22i22i2−2i2-222-2-222-200000000000000000000000000
χ634-4-444-44-4040-40-4040000004i−4i−4i4i000000000000000000000000000000000000000000
χ644-4-444-44-4040-40-404000000−4i4i4i−4i000000000000000000000000000000000000000000
χ654-4-444-44-40-404040-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ664-4-444-44-40-404040-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ674-4-4-444-440-40-404040022−2222−220000−22−22222200000000000000000000000000000000000000
χ684-4-4-444-440-40-4040400−2222−222200002222−22−2200000000000000000000000000000000000000

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