Finite Group Databasebeta

← Group #344144

Character table — Group #344144

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1111111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-111-1-11111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111111-1-1-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-1-11-1-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-1111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-11-11-1-111-1-111-1-111
χ172222222222-22-2-2-22-2-2000022220000-2-2-2-20000000022-2-20000-200200000000000000
χ182222222222-22-2-2-22-2-2000022220000-2-2-2-200000000-2-2220000200-200000000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-2000022220000000022220000-200-200000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000222200000000-2-2-2-20000200200000000000000
χ2122222222-2-22-2222-2-2-222220000-2-2-2-2000000000000000022220000-2-2000000000000
χ2222222222-2-22-2222-2-2-222220000-2-2-2-20000000000000000-2-2-2-2000022000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-200002222000000000000000022-2-20000-22000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000022220000000000000000-2-22200002-2000000000000
χ2522-22-2-2-2200-2022-200022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ2622-22-2-2-2200-2022-200022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ2722-22-2-2-2200-2022-200022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ2822-22-2-2-2200-2022-200022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ2922-22-2-2-2200-2022-2000-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-22000000000000i2−i2−i2i200
χ3022-22-2-2-2200-2022-2000-2-222i2i2−i2−i20000i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-2000000000000−i2i2i2−i200
χ3122-22-2-2-2200-2022-2000-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ3222-22-2-2-2200-2022-2000-2-222−i2−i2i2i20000−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ332-2222-2-2-2-2-222-22-222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000002-20002i−2i0000000000
χ342-2222-2-2-2-2-222-22-222-200000000000000002i2i−2i−2i2i2i−2i−2i000000000-22000−2i2i0000000000
χ352-2222-2-2-2-2-222-22-222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000002-2000−2i2i0000000000
χ362-2222-2-2-2-2-222-22-222-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000-220002i−2i0000000000
χ372-22-2-22-222-202000-2002−22−2000022−2−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i22-22i−2i0000000000002−2i2−i2000000
χ382-22-2-22-222-202000-2002−22−2000022−2−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2-22−2i2i000000000000−22−i2i2000000
χ392-22-2-22-222-202000-2002−22−2000022−2−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22-2−2i2i0000000000002−2−i2i2000000
χ402-22-2-22-222-202000-2002−22−2000022−2−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2-222i−2i000000000000−22i2−i2000000
χ412-22-2-22-222-202000-200−22−220000−2−2222i−2i2i−2i−i2i2−i2i2−i2i2−i2i22-22i−2i000000000000−22−i2i2000000
χ422-22-2-22-222-202000-200−22−220000−2−2222i−2i2i−2i−i2i2−i2i2−i2i2−i2i2-22−2i2i0000000000002−2i2−i2000000
χ432-22-2-22-222-202000-200−22−220000−2−222−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22-2−2i2i000000000000−22i2−i2000000
χ442-22-2-22-222-202000-200−22−220000−2−222−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2-222i−2i0000000000002−2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-44-40-400040000004i−4i4i−4i000000000000000000000000000000000000000000
χ47444-4-4-44-44-40-40004000000−4i4i−4i4i000000000000000000000000000000000000000000
χ48444-4-4-44-4-4404000-400000000000000000022−22−222222−22−222200000000000000000000000000
χ49444-4-4-44-4-4404000-4000000000000000000−222222−22−222222−2200000000000000000000000000
χ5044-44-4-4-440040-4-4400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ5144-44-4-4-440040-4-440000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ5244-4-444-4-40000000000000022−22−22222i2−2i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-444-4-40000000000000022−22−2222−2i22i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-444-4-400000000000000−222222−222i2−2i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-444-4-400000000000000−222222−22−2i22i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-4444-4-4-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000
χ574-4444-4-4-444-4-44-44-44-400000000000000000000000000000000000000000000000000
χ584-4444-4-4-4-4-4-444-444-4400000000000000000000000000000000000000000000000000
χ594-44-4-44-44-440-400040022−2222−220000−22−22222200000000000000000000000000000000000000
χ604-44-4-44-44-440-4000400−2222−222200002222−22−2200000000000000000000000000000000000000
χ614-4-44-444-400404-4-4000000000004i−4i−4i4i00000000000000000000000000000000000000
χ624-4-44-444-400404-4-400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ634-4-44-444-400-40-44400000000000000000002222−22−22−22−22222200000000000000000000000000
χ644-4-44-444-400-40-4440000000000000000000−22−2222222222−22−2200000000000000000000000000
χ654-4-4-44-444000000000022−22−22220000000022−22−22222-22-2-22-2200000000000000000000000000
χ664-4-4-44-444000000000022−22−222200000000−222222−22-22-222-22-200000000000000000000000000
χ674-4-4-44-4440000000000−222222−220000000022−22−2222-22-222-22-200000000000000000000000000
χ684-4-4-44-4440000000000−222222−2200000000−222222−222-22-2-22-2200000000000000000000000000

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