Finite Group Databasebeta

← Group #345560

Character table — Group #345560

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-11-1-111-1-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111111111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-11111-1-1111-1
χ9111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-111-1-1-1-1-1-1-11
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-111111-1
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-111-1-111-1-1-1-11-1
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1111111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-11111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-11-1-1-1-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-1-1-1-1-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-11111111-1-111-1-1-1-1
χ172222222222-2-22-2-22-2-2222200000000-2-2-2-200000000220000-2-2-220000000000000000
χ182222222222-2-22-2-22-2-2222200000000-2-2-2-200000000-2-20000222-20000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000000022220000000022000022-2-20000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-200000000222200000000-2-20000-2-2220000000000000000
χ2122222222-2-222-222-2-2-200002222-2-2-2-20000000000000022220000-2-200000000000000
χ2222222222-2-222-222-2-2-200002222-2-2-2-200000000000000-2-2-2-200002200000000000000
χ2322222222-2-222-222-2-2-20000-2-2-2-222220000000000000022-2-20000-2200000000000000
χ2422222222-2-222-222-2-2-20000-2-2-2-2222200000000000000-2-22200002-200000000000000
χ25222-2-2-22-22222-2-2-2-2-2200000000000000002222-2-2-2-20000000000002-22-20000000000
χ26222-2-2-22-22222-2-2-2-2-2200000000000000002222-2-2-2-2000000000000-22-220000000000
χ27222-2-2-22-22222-2-2-2-2-220000000000000000-2-2-2-222220000000000002-2-220000000000
χ28222-2-2-22-22222-2-2-2-2-220000000000000000-2-2-2-22222000000000000-222-20000000000
χ2922-2-222-2-22-200-200200000022−2−222−2−222-2-222−2−222−2−22i−2i00002i−2i00000000i2−i2i2−i2000000
χ3022-2-222-2-22-200-200200000022−2−222−2−222-2-222−2−222−2−2−2i2i0000−2i2i00000000−i2i2−i2i2000000
χ3122-2-222-2-22-200-200200000022−2−222−2−2-2-222−2−222−2−2222i−2i0000−2i2i00000000i2−i2−i2i2000000
χ3222-2-222-2-22-200-200200000022−2−222−2−2-2-222−2−222−2−222−2i2i00002i−2i00000000−i2i2i2−i2000000
χ3322-2-222-2-22-200-2002000000−2−222−2−22222-2-2−2−222−2−2222i−2i00002i−2i00000000−i2i2−i2i2000000
χ3422-2-222-2-22-200-2002000000−2−222−2−22222-2-2−2−222−2−222−2i2i0000−2i2i00000000i2−i2i2−i2000000
χ3522-2-222-2-22-200-2002000000−2−222−2−222-2-22222−2−222−2−22i−2i0000−2i2i00000000−i2i2i2−i2000000
χ3622-2-222-2-22-200-2002000000−2−222−2−222-2-22222−2−222−2−2−2i2i00002i−2i00000000i2−i2−i2i2000000
χ372-2-222-22-2002-202-2000i2i2−i2−i22i−2i2i−2i0000i2−i2i2−i22−22−22−22−2002-22i−2i00000000000000i2−i22−200
χ382-2-222-22-2002-202-2000i2i2−i2−i22i−2i2i−2i0000i2−i2i2−i22−22−22−22−200-22−2i2i00000000000000−i2i2−2200
χ392-2-222-22-2002-202-2000i2i2−i2−i2−2i2i−2i2i0000i2−i2i2−i2−22−22−22−22002-2−2i2i00000000000000i2−i2−2200
χ402-2-222-22-2002-202-2000i2i2−i2−i2−2i2i−2i2i0000i2−i2i2−i2−22−22−22−2200-222i−2i00000000000000−i2i22−200
χ412-2-222-22-2002-202-2000−i2−i2i2i22i−2i2i−2i0000−i2i2−i2i2−22−22−22−22002-22i−2i00000000000000−i2i2−2200
χ422-2-222-22-2002-202-2000−i2−i2i2i22i−2i2i−2i0000−i2i2−i2i2−22−22−22−2200-22−2i2i00000000000000i2−i22−200
χ432-2-222-22-2002-202-2000−i2−i2i2i2−2i2i−2i2i0000−i2i2−i2i22−22−22−22−2002-2−2i2i00000000000000−i2i22−200
χ442-2-222-22-2002-202-2000−i2−i2i2i2−2i2i−2i2i0000−i2i2−i2i22−22−22−22−200-222i−2i00000000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-444-4-4-444-44-400000000000000000000000000000000000000000000000000
χ47444-4-4-44-4-4-4444-4-444-400000000000000000000000000000000000000000000000000
χ48444-4-4-44-4-4-4-4-44444-4400000000000000000000000000000000000000000000000000
χ4944-44-4-4-444-400400-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ5044-44-4-4-444-400400-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5144-44-4-4-44-4400-4004004i−4i4i−4i0000000000000000000000000000000000000000000000
χ5244-44-4-4-44-4400-400400−4i4i−4i4i0000000000000000000000000000000000000000000000
χ5344-4-444-4-4-4400400-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5444-4-444-4-4-4400400-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ554-444-44-4-4000000000022−22−2222000022−2222−2200002-2-22-222-200000000000000000000000000
χ564-444-44-4-4000000000022−22−22220000−2222−22220000-222-22-2-2200000000000000000000000000
χ574-444-44-4-40000000000−222222−22000022−2222−220000-222-22-2-2200000000000000000000000000
χ584-444-44-4-40000000000−222222−220000−2222−222200002-2-22-222-200000000000000000000000000
χ594-44-44-4-44000000000000002i2−2i2−2i22i200002i2−2i2−2i22i22-2-222-2-2200000000000000000000000000
χ604-44-44-4-44000000000000002i2−2i2−2i22i20000−2i22i22i2−2i2-222-2-222-200000000000000000000000000
χ614-44-44-4-4400000000000000−2i22i22i2−2i200002i2−2i2−2i22i2-222-2-222-200000000000000000000000000
χ624-44-44-4-4400000000000000−2i22i22i2−2i20000−2i22i22i2−2i22-2-222-2-2200000000000000000000000000
χ634-4-444-44-400-440-440002i22i2−2i2−2i200000000−2i22i2−2i22i20000000000000000000000000000000000
χ644-4-444-44-400-440-44000−2i2−2i22i22i2000000002i2−2i22i2−2i20000000000000000000000000000000000
χ654-4-4-4-4444004-40-44000000000000000000022−2222−22−2222−222200000000000000000000000000
χ664-4-4-4-4444004-40-440000000000000000000−2222−222222−2222−2200000000000000000000000000
χ674-4-4-4-444400-4404-4000000000004-4-4400000000000000000000000000000000000000
χ684-4-4-4-444400-4404-400000000000-444-400000000000000000000000000000000000000

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