Finite Group Databasebeta

← Group #288384

Character table — Group #288384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1111-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-111-1-111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-111-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-11-1-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-11-1-11111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11111-1-111-1-111-1-1-11
χ172222222222-2-2-222-2-2-2000000002222-2-2-2-20000000022-2-20000200-200000000000000
χ182222222222-2-2-222-2-2-2000000002222-2-2-2-200000000-2-2220000-200200000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-222220000000022-2-20000-200200000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-2222200000000-2-2220000200-200000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-20000000000000000000022-2-20-22000000000000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-200000000000000000000-2-22202-2000000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-222220000000000000000000022220-2-2000000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2222200000000000000000000-2-2-2-2022000000000000000
χ2522-2-2-2-222222-22-2-2-2-2200000000000000002222-2-2-2-22i−2i2i−2i000000000000002i−2i000000
χ2622-2-2-2-222222-22-2-2-2-2200000000000000002222-2-2-2-2−2i2i−2i2i00000000000000−2i2i000000
χ2722-2-2-2-222222-22-2-2-2-220000000000000000-2-2-2-222222i−2i2i−2i00000000000000−2i2i000000
χ2822-2-2-2-222222-22-2-2-2-220000000000000000-2-2-2-22222−2i2i−2i2i000000000000002i−2i000000
χ2922-2-2-2-22222-22-2-2-222-222-2-222-2-200000000000000002i−2i−2i2i0000000000002i−2i00000000
χ3022-2-2-2-22222-22-2-2-222-222-2-222-2-20000000000000000−2i2i2i−2i000000000000−2i2i00000000
χ3122-2-2-2-22222-22-2-2-222-2-2-222-2-22200000000000000002i−2i−2i2i000000000000−2i2i00000000
χ3222-2-2-2-22222-22-2-2-222-2-2-222-2-2220000000000000000−2i2i2i−2i0000000000002i−2i00000000
χ3322-2-2-2-222-2-2-22-2222-2222-2-2-2-22200000000000000000000000000002-22-20000000000
χ3422-2-2-2-222-2-2-22-2222-2222-2-2-2-2220000000000000000000000000000-22-220000000000
χ3522-2-2-2-222-2-2-22-2222-22-2-22222-2-200000000000000000000000000002-2-220000000000
χ3622-2-2-2-222-2-2-22-2222-22-2-22222-2-20000000000000000000000000000-222-20000000000
χ372-222-2-2-22002-2-20020000002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i0000000000002−22−200
χ382-222-2-2-22002-2-20020000002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i000000000000−22−2200
χ392-222-2-2-22002-2-20020000002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i000000000000−22−2200
χ402-222-2-2-22002-2-20020000002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i0000000000002−22−200
χ412-222-2-2-22002-2-2002000000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i0000000000002−2−2200
χ422-222-2-2-22002-2-2002000000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i000000000000−222−200
χ432-222-2-2-22002-2-2002000000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i000000000000−222−200
χ442-222-2-2-22002-2-2002000000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i0000000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-44-40004-4000000000000000000022−2222−2222−2222−2200000000000000000000000000
χ47444-44-4-4-44-40004-40000000000000000000−2222−2222−2222−222200000000000000000000000000
χ48444-44-4-4-4-44000-440000000000000004-44-40000000000000000000000000000000000
χ49444-44-4-4-4-44000-44000000000000000-44-440000000000000000000000000000000000
χ5044-44-44-4-44-4000-44000000000000000000022−2222−22−2222−222200000000000000000000000000
χ5144-44-44-4-44-4000-440000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5244-44-44-4-4-440004-4000000000004-44-400000000000000000000000000000000000000
χ5344-44-44-4-4-440004-400000000000-44-4400000000000000000000000000000000000000
χ5444-4-4-4-444-4-44-4444-44-400000000000000000000000000000000000000000000000000
χ554-444-4-4-4400-44400-400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ564-444-4-4-4400-44400-40000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ574-44-4-444-4000000000022−2222−22000000002i2−2i2−2i22i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ584-44-4-444-4000000000022−2222−2200000000−2i22i22i2−2i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ594-44-4-444-40000000000−2222−2222000000002i2−2i2−2i22i2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ604-44-4-444-40000000000−2222−222200000000−2i22i22i2−2i22i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ614-4-444-44-4000000000022−22−222200002i2−2i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-4-444-44-4000000000022−22−22220000−2i22i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ634-4-444-44-40000000000−222222−2200002i2−2i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ644-4-444-44-40000000000−222222−220000−2i22i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ654-4-4-444-440044-400-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ664-4-4-444-440044-400-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ674-4-4-444-4400-4-440040000004-4-44000000000000000000000000000000000000000000
χ684-4-4-444-4400-4-44004000000-444-4000000000000000000000000000000000000000000

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