Finite Group Databasebeta

← Group #344156

Character table — Group #344156

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-111-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-111-1-1-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111-1-1-111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11-1-1-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1-1-1-1-111-1-111-1-111
χ172222222222-2-2-222-2-2-2000000002222-2-2-2-200000000220022000-2-2000000000000000
χ182222222222-2-2-222-2-2-2000000002222-2-2-2-200000000-2-200-2-200022000000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-22222000000002200-2-2000-22000000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-2222200000000-2-200220002-2000000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-2000000000000000000220022-200-200000000000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-2000000000000000000-2-200-2-2200200000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-222220000000000000000002200-2-2200-200000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-22222000000000000000000-2-20022-200200000000000000
χ2522-22-22-2-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000002-22i−2i0000000000
χ2622-22-22-2-2-2-22-2222-22-200000000000000002i2i2i2i−2i−2i−2i−2i000000000000-22−2i2i0000000000
χ2722-22-22-2-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000002-2−2i2i0000000000
χ2822-22-22-2-2-2-22-2222-22-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000000-222i−2i0000000000
χ2922-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i22i2i−2i−2i000022−2−222−2−22-2002i−2i0000000000i2−i22−2000000
χ3022-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i22i2i−2i−2i000022−2−222−2−2-2200−2i2i0000000000−i2i2−22000000
χ3122-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−222−2−2222-200−2i2i0000000000i2−i2−22000000
χ3222-2-22-22-22-20002-2000i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−222−2−222-22002i−2i0000000000−i2i22−2000000
χ3322-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−222−2−2222-2002i−2i0000000000−i2i2−22000000
χ3422-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−222−2−222-2200−2i2i0000000000i2−i22−2000000
χ3522-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i000022−2−222−2−22-200−2i2i0000000000−i2i22−2000000
χ3622-2-22-22-22-20002-2000−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i000022−2−222−2−2-22002i−2i0000000000i2−i2−22000000
χ372-222-2-22-2002-2-2002002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−22−22−2002-2002i−2i000000000000i2−i22−200
χ382-222-2-22-2002-2-2002002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i22−22−22−22−200-2200−2i2i000000000000−i2i2−2200
χ392-222-2-22-2002-2-2002002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−22−22002-2002i−2i000000000000−i2i2−2200
χ402-222-2-22-2002-2-2002002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−22−2200-2200−2i2i000000000000i2−i22−200
χ412-222-2-22-2002-2-200200−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−22−22002-200−2i2i000000000000i2−i2−2200
χ422-222-2-22-2002-2-200200−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−22−2200-22002i−2i000000000000−i2i22−200
χ432-222-2-22-2002-2-200200−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−22−22−2002-200−2i2i000000000000−i2i22−200
χ442-222-2-22-2002-2-200200−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−22−22−200-22002i−2i000000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-444-4000-440000000000000004i−4i4i−4i0000000000000000000000000000000000
χ47444-4-4-4-444-4000-44000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ48444-4-4-4-44-440004-400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ49444-4-4-4-44-440004-40000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5044-44-44-4-4444-44-4-4-4-4400000000000000000000000000000000000000000000000000
χ5144-44-44-4-444-44-4-4-444-400000000000000000000000000000000000000000000000000
χ5244-44-44-4-4-4-4-44-4444-4400000000000000000000000000000000000000000000000000
χ5344-4-44-44-4-44000-440002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5444-4-44-44-4-44000-44000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ554-444-4-44-400-44400-400000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ564-444-4-44-400-44400-40000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ574-44-444-4-4000000000000002i2−2i22i2−2i2000022−22−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-44-444-4-4000000000000002i2−2i22i2−2i20000−222222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ594-44-444-4-400000000000000−2i22i2−2i22i2000022−22−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-44-444-4-400000000000000−2i22i2−2i22i20000−222222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ614-4-444-4-440044-400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ624-4-444-4-440044-400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ634-4-444-4-4400-4-440040000004-4-44000000000000000000000000000000000000000000
χ644-4-444-4-4400-4-44004000000-444-4000000000000000000000000000000000000000000
χ654-4-4-4-4444000000000022−22−2222000022−22−222200002-2-222-2-2200000000000000000000000000
χ664-4-4-4-4444000000000022−22−22220000−222222−220000-222-2-222-200000000000000000000000000
χ674-4-4-4-44440000000000−222222−22000022−22−22220000-222-2-222-200000000000000000000000000
χ684-4-4-4-44440000000000−222222−220000−222222−2200002-2-222-2-2200000000000000000000000000

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