Finite Group Databasebeta

← Group #336854

Character table — Group #336854

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-11111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ61111111111111111111111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-11111-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-1111-1-1
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11
χ11111111111111111111-1-1-1-11111-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ172222222222-22-2-2-22-2-200002222000022-2-2002200-2-20000000000000-2000000000
χ182222222222-22-2-2-22-2-2000022220000-2-22200-2-200-2-200000000000002000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-20000222200-2-200220000000000000-2000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000-2-2-2-20022002200000000000002000000000
χ2122222222-2-22-2222-2-2-22222000022-2-20000-2-200-2-20000000000000020000000000
χ2222222222-2-22-2222-2-2-222220000-2-22200002200-2-200000000000000-20000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022220000-2-2002200000000000000-20000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-20000-2-2-2-200002200220000000000000020000000000
χ2522-22-22-2-200-202-220002i2i−2i−2i22−2−2002-200002i−2i00002−20000i2i2−i2−i2i2i2−i2−i20000002−2000
χ2622-22-22-2-200-202-220002i2i−2i−2i22−2−200-220000−2i2i00002−20000−i2−i2i2i2i2i2−i2−i2000000−22000
χ2722-22-22-2-200-202-220002i2i−2i−2i−2−222002-200002i−2i0000−220000−i2−i2i2i2−i2−i2i2i2000000−22000
χ2822-22-22-2-200-202-220002i2i−2i−2i−2−22200-220000−2i2i0000−220000i2i2−i2−i2−i2−i2i2i20000002−2000
χ2922-22-22-2-200-202-22000−2i−2i2i2i22−2−2002-20000−2i2i00002−20000−i2−i2i2i2−i2−i2i2i20000002−2000
χ3022-22-22-2-200-202-22000−2i−2i2i2i22−2−200-2200002i−2i00002−20000i2i2−i2−i2−i2−i2i2i2000000−22000
χ3122-22-22-2-200-202-22000−2i−2i2i2i−2−222002-20000−2i2i0000−220000i2i2−i2−i2i2i2−i2−i2000000−22000
χ3222-22-22-2-200-202-22000−2i−2i2i2i−2−22200-2200002i−2i0000−220000−i2−i2i2i2i2i2−i2−i20000002−2000
χ3322-2-22-22-22-20-20002002−22−22-22-200002i−2i00002i−2i2−200i2i2−i2−i200002−22−20000i2−i200000
χ3422-2-22-22-22-20-20002002−22−22-22-20000−2i2i0000−2i2i2−200−i2−i2i2i200002−22−20000−i2i200000
χ3522-2-22-22-22-20-20002002−22−2-22-2200002i−2i0000−2i2i2−200−i2−i2i2i20000−22−220000i2−i200000
χ3622-2-22-22-22-20-20002002−22−2-22-220000−2i2i00002i−2i2−200i2i2−i2−i20000−22−220000−i2i200000
χ3722-2-22-22-22-20-2000200−22−222-22-200002i−2i00002i−2i−2200−i2−i2i2i20000−22−220000−i2i200000
χ3822-2-22-22-22-20-2000200−22−222-22-20000−2i2i0000−2i2i−2200i2i2−i2−i20000−22−220000i2−i200000
χ3922-2-22-22-22-20-2000200−22−22-22-2200002i−2i0000−2i2i−2200i2i2−i2−i200002−22−20000−i2i200000
χ4022-2-22-22-22-20-2000200−22−22-22-220000−2i2i00002i−2i−2200−i2−i2i2i200002−22−20000i2−i200000
χ412-22-2-222-2-2-2-2222-222-20000000000000000000000002i−2i2i−2i2-22-20000002i−2i0000000
χ422-22-2-222-2-2-2-2222-222-20000000000000000000000002i−2i2i−2i-22-22000000−2i2i0000000
χ432-22-2-222-2-2-2-2222-222-2000000000000000000000000−2i2i−2i2i2-22-2000000−2i2i0000000
χ442-22-2-222-2-2-2-2222-222-2000000000000000000000000−2i2i−2i2i-22-220000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-4400000000002i2−2i2−2i22i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ47444-4-4-4-4400000000002i2−2i2−2i22i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ48444-4-4-4-440000000000−2i22i22i2−2i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ49444-4-4-4-440000000000−2i22i22i2−2i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ5044-44-44-4-40040-44-400000002222−22−2200000000000000−222200000000000000000000000
χ5144-44-44-4-40040-44-40000000−22−2222220000000000000022−2200000000000000000000000
χ5244-4-44-44-4-4404000-40022−2222−220000000000000000−22220000000000000000000000000
χ5344-4-44-44-4-4404000-400−2222−2222000000000000000022−220000000000000000000000000
χ544-44-4-444-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ554-44-4-444-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ564-44-4-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000
χ574-4-44-4-4444-404000-400000000000000004i−4i0000000000000000000000000000000
χ584-4-44-4-4444-404000-40000000000000000−4i4i0000000000000000000000000000000
χ594-4-44-4-444-440-400040000000000000000000000000022−22−22220000000000000000000
χ604-4-44-4-444-440-4000400000000000000000000000000−222222−220000000000000000000
χ614-4-4-444-4400404-4-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-4-444-4400404-4-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-4-444-4400-40-444000000000004-40000000000000000000000000000000000000
χ644-4-4-444-4400-40-44400000000000-440000000000000000000000000000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000

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