Finite Group Databasebeta

← Group #336785

Character table — Group #336785

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888824448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ61111111111111111111111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-1111-1-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11-1-111-1-11-11
χ172222222222-22-2-2-22-2-20000222200002200-2-22200-2-2000000000000-20000000000
χ182222222222-22-2-2-22-2-2000022220000-2-20022-2-200-2-200000000000020000000000
χ192222222222-22-2-2-22-2-20000-2-2-2-20000220022-2-20022000000000000-20000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-20000-2-200-2-222002200000000000020000000000
χ2122222222-2-22-2222-2-2-22222000022-2-200-2-20000-2-20000000000000002000000000
χ2222222222-2-22-2222-2-2-222220000-2-22200220000-2-2000000000000000-2000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022-2-20022000022000000000000000-2000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-20000-2-22200-2-20000220000000000000002000000000
χ25222-22-2-2-22-20-200020022−2−222-2-200002i−2i00002i−2i2−200i2i2−i2−i2000022−2−20000i2−i200000
χ26222-22-2-2-22-20-200020022−2−222-2-20000−2i2i0000−2i2i2−200−i2−i2i2i2000022−2−20000−i2i200000
χ27222-22-2-2-22-20-200020022−2−2-2-22200002i−2i0000−2i2i2−200−i2−i2i2i20000−2−2220000i2−i200000
χ28222-22-2-2-22-20-200020022−2−2-2-2220000−2i2i00002i−2i2−200i2i2−i2−i20000−2−2220000−i2i200000
χ29222-22-2-2-22-20-2000200−2−22222-2-200002i−2i00002i−2i−2200−i2−i2i2i20000−2−2220000−i2i200000
χ30222-22-2-2-22-20-2000200−2−22222-2-20000−2i2i0000−2i2i−2200i2i2−i2−i20000−2−2220000i2−i200000
χ31222-22-2-2-22-20-2000200−2−222-2-22200002i−2i0000−2i2i−2200i2i2−i2−i2000022−2−20000−i2i200000
χ32222-22-2-2-22-20-2000200−2−222-2-2220000−2i2i00002i−2i−2200−i2−i2i2i2000022−2−20000i2−i200000
χ332-222-2-22-2-2-2-2222-222-20000000000000000000000002i−2i2i−2i22-2-20000002i−2i0000000
χ342-222-2-22-2-2-2-2222-222-20000000000000000000000002i−2i2i−2i-2-222000000−2i2i0000000
χ352-222-2-22-2-2-2-2222-222-2000000000000000000000000−2i2i−2i2i22-2-2000000−2i2i0000000
χ362-222-2-22-2-2-2-2222-222-2000000000000000000000000−2i2i−2i2i-2-2220000002i−2i0000000
χ372-2-222-2-2200202-2-20002i−2i2i−2i2−22−2002i−2i002-20000002−20000i2−i2i2−i2i2−i2i2−i20000002−2000
χ382-2-222-2-2200202-2-20002i−2i2i−2i2−22−200−2i2i00-220000002−20000−i2i2−i2i2i2−i2i2−i2000000−22000
χ392-2-222-2-2200202-2-20002i−2i2i−2i−22−22002i−2i002-2000000−220000−i2i2−i2i2−i2i2−i2i2000000−22000
χ402-2-222-2-2200202-2-20002i−2i2i−2i−22−2200−2i2i00-22000000−220000i2−i2i2−i2−i2i2−i2i20000002−2000
χ412-2-222-2-2200202-2-2000−2i2i−2i2i2−22−2002i−2i00-220000002−20000i2−i2i2−i2−i2i2−i2i2000000−22000
χ422-2-222-2-2200202-2-2000−2i2i−2i2i2−22−200−2i2i002-20000002−20000−i2i2−i2i2−i2i2−i2i20000002−2000
χ432-2-222-2-2200202-2-2000−2i2i−2i2i−22−22002i−2i00-22000000−220000−i2i2−i2i2i2−i2i2−i20000002−2000
χ442-2-222-2-2200202-2-2000−2i2i−2i2i−22−2200−2i2i002-2000000−220000i2−i2i2−i2i2−i2i2−i2000000−22000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-44-4-4-4-4404000-4002222−22−220000000000000000−22220000000000000000000000000
χ47444-44-4-4-4-4404000-400−22−222222000000000000000022−220000000000000000000000000
χ4844-44-44-4-40040-44-4000000000004-40000000000000000000000000000000000000
χ4944-44-44-4-40040-44-400000000000-440000000000000000000000000000000000000
χ5044-44-44-4-400-404-4400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5144-44-44-4-400-404-440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ524-444-4-44-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ534-444-4-44-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ544-444-4-44-4-4-444-4-444-4400000000000000000000000000000000000000000000000
χ554-44-4-44-444-404000-40000000000000000004i−4i00000000000000000000000000000
χ564-44-4-44-444-404000-4000000000000000000−4i4i00000000000000000000000000000
χ574-44-4-44-44-440-400040000000000000000000000000022−22−22220000000000000000000
χ584-44-4-44-44-440-4000400000000000000000000000000−222222−220000000000000000000
χ594-4-444-4-4400-40-444000000022−2222−2200000000000000−222200000000000000000000000
χ604-4-444-4-4400-40-4440000000−2222−22220000000000000022−2200000000000000000000000
χ614-4-4-4444-400000000002i2−2i2−2i22i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ624-4-4-4444-400000000002i2−2i2−2i22i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ634-4-4-4444-40000000000−2i22i22i2−2i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ644-4-4-4444-40000000000−2i22i22i2−2i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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