Finite Group Databasebeta

← Group #343530

Character table — Group #343530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11111-1-1-1-111-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-111111111-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111-1-1-11111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1-11111-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-11111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11111111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-11-11-1-1-1-11111-1-1-1-111
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000002222-2-20000000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-2000000000000-2-2-2-2220000000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-20000222200000000000022-2-2-220000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200002222000000000000-2-2222-20000000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-20000000000002222000000-2-200000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-2-2-20000002200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000222200000000000022-2-2000000-2200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-2220000002-200000000000000
χ25222-2-2-22-2-20-2020200022−2−22i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i200002i−2i2-20000000000i2−i2002−200
χ26222-2-2-22-2-20-2020200022−2−22i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i20000−2i2i-220000000000−i2i200−2200
χ27222-2-2-22-2-20-2020200022−2−2−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i200002i−2i-220000000000i2−i200−2200
χ28222-2-2-22-2-20-2020200022−2−2−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i20000−2i2i2-20000000000−i2i2002−200
χ29222-2-2-22-2-20-20202000−2−2222i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i200002i−2i2-20000000000−i2i200−2200
χ30222-2-2-22-2-20-20202000−2−2222i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i20000−2i2i-220000000000i2−i2002−200
χ31222-2-2-22-2-20-20202000−2−222−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i200002i−2i-220000000000−i2i2002−200
χ32222-2-2-22-2-20-20202000−2−222−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i20000−2i2i2-20000000000i2−i200−2200
χ3322-2-2-22-220-202020-2002-22-2i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0000000000002−2002−20000
χ3422-2-2-22-220-202020-2002-22-2i2−i2i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i000000000000−2200−220000
χ3522-2-2-22-220-202020-2002-22-2−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i2i−2i000000000000−2200−220000
χ3622-2-2-22-220-202020-2002-22-2−i2i2−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0000000000002−2002−20000
χ3722-2-2-22-220-202020-200-22-22i2−i2i2−i20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i−2i2i0000000000002−200−220000
χ3822-2-2-22-220-202020-200-22-22i2−i2i2−i20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i2i−2i000000000000−22002−20000
χ3922-2-2-22-220-202020-200-22-22−i2i2−i2i20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i−2i2i000000000000−22002−20000
χ4022-2-2-22-220-202020-200-22-22−i2i2−i2i20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i2i−2i0000000000002−200−220000
χ412-222-22-2-2-2-222-2-222-2200000000000000002-22-22-22-20000000000002i−2i2i−2i0000000000
χ422-222-22-2-2-2-222-2-222-2200000000000000002-22-22-22-2000000000000−2i2i−2i2i0000000000
χ432-222-22-2-2-2-222-2-222-220000000000000000-22-22-22-220000000000002i−2i−2i2i0000000000
χ442-222-22-2-2-2-222-2-222-220000000000000000-22-22-22-22000000000000−2i2i2i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-40002222−22−220000−22−22222200000000000000000000000000000000000000
χ47444-4-4-44-44040-40-4000−22−22222200002222−22−2200000000000000000000000000000000000000
χ4844-444-4-4-4000000000022−22−222222−22−22220000000022-2-2-2-22200000000000000000000000000
χ4944-444-4-4-4000000000022−22−2222−222222−2200000000-2-22222-2-200000000000000000000000000
χ5044-444-4-4-40000000000−222222−2222−22−222200000000-2-22222-2-200000000000000000000000000
χ5144-444-4-4-40000000000−222222−22−222222−220000000022-2-2-2-22200000000000000000000000000
χ5244-4-4-44-44040-40-4040000002i2−2i22i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ5344-4-4-44-44040-40-404000000−2i22i2−2i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ544-444-44-4-444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ554-444-44-4-44-4-444-4-444-400000000000000000000000000000000000000000000000000
χ564-444-44-4-4-444-4-444-44-400000000000000000000000000000000000000000000000000
χ574-44-44-4-4440-40-40400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ584-44-44-4-4440-40-4040000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ594-44-44-4-44-404040-40000000000000004i−4i4i−4i0000000000000000000000000000000000
χ604-44-44-4-44-404040-4000000000000000−4i4i−4i4i0000000000000000000000000000000000
χ614-4-44-4-44400000000000000000022−2222−2222−22−22222-2-22-222-200000000000000000000000000
χ624-4-44-4-44400000000000000000022−2222−22−222222−22-222-22-2-2200000000000000000000000000
χ634-4-44-4-444000000000000000000−2222−222222−22−2222-222-22-2-2200000000000000000000000000
χ644-4-44-4-444000000000000000000−2222−2222−222222−222-2-22-222-200000000000000000000000000
χ654-4-4-4444-404040-40-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ664-4-4-4444-404040-40-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ674-4-4-4444-40-40-4040400000000004-4-4400000000000000000000000000000000000000
χ684-4-4-4444-40-40-404040000000000-444-400000000000000000000000000000000000000

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