Finite Group Databasebeta

← Group #345110

Character table — Group #345110

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-111-1-111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1-111-1-1-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-11-1111-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111-11-111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1111-111111-1-111-1-1-1-1
χ1722222222222-2-2-2-22-2-2000000002222-2-2-2-20000000022220000-200-200000000000000
χ1822222222222-2-2-2-22-2-2000000002222-2-2-2-200000000-2-2-2-20000200200000000000000
χ1922222222222-2-2-2-22-2-200000000-2-2-2-222220000000022-2-20000-200200000000000000
χ2022222222222-2-2-2-22-2-200000000-2-2-2-2222200000000-2-2220000200-200000000000000
χ2122222222-2-2-22222-2-2-22222-2-2-2-20000000000000000000022220000-2-2000000000000
χ2222222222-2-2-22222-2-2-22222-2-2-2-200000000000000000000-2-2-2-2000022000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-222220000000000000000000022-2-20000-22000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2222200000000000000000000-2-22200002-2000000000000
χ25222-22-2-2-22-2-2000020022−2−222−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22i−2i2-2000000000000i2−i22−2000000
χ26222-22-2-2-22-2-2000020022−2−222−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2−2i2i-22000000000000−i2i2−22000000
χ27222-22-2-2-22-2-2000020022−2−222−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22i−2i-22000000000000i2−i2−22000000
χ28222-22-2-2-22-2-2000020022−2−222−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2−2i2i2-2000000000000−i2i22−2000000
χ29222-22-2-2-22-2-20000200−2−222−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i22i−2i2-2000000000000−i2i2−22000000
χ30222-22-2-2-22-2-20000200−2−222−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2i2i-22000000000000i2−i22−2000000
χ31222-22-2-2-22-2-20000200−2−222−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i22i−2i-22000000000000−i2i22−2000000
χ32222-22-2-2-22-2-20000200−2−222−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2i2i2-2000000000000i2−i2−22000000
χ332-222-2-22-222-2-2-222-2-22000000000000000022-2-222-2-20000000002i−2i0002i−2i0000000000
χ342-222-2-22-222-2-2-222-2-22000000000000000022-2-222-2-2000000000−2i2i000−2i2i0000000000
χ352-222-2-22-222-2-2-222-2-220000000000000000-2-222-2-2220000000002i−2i000−2i2i0000000000
χ362-222-2-22-222-2-2-222-2-220000000000000000-2-222-2-222000000000−2i2i0002i−2i0000000000
χ372-2-2222-2-20002-22-20002-22-20000i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200002-22-2000000000000i2−i2i2−i200
χ382-2-2222-2-20002-22-20002-22-20000i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000-22-22000000000000−i2i2−i2i200
χ392-2-2222-2-20002-22-20002-22-20000−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200002-22-2000000000000−i2i2−i2i200
χ402-2-2222-2-20002-22-20002-22-20000−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000-22-22000000000000i2−i2i2−i200
χ412-2-2222-2-20002-22-2000-22-220000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200002-2-22000000000000i2−i2−i2i200
χ422-2-2222-2-20002-22-2000-22-220000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000-222-2000000000000−i2i2i2−i200
χ432-2-2222-2-20002-22-2000-22-220000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200002-2-22000000000000−i2i2i2−i200
χ442-2-2222-2-20002-22-2000-22-220000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000-222-2000000000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-4-4440000-4002222−22−22−22−222222000000000000000000000000000000000000000000
χ47444-44-4-4-4-4440000-400−22−2222222222−22−22000000000000000000000000000000000000000000
χ4844-44-4-4-440004-4-4400000004i−4i4i−4i000000000000000000000000000000000000000000
χ4944-44-4-4-440004-4-440000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5044-44-4-4-44000-444-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5144-44-4-4-44000-444-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5244-4-4-444-4000000000000002i2−2i2−2i22i200002i2−2i22i2−2i22-2-22-222-200000000000000000000000000
χ5344-4-4-444-4000000000000002i2−2i2−2i22i20000−2i22i2−2i22i2-222-22-2-2200000000000000000000000000
χ5444-4-4-444-400000000000000−2i22i22i2−2i200002i2−2i22i2−2i2-222-22-2-2200000000000000000000000000
χ5544-4-4-444-400000000000000−2i22i22i2−2i20000−2i22i2−2i22i22-2-22-222-200000000000000000000000000
χ564-444-4-44-444-444-4-4-44-400000000000000000000000000000000000000000000000000
χ574-444-4-44-4-4-4444-4-44-4400000000000000000000000000000000000000000000000000
χ584-444-4-44-4-4-44-4-44444-400000000000000000000000000000000000000000000000000
χ594-44-4-44-444-440000-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ604-44-4-44-444-440000-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ614-44-4-44-44-44-400004000000000000004-4-440000000000000000000000000000000000
χ624-44-4-44-44-44-40000400000000000000-444-40000000000000000000000000000000000
χ634-4-4444-4-4000-44-44000000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ644-4-4444-4-4000-44-4400000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ654-4-4-44-444000000000022−22−2222000022−22−222200002-22-2-22-2200000000000000000000000000
χ664-4-4-44-444000000000022−22−22220000−222222−220000-22-222-22-200000000000000000000000000
χ674-4-4-44-4440000000000−222222−22000022−22−22220000-22-222-22-200000000000000000000000000
χ684-4-4-44-4440000000000−222222−220000−222222−2200002-22-2-22-2200000000000000000000000000

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