Finite Group Databasebeta

← Group #309286

Character table — Group #309286

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111111-1-1-111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-111-111-1-11111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-111-1-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-111111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-11111-1-1111-1-111-1-1-11
χ172222222222-2-2-222-2-2-2000000002222-2-2-2-200000000000022-2-202-2000000000000000
χ182222222222-2-2-222-2-2-2000000002222-2-2-2-2000000000000-2-2220-22000000000000000
χ192222222222-2-2-222-2-2-200000000-2-2-2-2222200000000000022-2-20-22000000000000000
χ202222222222-2-2-222-2-2-200000000-2-2-2-22222000000000000-2-22202-2000000000000000
χ2122222222-2-2222-2-22-2-22222-2-2-2-2000000000000000022220000-2000000-20000000000
χ2222222222-2-2222-2-22-2-22222-2-2-2-20000000000000000-2-2-2-20000200000020000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-22222000000000000000022-2-20000-200000020000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-222220000000000000000-2-22200002000000-20000000000
χ25222-2-2-22-222-222-2-2-22-222-2-222-2-20000000000000000000000000002-22-200000000000
χ26222-2-2-22-222-222-2-2-22-222-2-222-2-2000000000000000000000000000-22-2200000000000
χ27222-2-2-22-222-222-2-2-22-2-2-222-2-2220000000000000000000000000002-2-2200000000000
χ28222-2-2-22-222-222-2-2-22-2-2-222-2-222000000000000000000000000000-222-200000000000
χ29222-2-2-22-2-2-22-2-22222-200000000000000002i2i2i2i−2i−2i−2i−2i00002i−2i2i−2i000000000000002-200
χ30222-2-2-22-2-2-22-2-22222-200000000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i−2i2i00000000000000-2200
χ31222-2-2-22-2-2-22-2-22222-20000000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i2i−2i00000000000000-2200
χ32222-2-2-22-2-2-22-2-22222-20000000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i−2i2i000000000000002-200
χ33222-2-2-22-2-2-2-22222-2-2222-2-2-2-222000000000000000000002i−2i−2i2i0000000000002i−2i0000
χ34222-2-2-22-2-2-2-22222-2-2222-2-2-2-22200000000000000000000−2i2i2i−2i000000000000−2i2i0000
χ35222-2-2-22-2-2-2-22222-2-22-2-22222-2-2000000000000000000002i−2i−2i2i000000000000−2i2i0000
χ36222-2-2-22-2-2-2-22222-2-22-2-22222-2-200000000000000000000−2i2i2i−2i0000000000002i−2i0000
χ372-2-22-2-2220022-200-2002-22-2000022−2−222−2−222−2−222−2−22i−2i2i−2i000000000000i2−i2i2−i2000000
χ382-2-22-2-2220022-200-2002-22-2000022−2−222−2−222−2−222−2−2−2i2i−2i2i000000000000−i2i2−i2i2000000
χ392-2-22-2-2220022-200-2002-22-20000−2−222−2−222−2−222−2−2222i−2i2i−2i000000000000−i2i2−i2i2000000
χ402-2-22-2-2220022-200-2002-22-20000−2−222−2−222−2−222−2−222−2i2i−2i2i000000000000i2−i2i2−i2000000
χ412-2-22-2-2220022-200-200-22-22000022−2−222−2−2−2−222−2−2222i−2i−2i2i000000000000i2−i2−i2i2000000
χ422-2-22-2-2220022-200-200-22-22000022−2−222−2−2−2−222−2−222−2i2i2i−2i000000000000−i2i2i2−i2000000
χ432-2-22-2-2220022-200-200-22-220000−2−222−2−22222−2−222−2−22i−2i−2i2i000000000000−i2i2i2−i2000000
χ442-2-22-2-2220022-200-200-22-220000−2−222−2−22222−2−222−2−2−2i2i2i−2i000000000000i2−i2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-4444-4-4-4-44-4400000000000000000000000000000000000000000000000000
χ4744-444-4-4-40000000000000022−2222−22000022−2222−222-22-22-22-200000000000000000000000000
χ4844-444-4-4-40000000000000022−2222−220000−2222−2222-22-22-22-2200000000000000000000000000
χ4944-444-4-4-400000000000000−2222−2222000022−2222−22-22-22-22-2200000000000000000000000000
χ5044-444-4-4-400000000000000−2222−22220000−2222−22222-22-22-22-200000000000000000000000000
χ5144-4-4-44-440000000000000022−22−22222i2−2i22i2−2i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4-44-440000000000000022−22−2222−2i22i2−2i22i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-4-44-4400000000000000−222222−222i2−2i22i2−2i20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5444-4-4-44-4400000000000000−222222−22−2i22i2−2i22i200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ554-444-44-4-44-40004-4000000000000000000022−22−222222−22−222200000000000000000000000000
χ564-444-44-4-44-40004-40000000000000000000−222222−22−222222−2200000000000000000000000000
χ574-444-44-4-4-44000-440000000000000004-4-440000000000000000000000000000000000
χ584-444-44-4-4-44000-44000000000000000-444-40000000000000000000000000000000000
χ594-44-44-4-444-4000-44000000000004i−4i−4i4i00000000000000000000000000000000000000
χ604-44-44-4-444-4000-4400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ614-44-44-4-44-440004-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ624-44-44-4-44-440004-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ634-4-44-4-44400-4-4400400000000002222−22−22−22−2222220000000000000000000000000000000000
χ644-4-44-4-44400-4-440040000000000−22−2222222222−22−220000000000000000000000000000000000
χ654-4-4-4444-4004-4400-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ664-4-4-4444-4004-4400-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ674-4-4-4444-400-44-4004004-4-440000000000000000000000000000000000000000000000
χ684-4-4-4444-400-44-400400-444-40000000000000000000000000000000000000000000000

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