Finite Group Databasebeta

← Group #345007

Character table — Group #345007

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-11-1-111-1-1-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-11111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111-1-1111111-1-11-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-1-1-1-1111-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-11111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-111111-1-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-1-1-1-11-1-1-11111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111111-1111-1-111-1-1-1-1
χ17222222222-2-222-22-2-2-22222-2-2-2-2000000000000000022220000-2-20000000000000000
χ18222222222-2-222-22-2-2-22222-2-2-2-20000000000000000-2-2-2-20000220000000000000000
χ19222222222-2-222-22-2-2-2-2-2-2-22222000000000000000022-2-20000-220000000000000000
χ20222222222-2-222-22-2-2-2-2-2-2-222220000000000000000-2-22200002-20000000000000000
χ2122222222-222-2-22-22-2-2000000002222-2-2-2-20000000000002222000000-2-20000000000
χ2222222222-222-2-22-22-2-2000000002222-2-2-2-2000000000000-2-2-2-2000000220000000000
χ2322222222-222-2-22-22-2-200000000-2-2-2-2222200000000000022-2-2000000-220000000000
χ2422222222-222-2-22-22-2-200000000-2-2-2-22222000000000000-2-2220000002-20000000000
χ252222-2-2-2-2-2002-2020002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i22-22i−2i00000000000000002−2i2−i200
χ262222-2-2-2-2-2002-2020002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i2-22−2i2i0000000000000000−22−i2i200
χ272222-2-2-2-2-2002-2020002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i22-22i−2i0000000000000000−22−i2i200
χ282222-2-2-2-2-2002-2020002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i2-22−2i2i00000000000000002−2i2−i200
χ292222-2-2-2-2-2002-202000−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i22-2−2i2i00000000000000002−2−i2i200
χ302222-2-2-2-2-2002-202000−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i2-222i−2i0000000000000000−22i2−i200
χ312222-2-2-2-2-2002-202000−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i22-2−2i2i0000000000000000−22i2−i200
χ322222-2-2-2-2-2002-202000−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i2-222i−2i00000000000000002−2−i2i200
χ3322-2-2-2-222222-2-2-22-2-22000000000000000022-2-222-2-200000000002i−2i2i−2i000000000000
χ3422-2-2-2-222222-2-2-22-2-22000000000000000022-2-222-2-20000000000−2i2i−2i2i000000000000
χ3522-2-2-2-222222-2-2-22-2-220000000000000000-2-222-2-22200000000002i−2i−2i2i000000000000
χ3622-2-2-2-222222-2-2-22-2-220000000000000000-2-222-2-2220000000000−2i2i2i−2i000000000000
χ372-22-22-2-2202-20020-2002−22−222−2−22-22-200002−22−22−22−200002i−2i2i−2i00000000i2−i2i2−i2000000
χ382-22-22-2-2202-20020-2002−22−222−2−22-22-200002−22−22−22−20000−2i2i−2i2i00000000−i2i2−i2i2000000
χ392-22-22-2-2202-20020-2002−22−222−2−2-22-220000−22−22−22−2200002i−2i−2i2i00000000i2−i2−i2i2000000
χ402-22-22-2-2202-20020-2002−22−222−2−2-22-220000−22−22−22−220000−2i2i2i−2i00000000−i2i2i2−i2000000
χ412-22-22-2-2202-20020-200−22−22−2−2222-22-20000−22−22−22−2200002i−2i2i−2i00000000−i2i2−i2i2000000
χ422-22-22-2-2202-20020-200−22−22−2−2222-22-20000−22−22−22−220000−2i2i−2i2i00000000i2−i2i2−i2000000
χ432-22-22-2-2202-20020-200−22−22−2−222-22-2200002−22−22−22−200002i−2i−2i2i00000000−i2i2i2−i2000000
χ442-22-22-2-2202-20020-200−22−22−2−222-22-2200002−22−22−22−20000−2i2i2i−2i00000000i2−i2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4400-440-4000000000002222−22−22−22−2222220000000000000000000000000000000000
χ474444-4-4-4-4400-440-400000000000−22−2222222222−22−220000000000000000000000000000000000
χ4844-4-444-4-44004-40-400000004-44-4000000000000000000000000000000000000000000
χ4944-4-444-4-44004-40-40000000-44-44000000000000000000000000000000000000000000
χ5044-4-444-4-4-400-440400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5144-4-444-4-4-400-44040000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5244-4-4-4-4444-4-4-4-44444-400000000000000000000000000000000000000000000000000
χ5344-4-4-4-444-44444-4-4-44-400000000000000000000000000000000000000000000000000
χ5444-4-4-4-444-4-4-4444-44-4400000000000000000000000000000000000000000000000000
χ554-44-44-4-440-4400-4040022−2222−22−22−222222000000000000000000000000000000000000000000
χ564-44-44-4-440-4400-40400−2222−22222222−22−22000000000000000000000000000000000000000000
χ574-44-4-444-400000000002i2−2i2−2i22i2000022−22−222200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ584-44-4-444-400000000002i2−2i2−2i22i20000−222222−220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ594-44-4-444-40000000000−2i22i22i2−2i2000022−22−22220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ604-44-4-444-40000000000−2i22i22i2−2i20000−222222−2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ614-4-444-44-40000000000000022−22−222200002i2−2i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ624-4-444-44-40000000000000022−22−22220000−2i22i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ634-4-444-44-400000000000000−222222−2200002i2−2i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ644-4-444-44-400000000000000−222222−220000−2i22i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ654-4-44-44-4404-400-40400000000000000000022−22−222222−22−222200000000000000000000000000
χ664-4-44-44-4404-400-404000000000000000000−222222−22−222222−2200000000000000000000000000
χ674-4-44-44-440-440040-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ684-4-44-44-440-440040-400000000000000−4i4i4i−4i0000000000000000000000000000000000

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