Finite Group Databasebeta

← Group #247162

Character table — Group #247162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444422444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-22222-2-20000-2-2-2-2-222000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-200002222-2-2-2000000000000000000000000000000
χ19222222222222-2-2-22222-2-2-2220000-2-222220000-2000000000000000000-200-20000000000
χ20222222222222-2-2-22222-2-2-2220000-2-2-2-2-2-20000-200000000000000000020020000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200000000200000000000000000002-202-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000000020000000000000000000-220-2200000000
χ2322222222-2-2-2-2222-2-2-2-22-2-2222222-2-20000-2-2222-2-2000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-222-2-2-2-2-2-2000022-2-2222000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-20000-2-222-2-200002000000000000000000200-20000000000
χ2622222222-2-2-2-2-2-2-22222-222-2-20000-2-2-2-22200002000000000000000000-20020000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-200000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-20000000000000000000-2202-200000000
χ29222-2-2-22-222-2-2000-2-2220002-20000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-2-22-222-2-2000-2-2220002-20000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-2-22-222-2-2000-2-2220002-2000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-2-22-222-2-2000-2-2220002-2000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-2-22-2-2-222000-2-222000-220000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-2-22-2-2-222000-2-222000-220000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-2-22-2-2-222000-2-222000-22000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-2-22-2-2-222000-2-222000-22000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ372-222-22-2-22-22-22-2-2000022-2002i2i−2i−2i000000000002i−2i000000002−22−22−22−20000000000i2−i2i2−i2
χ382-222-22-2-22-22-22-2-2000022-2002i2i−2i−2i000000000002i−2i00000000−22−22−22−220000000000−i2i2−i2i2
χ392-222-22-2-22-22-22-2-2000022-200−2i−2i2i2i00000000000−2i2i000000002−22−22−22−20000000000−i2i2−i2i2
χ402-222-22-2-22-22-22-2-2000022-200−2i−2i2i2i00000000000−2i2i00000000−22−22−22−220000000000i2−i2i2−i2
χ412-222-22-2-2-22-222-2-200002-22002i2i−2i−2i00000000000−2i2i000000002−22−2−22−220000000000i2−i2−i2i2
χ422-222-22-2-2-22-222-2-200002-22002i2i−2i−2i00000000000−2i2i00000000−22−222−22−20000000000−i2i2i2−i2
χ432-222-22-2-2-22-222-2-200002-2200−2i−2i2i2i000000000002i−2i000000002−22−2−22−220000000000−i2i2i2−i2
χ442-222-22-2-2-22-222-2-200002-2200−2i−2i2i2i000000000002i−2i00000000−22−222−22−20000000000i2−i2−i2i2
χ452-2-2-2-22220000-22-22-22-2200002-22-22-200002-20000000002-22-200000000000000002-20000
χ462-2-2-2-22220000-22-22-22-2200002-22-22-200002-2000000000-22-220000000000000000-220000
χ472-2-2-2-22220000-22-22-22-220000-22-222-20000-220000000002-22-20000000000000000-220000
χ482-2-2-2-22220000-22-22-22-220000-22-222-20000-22000000000-22-2200000000000000002-20000
χ492-2-2-2-22220000-22-2-22-22200002-22-2-220000-22000002-22-20000000000000000002-2000000
χ502-2-2-2-22220000-22-2-22-22200002-22-2-220000-2200000-22-22000000000000000000-22000000
χ512-2-2-2-22220000-22-2-22-2220000-22-22-2200002-2000002-22-2000000000000000000-22000000
χ522-2-2-2-22220000-22-2-22-2220000-22-22-2200002-200000-22-220000000000000000002-2000000
χ53444-4-4-44-444-4-400044-4-4000-4400000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-44400044-4-40004-400000000000000000000000000000000000000000000000
χ5544-4-444-4-4000044-40000-400000000000000004-4000000000000000000000000000000000
χ5644-4-444-4-4000044-40000-40000000000000000-44000000000000000000000000000000000
χ5744-4-444-4-40000-4-440000400004i−4i−4i4i0000000000000000000000000000000000000000000
χ5844-4-444-4-40000-4-44000040000−4i4i4i−4i0000000000000000000000000000000000000000000
χ594-444-44-4-44-44-4-4440000-4-440000000000000000000000000000000000000000000000000
χ604-444-44-4-4-44-44-4440000-44-40000000000000000000000000000000000000000000000000
χ614-44-44-4-444-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-44-44-4-444-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-44-44-4-44-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ644-44-44-4-44-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ654-4-444-44-400000004-4-4400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ664-4-444-44-400000004-4-440000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ674-4-444-44-40000000-444-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ684-4-444-44-40000000-444-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ694-4-4-4-444400004-444-44-4-400000000-4400000000000000000000000000000000000000000
χ704-4-4-4-444400004-44-44-44-4000000004-400000000000000000000000000000000000000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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