Finite Group Databasebeta

← Group #255461

Character table — Group #255461

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
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-1-111
χ1722222222222222-2-2-222-222-2-20000-2-2220000-200220000000000000000-200-20000000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-20000-200-2-2000000000000000020020000000000
χ19222222222222-2-2222-2-22-2-2222222-2-200-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-2002222-2-2-200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200000020000000000000000000002-202-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000002000000000000000000000-220-2200000000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-2220000200-2-20000000000000000200-20000000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-20000200220000000000000000-20020000000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-200-2-2222-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-20022-2-222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-20000000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000000-2000000000000000000000-2202-200000000
χ29222-2-2-22-222-2-2-2-20002202-2000000002-200000002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-2-22-222-2-2-2-20002202-2000000002-200000002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-2-22-222-2-2-2-20002202-200000000-220000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-2-22-222-2-2-2-20002202-200000000-220000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-2-22-2-2-222-2-2000220-22000000002-20000000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-2-22-2-2-222-2-2000220-22000000002-20000000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-2-22-2-2-222-2-2000220-2200000000-2200000002-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-2-22-2-2-222-2-2000220-2200000000-2200000002-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ372-22-2-22-2200002-222-22-2-2000022-2-22-2002-2000000000002i−2i2i−2i00000000000000002i−2i0000
χ382-22-2-22-2200002-222-22-2-2000022-2-22-2002-200000000000−2i2i−2i2i0000000000000000−2i2i0000
χ392-22-2-22-2200002-222-22-2-20000-2-2222-200-22000000000002i−2i2i−2i0000000000000000−2i2i0000
χ402-22-2-22-2200002-222-22-2-20000-2-2222-200-2200000000000−2i2i−2i2i00000000000000002i−2i0000
χ412-22-2-22-220000-2222-2-22-2000022-2-2-2200-2200000002i−2i2i−2i0000000000000000002i−2i000000
χ422-22-2-22-220000-2222-2-22-2000022-2-2-2200-220000000−2i2i−2i2i000000000000000000−2i2i000000
χ432-22-2-22-220000-2222-2-22-20000-2-222-22002-200000002i−2i2i−2i000000000000000000−2i2i000000
χ442-22-2-22-220000-2222-2-22-20000-2-222-22002-20000000−2i2i−2i2i0000000000000000002i−2i000000
χ452-2-22-222-22-22-2002-2200-2002-22i−2i2i−2i0000000002i−2i0000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-2-22-222-22-22-2002-2200-2002-22i−2i2i−2i0000000002i−2i0000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-2-22-222-22-22-2002-2200-2002-2−2i2i−2i2i000000000−2i2i0000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-2-22-222-22-22-2002-2200-2002-2−2i2i−2i2i000000000−2i2i0000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-2-22-222-2-22-22002-2200-200-222i−2i2i−2i000000000−2i2i0000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ502-2-22-222-2-22-22002-2200-200-222i−2i2i−2i000000000−2i2i0000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ512-2-22-222-2-22-22002-2200-200-22−2i2i−2i2i0000000002i−2i0000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ522-2-22-222-2-22-22002-2200-200-22−2i2i−2i2i0000000002i−2i0000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ53444-4-4-44-444-4-444000-4-40-440000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-44444000-4-404-40000000000000000000000000000000000000000000000000
χ5544-4-444-4-40000004-4-400400004i−4i−4i4i0000000000000000000000000000000000000000000
χ5644-4-444-4-40000004-4-40040000−4i4i4i−4i0000000000000000000000000000000000000000000
χ5744-4-444-4-4000000-44400-4000000000000004-400000000000000000000000000000000000
χ5844-4-444-4-4000000-44400-400000000000000-4400000000000000000000000000000000000
χ594-4444-4-4-400004-4000-44000000000000000000000022−22−222200000000000000000000000000
χ604-4444-4-4-400004-4000-440000000000000000000000−222222−2200000000000000000000000000
χ614-4444-4-4-40000-440004-40000000000000000000000000022−22−22220000000000000000000000
χ624-4444-4-4-40000-440004-400000000000000000000000000−222222−220000000000000000000000
χ634-44-4-44-4400004-4-4-444-4400000000-4400000000000000000000000000000000000000000
χ644-44-4-44-440000-44-4-44-444000000004-400000000000000000000000000000000000000000
χ654-4-44-444-44-44-400-44-400400-4400000000000000000000000000000000000000000000000
χ664-4-44-444-4-44-4400-44-4004004-400000000000000000000000000000000000000000000000
χ674-4-4-44-4444-4-4400000000000000000000000000000000000002-2-222-2-2200000000000000
χ684-4-4-44-4444-4-440000000000000000000000000000000000000-222-2-222-200000000000000
χ694-4-4-44-444-444-400000000000000000000000000000000000002-2-22-222-200000000000000
χ704-4-4-44-444-444-40000000000000000000000000000000000000-222-22-2-2200000000000000
χ7188-88-8-8-88000000000000000000000000000000000000000000000000000000000000000

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