Finite Group Databasebeta

← Group #125708

Character table — Group #125708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111111122228888881616161616161616161616161616161616161616161616163232
order12222222222244444422444444444488888888888824
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ6111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ92222222222222-2-22-2-20022000000-2-200000000000000
χ102222222222222-2-22-2-200-2-20000002200000000000000
χ11222222222222-22-2-22-222000000-2-20000000000000000
χ12222222222222-22-2-22-2-2-2000000220000000000000000
χ13222222222222-2-22-2-22000022-2-2000000000000000000
χ14222222222222-2-22-2-220000-2-222000000000000000000
χ1522-2-22-2-222-22-20200-20000000002i−2i0022−2−2i2i2−i2−i2000000
χ1622-2-22-2-222-22-20200-20000000002i−2i00−2−222−i2−i2i2i2000000
χ1722-2-22-2-222-22-20200-2000000000−2i2i0022−2−2−i2−i2i2i2000000
χ1822-2-22-2-222-22-20200-2000000000−2i2i00−2−222i2i2−i2−i2000000
χ192-22-2-22-22-2-222-20020000000000002-22−22−2000022−2−200
χ202-22-2-22-22-2-222-20020000000000002-2−22−220000−2−22200
χ212-22-2-22-22-2-222-2002000000000000-222−22−20000−2−22200
χ222-22-2-22-22-2-222-2002000000000000-22−22−22000022−2−200
χ232-2-22-2-2222-2-2200-200200002-200000000002−22−22−22−200
χ242-2-22-2-2222-2-2200-200200002-20000000000−22−22−22−2200
χ252-2-22-2-2222-2-2200-20020000-2200000000002−22−2−22−2200
χ262-2-22-2-2222-2-2200-20020000-220000000000−22−222−22−200
χ2744444444-4-4-4-40000000000000000000000000000002-2
χ2844444444-4-4-4-4000000000000000000000000000000-22
χ2944-4-44-4-444-44-40-4004000000000000000000000000000
χ3044-4-44-4-44-44-44000000000000000000000000002-2-2200
χ3144-4-44-4-44-44-4400000000000000000000000000-222-200
χ324-44-4-44-4444-4-400000000000000000000002i−2i−2i2i000000
χ334-44-4-44-4444-4-40000000000000000000000−2i2i2i−2i000000
χ344-44-4-44-44-4-444400-40000000000000000000000000000
χ354-4-4444-4-400000000002-22i−2i002i−2i000000000000000000
χ364-4-4444-4-400000000002-2−2i2i00−2i2i000000000000000000
χ374-4-4444-4-40000000000-222i−2i00−2i2i000000000000000000
χ384-4-4444-4-40000000000-22−2i2i002i−2i000000000000000000
χ394-4-44-4-4444-4-4400400-400000000000000000000000000
χ404-4-44-4-444-444-40000000000000000002-2-220000000000
χ414-4-44-4-444-444-4000000000000000000-222-20000000000
χ428888-8-8-8-8000000000000000000000000000000000000
χ4388-8-8-888-8000000000000000000000000000000000000
χ448-88-88-88-8000000000000000000000000000000000000

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