Finite Group Databasebeta

← Group #257405

Character table — Group #257405

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888824444444448888
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
χ5111111111111111111111111-1-1-1-11111111-1-1-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-1-111
χ1722222222222222-2-2-222-222-2-20000-2-22222-20000000000000000000000-200-20000000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-2-2-2-2000000000000000000000020020000000000
χ19222222222222-2-2222-2-22-2-2222222-2-20000-2-2-2-2-222000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-20000-22222-2-2000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200002000000000000000000000002-202-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000200000000000000000000000-220-2200000000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-222-2-220000000000000000000000200-20000000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-22220000000000000000000000-20020000000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-200002-2-222-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-20000222-2-222000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-2000000000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000000-2202-200000000
χ2922-22-22-2-200002-22-2-22-2200002i2i−2i−2i2-2000002i−2i0000000022-2-200000000000000002i−2i0000
χ3022-22-22-2-200002-22-2-22-2200002i2i−2i−2i2-2000002i−2i00000000-2-2220000000000000000−2i2i0000
χ3122-22-22-2-200002-22-2-22-220000−2i−2i2i2i2-200000−2i2i0000000022-2-20000000000000000−2i2i0000
χ3222-22-22-2-200002-22-2-22-220000−2i−2i2i2i2-200000−2i2i00000000-2-22200000000000000002i−2i0000
χ3322-22-22-2-20000-222-2-2-22200002i2i−2i−2i-2200000−2i2i000022-2-20000000000000000002i−2i000000
χ3422-22-22-2-20000-222-2-2-22200002i2i−2i−2i-2200000−2i2i0000-2-222000000000000000000−2i2i000000
χ3522-22-22-2-20000-222-2-2-2220000−2i−2i2i2i-22000002i−2i000022-2-2000000000000000000−2i2i000000
χ3622-22-22-2-20000-222-2-2-2220000−2i−2i2i2i-22000002i−2i0000-2-2220000000000000000002i−2i000000
χ3722-2-2-2-22222-2-222000-2-202-2000000002i−2i2i−2i00000002−22−22−22−2i2i2−i2−i2i2i2−i2−i200000000000000
χ3822-2-2-2-22222-2-222000-2-202-2000000002i−2i2i−2i0000000−22−22−22−22−i2−i2i2i2−i2−i2i2i200000000000000
χ3922-2-2-2-22222-2-222000-2-202-200000000−2i2i−2i2i00000002−22−22−22−2−i2−i2i2i2−i2−i2i2i200000000000000
χ4022-2-2-2-22222-2-222000-2-202-200000000−2i2i−2i2i0000000−22−22−22−22i2i2−i2−i2i2i2−i2−i200000000000000
χ4122-2-2-2-222-2-22222000-2-20-22000000002i−2i−2i2i00000002−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000000000
χ4222-2-2-2-222-2-22222000-2-20-22000000002i−2i−2i2i0000000−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000000000
χ4322-2-2-2-222-2-22222000-2-20-2200000000−2i2i2i−2i00000002−22−2−22−22−i2−i2i2i2i2i2−i2−i200000000000000
χ4422-2-2-2-222-2-22222000-2-20-2200000000−2i2i2i−2i0000000−22−222−22−2i2i2−i2−i2−i2−i2i2i200000000000000
χ452-222-2-22-22-22-200-22-2002002-22i−2i2i−2i000000000002i−2i000000002−22−22−22−20000000000i2−i2i2−i2
χ462-222-2-22-22-22-200-22-2002002-22i−2i2i−2i000000000002i−2i00000000−22−22−22−220000000000−i2i2−i2i2
χ472-222-2-22-22-22-200-22-2002002-2−2i2i−2i2i00000000000−2i2i000000002−22−22−22−20000000000−i2i2−i2i2
χ482-222-2-22-22-22-200-22-2002002-2−2i2i−2i2i00000000000−2i2i00000000−22−22−22−220000000000i2−i2i2−i2
χ492-222-2-22-2-22-2200-22-200200-222i−2i2i−2i00000000000−2i2i000000002−22−2−22−220000000000i2−i2−i2i2
χ502-222-2-22-2-22-2200-22-200200-222i−2i2i−2i00000000000−2i2i00000000−22−222−22−20000000000−i2i2i2−i2
χ512-222-2-22-2-22-2200-22-200200-22−2i2i−2i2i000000000002i−2i000000002−22−2−22−220000000000−i2i2i2−i2
χ522-222-2-22-2-22-2200-22-200200-22−2i2i−2i2i000000000002i−2i00000000−22−222−22−20000000000i2−i2−i2i2
χ53444-44-4-4-400004-4000-440000000000000000000000000022−22−22220000000000000000000000
χ54444-44-4-4-400004-4000-4400000000000000000000000000−222222−220000000000000000000000
χ55444-44-4-4-40000-440004-4000000000000000000000022−22−222200000000000000000000000000
χ56444-44-4-4-40000-440004-40000000000000000000000−222222−2200000000000000000000000000
χ5744-44-44-4-400004-4-4444-4-400000000-4400000000000000000000000000000000000000000
χ5844-44-44-4-40000-44-444-44-4000000004-400000000000000000000000000000000000000000
χ5944-4-4-4-44444-4-4-4-4000440-440000000000000000000000000000000000000000000000000
χ6044-4-4-4-444-4-444-4-40004404-40000000000000000000000000000000000000000000000000
χ614-444-4-44-44-44-4004-4400-400-4400000000000000000000000000000000000000000000000
χ624-444-4-44-4-44-44004-4400-4004-400000000000000000000000000000000000000000000000
χ634-4-444-4-4400000044-400-4000000000000000004i−4i00000000000000000000000000000000
χ644-4-444-4-4400000044-400-400000000000000000−4i4i00000000000000000000000000000000
χ654-4-444-4-44000000-4-4400400004-4-440000000000000000000000000000000000000000000
χ664-4-444-4-44000000-4-440040000-444-40000000000000000000000000000000000000000000
χ674-4-4-4444-44-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ684-4-4-4444-44-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ694-4-4-4444-4-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ704-4-4-4444-4-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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