Finite Group Databasebeta

← Group #72317660

Character table — Group #72317660

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222222244444444448888888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222222222222222442222244444444444222244444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111111-1-1-1-1
χ911111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-11111-1-1-1-111-11111-1-1-1-11-111-1-111-1-1-11-1111-1-111-1-111-1-1
χ1011111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-11111-1-1-1-111-1-1-111-1-1111-1-1-11111-1-11-11-111-1-1-1-111-1-111
χ1111111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-11111-1-1-1-11-1111-1-111-1-1-1111-1-111-1-1-11-11-1-111-1-111-1-111
χ1211111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-11111-1-1-1-11-11-1-1-1-11111-11-1-11111-1-11-11-1-1-11111-1-111-1-1
χ1311111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-1-1-1-1-1111111-11111-1-1-1-11-1-1-111-1-111-1-111-1-11111-1-1-1-111
χ1411111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-1-1-1-1-1111111-1-1-111-1-1111-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ1511111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-1-1-1-1-111111-1111-1-111-1-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1
χ1611111-1-1-1-111111-1-1-1-11111-1-111-1-1-11-1-1-1-1-111111-11-1-1-1-11111-1111-1-1-1-11111-1-111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-22-22-2-2-2-222222222-20000000000000000-2-2-2-20000000000000000
χ1822222222222222222222-2-2-2-22-22-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ192222222222222222-2-2-2-222-2-2-22-222-2-200000000-200220000220000000000-200-2000000000000
χ202222222222222222-2-2-2-222-2-2-22-222-2-200000000-200-2-20000-2-200000000002002000000000000
χ212222222222222222-2-2-2-2-2-222-2-2-2-2-222000000002000000000000222200000-2-20000000000000
χ222222222222222222-2-2-2-2-2-222-2-2-2-2-222000000002000000000000-2-2-2-200000220000000000000
χ2322222-2-2-2-222222-2-222-2-22222-222-2-2-2200000000-200220000-2-20000000000200-2000000000000
χ2422222-2-2-2-222222-2-222-2-22222-222-2-2-2200000000-200-2-20000220000000000-2002000000000000
χ2522222-2-2-2-222222-2-222-2-2-2-2-2-2-2-22222-200000000200000000000022-2-200000-220000000000000
χ2622222-2-2-2-222222-2-222-2-2-2-2-2-2-2-22222-2000000002000000000000-2-222000002-20000000000000
χ2722222-2-2-2-222222-2-2-2-222-2-2222-2-222-222222-2-2-2-2-20000000000000000-2-2220000000000000000
χ2822222-2-2-2-222222-2-2-2-222-2-2222-2-222-22-2-2-2-22222-2000000000000000022-2-20000000000000000
χ292222-222-2-22-2-2-222-222222222-2-2-22-22-200000000-222002-22-200-2-2000000000000000000000000
χ302222-222-2-22-2-2-222-222222222-2-2-22-22-200000000-2-2-200-22-220022000000000000000000000000
χ312222-222-2-22-2-2-222-22222-2-2-2-2-22-2-22-220000000020000000000000000000000002-22-200000000
χ322222-222-2-22-2-2-222-22222-2-2-2-2-22-2-22-22000000002000000000000000000000000-22-2200000000
χ332222-222-2-22-2-2-222-2-2-2-2-222-2-22-222-2-2200000000200000000000000000000000000002-22-20000
χ342222-222-2-22-2-2-222-2-2-2-2-222-2-22-222-2-220000000020000000000000000000000000000-22-220000
χ352222-222-2-22-2-2-222-2-2-2-2-2-2-222222-222-200000000-2000000000000000000000000000000002i−2i2i−2i
χ362222-222-2-22-2-2-222-2-2-2-2-2-2-222222-222-200000000-200000000000000000000000000000000−2i2i−2i2i
χ372222-2-2-2222-2-2-22-2222-2-222222-2-2-22-2-200000000200000000000000000000000000002-2-220000
χ382222-2-2-2222-2-2-22-2222-2-222222-2-2-22-2-20000000020000000000000000000000000000-222-20000
χ392222-2-2-2222-2-2-22-2222-2-2-2-2-2-222-22-22200000000-2000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2222-2-2-22-2222-2-2-2-2-2-222-22-22200000000-200000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2222-2-2-22-22-2-22222-2-2-2-22-222200000000-22-2002-2-2200-22000000000000000000000000
χ422222-2-2-2222-2-2-22-22-2-22222-2-2-2-22-222200000000-2-2200-222-2002-2000000000000000000000000
χ432222-2-2-2222-2-2-22-22-2-222-2-222-2222-2-2-20000000020000000000000000000000002-2-2200000000
χ442222-2-2-2222-2-2-22-22-2-222-2-222-2222-2-2-2000000002000000000000000000000000-222-200000000
χ45444444444-4-4-44-4-4-40000000000000000000000002200-22-2200-2-2000000000000000000000000
χ46444444444-4-4-44-4-4-4000000000000000000000000-2-2002-22-20022000000000000000000000000
χ4744444-4-4-4-4-4-4-44-4440000000000000000000000002-200-222-200-22000000000000000000000000
χ4844444-4-4-4-4-4-4-44-444000000000000000000000000-22002-2-22002-2000000000000000000000000
χ494444-444-4-4-444-4-4-440000000000000000000000002200-2-2-2-20022000000000000000000000000
χ504444-444-4-4-444-4-4-44000000000000000000000000-2-200222200-2-2000000000000000000000000
χ514444-4-4-444-444-4-44-40000000000000000000000002-200-2-222002-2000000000000000000000000
χ524444-4-4-444-444-4-44-4000000000000000000000000-220022-2-200-22000000000000000000000000
χ5344-4-4000004000-4004-4004-44-400000002i2i−2i−2i2i2i−2i−2i000000000000000002i−2i2i−2i0000000000000000
χ5444-4-4000004000-4004-4004-44-40000000−2i−2i2i2i−2i−2i2i2i00000000000000000−2i2i−2i2i0000000000000000
χ5544-4-4000004000-4004-400-44-4400000002i2i−2i−2i2i2i−2i−2i00000000000000000−2i2i−2i2i0000000000000000
χ5644-4-4000004000-4004-400-44-440000000−2i−2i2i2i−2i−2i2i2i000000000000000002i−2i2i−2i0000000000000000
χ5744-4-4000004000-400-44004-4-4400000002i2i−2i−2i−2i−2i2i2i000000000000000002i−2i−2i2i0000000000000000
χ5844-4-4000004000-400-44004-4-440000000−2i−2i2i2i2i2i−2i−2i00000000000000000−2i2i2i−2i0000000000000000
χ5944-4-4000004000-400-4400-444-400000002i2i−2i−2i−2i−2i2i2i00000000000000000−2i2i2i−2i0000000000000000
χ6044-4-4000004000-400-4400-444-40000000−2i−2i2i2i2i2i−2i−2i000000000000000002i−2i−2i2i0000000000000000
χ614-44-444-44-4000-40000000000000000002i−2i2i−2i2i−2i2i−2i0002-200002-2002i−2i2i−2i00000000000000000000
χ624-44-444-44-4000-40000000000000000002i−2i2i−2i2i−2i2i−2i000-220000-2200−2i2i−2i2i00000000000000000000
χ634-44-444-44-4000-4000000000000000000−2i2i−2i2i−2i2i−2i2i0002-200002-200−2i2i−2i2i00000000000000000000
χ644-44-444-44-4000-4000000000000000000−2i2i−2i2i−2i2i−2i2i000-220000-22002i−2i2i−2i00000000000000000000
χ654-44-44-44-44000-40000000000000000002i−2i2i−2i−2i2i−2i2i0002-20000-22002i−2i−2i2i00000000000000000000
χ664-44-44-44-44000-40000000000000000002i−2i2i−2i−2i2i−2i2i000-2200002-200−2i2i2i−2i00000000000000000000
χ674-44-44-44-44000-4000000000000000000−2i2i−2i2i2i−2i2i−2i0002-20000-2200−2i2i2i−2i00000000000000000000
χ684-44-44-44-44000-4000000000000000000−2i2i−2i2i2i−2i2i−2i000-2200002-2002i−2i−2i2i00000000000000000000
χ6988-8-800000-8000800008-800000000000000000000000000000000000000000000000000000000
χ7088-8-800000-800080000-8800000000000000000000000000000000000000000000000000000000
χ718-88-8-88-8-880008000000000000000000000000000000000000000000000000000000000000000
χ728-88-8-8-888-80008000000000000000000000000000000000000000000000000000000000000000
χ738-8-880000008-8000000000000000000000004-4-440000000000000000000000000000000000000
χ748-8-880000008-800000000000000000000000-444-40000000000000000000000000000000000000
χ758-8-88000000-8800000000000000000004-4-4400000000000000000000000000000000000000000
χ768-8-88000000-880000000000000000000-444-400000000000000000000000000000000000000000

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