Finite Group Databasebeta

← Group #72263331

Character table — Group #72263331

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111122222288888888881616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232646464646464128128128128
order12222222222222222222222222222444444444444444444444444424444444444444444444444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11-111-1111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-111111-111-111-1-1-11-1-11-111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1111-1-1-1-11-1-11-1-1-11-1-11-1-1-11111-1-111
χ511111111111111111111-1-1-1-111-1-11-1-111-1-1-1-1-1-111111111-1-11111111-11111-111-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-111-1-11-1-111-1-1-1-1-1-111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-11-111-11111111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-11-11-1-1-1-1-11-111-11-1-1-1-1-1-11111
χ91111111111111-1-1-1-111111-1-111111-1-11111-1-11111-1-1-1-1-1-111-1-11111111-1-1111-1-1-11-1-1-1-1-111-1-1-111-1
χ101111111111111-1-1-1-111111-1-111111-1-11111-1-11111-1-1-1-1-1-111-1-1111-1-11-1-1-1-111-1-1-11-1-1-111-1-1111-1-11
χ111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1111111111-11-1111-111-1-11-11-1-1-1-111-11-11
χ121111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111111-1-1-1-1-11-11-111-1-11-111111-1-11-11-1
χ131111111111111-1-1-1-1111-1-11111-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-11-1-11-11-111-1111-1-1-1-1111-11-1
χ141111111111111-1-1-1-1111-1-11111-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-111-11111111-1-1-11-11
χ151111111111111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-11-111-11-1-1-111-1-11-1-11
χ161111111111111-1-1-1-1111-1-111-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-1-11-1-11-1-1-11-111-11-111-1-111-111-1
χ172222222222222222222200000022-20000-2-2-2-2000000-2-2-2-20000-2-2-2002020000020-2-2020000000000
χ1822222222222222222222000000-2-2-200002222000000-2-2-2-20000-2-2-200-20200000-20220-20000000000
χ192222222222222-2-2-2-222200000022-20000-2-22200000022220000-2-2-20020-200000-20-220-20000000000
χ202222222222222-2-2-2-2222000000-2-2-2000022-2-200000022220000-2-2-200-20-200000202-2020000000000
χ2122222222222-2-200002-2-2002200222-2-200-2-2000000-2-200000022-22-200-200-200020220-200000000000
χ2222222222222-2-200002-2-2002200-2-22-2-2002200000022000000-2-2-22-2002002000-202-20-200000000000
χ2322222222222-2-200002-2-200-2-2002222200-2-200000022000000-2-2-22-200-2002000-20-220200000000000
χ2422222222222-2-200002-2-200-2-200-2-22220022000000-2-200000022-22-200200-200020-2-20200000000000
χ2522222222222-2-200002-2-222002222-200-2-222002222000000-2-2002-2200-20000-2-2000-20000000000000
χ2622222222222-2-200002-2-22200-2-2-2-2-20022-2-20022-2-2000000-2-2002-220020000-2200020000000000000
χ2722222222222-2-200002-2-2-2-20022-2-2-200-2-2-2-200-2-22200000022002-2200200002-200020000000000000
χ2822222222222-2-200002-2-2-2-200-2-222-200222200-2-2-2-200000022002-2200-2000022000-20000000000000
χ292222222222-22-20000-22-2002222002222200-2-200-2-20000000000-2-2200000000-20-2-202-220000000000
χ302222222222-22-20000-22-20022-2-200222-2-2002200220000000000-2-2200000000202-20-2-2-20000000000
χ312222222222-22-20000-22-200-2-222002-2-222002200-2-20000000000-2-2200000000-20220-22-20000000000
χ322222222222-22-20000-22-200-2-2-2-2002-2-2-2-200-2-200220000000000-2-220000000020-2202220000000000
χ332222222222-22-20000-22-222000000-200000022-2-200220000-2-22222-200000-2020-2-200-2020000000000
χ342222222222-22-20000-22-222000000-2000000-2-2-2-200-2-20000-2-2-2-222-2000002020220020-20000000000
χ352222222222-22-20000-22-2-2-2000000-2000000222200-2-2000022-2-222-20000020-202-200-2020000000000
χ362222222222-22-20000-22-2-2-2000000-2000000-2-22200220000222222-200000-20-20-220020-20000000000
χ372222222222-2-222222-2-2200002200-200-2-2000000-2-2-2-222-2-20022-2220000-22002-20000000000000000
χ382222222222-2-222222-2-220000-2-200-20022000000222222-2-200-2-2-2220000-2-200-220000000000000000
χ392222222222-2-222222-2-22222200002-2-2000000-2-20000-2-22222002-2-20000-200-2000-200200000000000
χ402222222222-2-222222-2-22-2-2-2-20000222000000220000-2-222-2-2002-2-20000-2002000200-200000000000
χ412222222222-2-22-2-2-2-2-2-2200002200-200-2-2000000-2-222-2-22200-2-2-22200002-200220000000000000000
χ422222222222-2-22-2-2-2-2-2-220000-2-200-2002200000022-2-2-2-2220022-22200002200-2-20000000000000000
χ432222222222-2-22-2-2-2-2-2-2222-2-20000222000000-2-2000022-2-222002-2-20000200-2000200-200000000000
χ442222222222-2-22-2-2-2-2-2-22-2-22200002-2-200000022000022-2-2-2-2002-2-200002002000-200200000000000
χ45444444-4-4-4-404000000-400000000000000004i−4i000000000000000002-20-200200000000000002i−2i0000
χ46444444-4-4-4-404000000-400000000000000004i−4i00000000000000000-220200-20000000000000−2i2i0000
χ47444444-4-4-4-404000000-40000000000000000−4i4i000000000000000002-20-20020000000000000−2i2i0000
χ48444444-4-4-4-404000000-40000000000000000−4i4i00000000000000000-220200-200000000000002i−2i0000
χ494444-4-44-4-4400-444-4-40040000000000000000000000000000000000220-200-20000000002-200000000
χ504444-4-44-4-4400-444-4-40040000000000000000000000000000000000-2-202002000000000-2200000000
χ514444-4-44-4-4400-4-4-4440040000000000000000000000000000000000220-200-2000000000-2200000000
χ524444-4-44-4-4400-4-4-4440040000000000000000000000000000000000-2-2020020000000002-200000000
χ534444-4-4-444-4-400000040000000000000004-400000000000000000002-20200-2000000000002-2000000
χ544444-4-4-444-4-400000040000000000000004-40000000000000000000-220-200200000000000-22000000
χ554444-4-4-444-4-40000004000000000000000-4400000000000000000002-20200-200000000000-22000000
χ564444-4-4-444-4-40000004000000000000000-440000000000000000000-220-2002000000000002-2000000
χ57888888-8-8-8-80-800000080000000000000000000000000000000000000000000000000000000000000
χ588888-8-88-8-88008000000-8000000000000000000000000000000000000000000000000000000000000
χ598888-8-8-888-88000000-800000000000000000000000000000000000000000000000000000000000000
χ6088-8-800800-8000000000000000000000000000004-44i−4i4i−4i00000000000000000000000000000000000
χ6188-8-800800-8000000000000000000000000000004-4−4i4i−4i4i00000000000000000000000000000000000
χ6288-8-800800-800000000000000000000000000000-444i−4i−4i4i00000000000000000000000000000000000
χ6388-8-800800-800000000000000000000000000000-44−4i4i4i−4i00000000000000000000000000000000000
χ6488-8-800-800800000000004-44-40000000000000000000004-4000000000000000000000000000000000
χ6588-8-800-800800000000004-4-44000000000000000000000-44000000000000000000000000000000000
χ6688-8-800-80080000000000-444-4000000000000000000000-44000000000000000000000000000000000
χ6788-8-800-80080000000000-44-440000000000000000000004-4000000000000000000000000000000000
χ688-88-8000-88000000000000000004-40004-4000000000000004-40000000000000000000000000000000
χ698-88-8000-88000000000000000004-4000-4400000000000000-440000000000000000000000000000000
χ708-88-8000-8800000000000000000-440004-400000000000000-440000000000000000000000000000000
χ718-88-8000-8800000000000000000-44000-44000000000000004-40000000000000000000000000000000
χ728-8-888-800000004-44-40000000000004-40000004-400000000000000000000000000000000000000000
χ738-8-888-800000004-44-4000000000000-44000000-4400000000000000000000000000000000000000000
χ748-8-888-80000000-44-440000000000004-4000000-4400000000000000000000000000000000000000000
χ758-8-888-80000000-44-44000000000000-440000004-400000000000000000000000000000000000000000
χ768-8-88-8800000004-4-4400000004-4000000000000000000000004-400000000000000000000000000000
χ778-8-88-8800000004-4-440000000-4400000000000000000000000-4400000000000000000000000000000
χ788-8-88-880000000-444-400000004-400000000000000000000000-4400000000000000000000000000000
χ798-8-88-880000000-444-40000000-44000000000000000000000004-400000000000000000000000000000
χ8016-1616-1600016-1600000000000000000000000000000000000000000000000000000000000000000000000

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