Finite Group Databasebeta

← Group #72262371

Character table — Group #72262371

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122444444888888888888888816161616161616161616161616163232323232323232323232326464646464646464646464646464646464646464
order12222222222222222222222244442222224444444424444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-111-111-1-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i
χ1011111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-111-111-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii11-1-1−i−iii
χ1111111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-111-111-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii-1-111−i−iii
χ1211111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-111-111-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−i-1-111ii−i−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-111-11111-1-111-1-1-1-1ii−i−i−i−iiiii−i−i-1-111−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-111-11111-1-111-1-1-1-1−i−iiiii−i−i−i−iii-1-111ii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-111-1-1-1-1-1-1-1111111ii−i−i−i−iii−i−iii11-1-1ii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-111-1-1-1-1-1-1-1111111−i−iiiii−i−iii−i−i11-1-1−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2220000-2-2-20000-200000000000000002i−2i2i−2i000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2220000-2-2-20000-20000000000000000−2i2i−2i2i000000000000
χ1922222222222222-2-2-2-2-2-22222-2-2-2-22-20000-2-220000200000000000000002-2-22000000000000
χ2022222222222222-2-2-2-2-2-22222-2-2-2-22-20000-2-22000020000000000000000-222-2000000000000
χ21222222222222-2-22222-2-222222222-2-22222-2-2-22222-20000-2-2-2-2000000000000000000000000
χ22222222222222-2-22222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000000000000000
χ23222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000222000020000000000002i−2i2i−2i0000000000000000
χ24222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000022200002000000000000−2i2i−2i2i0000000000000000
χ25222222222222-2-2-2-2-2-2222222-2-2-2-2-22000022-20000-20000000000002-2-220000000000000000
χ26222222222222-2-2-2-2-2-2222222-2-2-2-2-22000022-20000-2000000000000-222-20000000000000000
χ27222222222222-2-2-2-2-2-222-2-2-2-22222-2222-2-2-2-2222-2-220000-2-222000000000000000000000000
χ28222222222222-2-2-2-2-2-222-2-2-2-22222-22-2-222-2-22-2-2222000022-2-2000000000000000000000000
χ292222-2-22-2-2-2222222-2-22222-2-222-2-2-2-200002-2-20000200000000000000000000000000002-22-2
χ302222-2-22-2-2-2222222-2-22222-2-222-2-2-2-200002-2-2000020000000000000000000000000000-22-22
χ312222-2-22-2-2-2222222-2-222-2-222-2-222-2-20000-2220000-222-2-2000022-2-200000000000000000000
χ322222-2-22-2-2-2222222-2-222-2-222-2-222-2-20000-2220000-2-2-2220000-2-22200000000000000000000
χ332222-2-22-2-2-22222-2-222-2-222-2-2-2-222-220000-22-20000222-2-20000-2-22200000000000000000000
χ342222-2-22-2-2-22222-2-222-2-222-2-2-2-222-220000-22-200002-2-222000022-2-200000000000000000000
χ352222-2-22-2-2-22222-2-222-2-2-2-22222-2-2-2200002-220000-200000000000000000000000000002i−2i−2i2i
χ362222-2-22-2-2-22222-2-222-2-2-2-22222-2-2-2200002-220000-20000000000000000000000000000−2i2i2i−2i
χ372222-2-22-2-2-222-2-222-2-2-2-222-2-222-2-2220000-2220000-2000000000000000000002i−2i2i−2i00000000
χ382222-2-22-2-2-222-2-222-2-2-2-222-2-222-2-2220000-2220000-200000000000000000000−2i2i−2i2i00000000
χ392222-2-22-2-2-222-2-222-2-2-2-2-2-222-2-2222200002-2-2000020000000000000000000000002-22-20000
χ402222-2-22-2-2-222-2-222-2-2-2-2-2-222-2-2222200002-2-200002000000000000000000000000-22-220000
χ412222-2-22-2-2-222-2-2-2-2222222-2-2-2-2222-200002-220000-20000000000000000000000002-2-220000
χ422222-2-22-2-2-222-2-2-2-2222222-2-2-2-2222-200002-220000-2000000000000000000000000-222-20000
χ432222-2-22-2-2-222-2-2-2-22222-2-22222-2-22-20000-22-200002000000000000000000002-2-2200000000
χ442222-2-22-2-2-222-2-2-2-22222-2-22222-2-22-20000-22-20000200000000000000000000-222-200000000
χ45444444-44-4-44-40000000000004-44-400004400000-4-4000000000000000000000000000000000
χ46444444-44-4-44-40000000000004-44-40000-4-40000044000000000000000000000000000000000
χ47444444-44-4-44-4000000000000-44-44004400000-4-400000000000000000000000000000000000
χ48444444-44-4-44-4000000000000-44-4400-4-4000004400000000000000000000000000000000000
χ49444444-4-44-4-44000000004-44-40000000000000000002-2-2200002-22-200000000000000000000
χ50444444-4-44-4-44000000004-44-4000000000000000000-222-20000-22-2200000000000000000000
χ51444444-4-44-4-4400000000-44-440000000000000000002-2-220000-22-2200000000000000000000
χ52444444-4-44-4-4400000000-44-44000000000000000000-222-200002-22-200000000000000000000
χ534444-4-4-44-44-44000000004-4-440000000000000000002-22-20000-222-200000000000000000000
χ544444-4-4-44-44-44000000004-4-44000000000000000000-22-2200002-2-2200000000000000000000
χ554444-4-4-44-44-4400000000-444-40000000000000000002-22-200002-2-2200000000000000000000
χ564444-4-4-44-44-4400000000-444-4000000000000000000-22-220000-222-200000000000000000000
χ574444-4-4-4-4444-40000000000004-4-440000000000000000004-400000000000000000000000000
χ584444-4-4-4-4444-40000000000004-4-44000000000000000000-4400000000000000000000000000
χ594444-4-4-4-4444-4000000000000-444-4000000000000000000004-4000000000000000000000000
χ604444-4-4-4-4444-4000000000000-444-400000000000000000000-44000000000000000000000000
χ618888888-8-88-8-800000000000000000000000000000000000000000000000000000000000000
χ628888-8-8888-8-8-800000000000000000000000000000000000000000000000000000000000000
χ638-8-888-8000000004-44-400000000000000000004-44-4000000000000000000000000000000000
χ648-8-888-8000000004-44-40000000000000000000-44-44000000000000000000000000000000000
χ658-8-888-800000000-44-4400000000000000000004-4-44000000000000000000000000000000000
χ668-8-888-800000000-44-440000000000000000000-444-4000000000000000000000000000000000
χ678-8-88-88000000004-4-440000000000004-44-40000000000000000000000000000000000000000
χ688-8-88-88000000004-4-44000000000000-44-440000000000000000000000000000000000000000
χ698-8-88-8800000000-444-40000000000004-4-440000000000000000000000000000000000000000
χ708-8-88-8800000000-444-4000000000000-444-40000000000000000000000000000000000000000
χ711616-16-16000000000000008-8000000000000000000000000000000000000000000000000000000
χ721616-16-1600000000000000-88000000000000000000000000000000000000000000000000000000
χ7316-1616-16000000008-8000000000000000000000000000000000000000000000000000000000000
χ7416-1616-1600000000-88000000000000000000000000000000000000000000000000000000000000

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