Finite Group Databasebeta

← Group #72319673

Character table — Group #72319673

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11222444444444444888888888161616161616161616161616161616161616161632323232323232323232323232323232323264646464646464646464646464646464
order12222222244444444222222244222222244444444444442444444444888888884444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-1111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ811111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ9111111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-11-11-11111-1-1-1-111111-1-1-1-11-111-1-111-1-11-111-1-111-1-1-1111-1-1
χ10111111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-11-11-11111-1-1-1-11-1-111-1-1111-1-1-11111-1-1-1111-1-1-1-1111-1-1-111
χ11111111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-11-11-1-1-1-1-1111111111-1-1-1-11-1-1-111-1-111-11-1-11111-1-1-11-1-111
χ12111111-1-11-1-1-1-11111-1-1-11111-1-11-1-111-1-11-11-1-1-1-1-111111-1-111-1-1111-111-1-1-1-1111-1-1-111-1-1111-111-1-1
χ13111111-1-11-1-1-1-11111-1-1-11111-1-11-1-1-1-1111-11-11111-1-1-1-1111-1-111-1-1-1111-1-111-1-11-1-1-111-1-111-11-1-111
χ14111111-1-11-1-1-1-11111-1-1-11111-1-11-1-1-1-1111-11-11111-1-1-1-11-1-1-1-11111-11-1-11111-1-1-11-1-11111-1-11-111-1-1
χ15111111-1-11-1-1-1-11111-1-1-11111-1-11-1-1-1-1111-11-1-1-1-1-11111111-1-111-1-1-11-1-111-1-111-1111-1-1-1-111-1111-1-1
χ16111111-1-11-1-1-1-11111-1-1-11111-1-11-1-1-1-1111-11-1-1-1-1-111111-1-1-1-11111-1111-1-1-1-1111-111-1-111-1-11-1-1-111
χ17222222222222222222-2-2-2-2-2-222-2-2-20000-2-222000000002000000000022220000-2-200000000000000
χ18222222222222222222-2-2-2-2-2-222-2-2-20000-2-2220000000020000000000-2-2-2-200002200000000000000
χ1922222222222-2-2222222222-2-22-2-22-200002-2-2-222222222-200000000000000-2-2-2-20000000000000000
χ2022222222222-2-2222222222-2-22-2-22-200002-2-2-2-2-2-2-2-2-2-2-2-20000000000000022220000000000000000
χ2122222222222-2-222222-2-2-2-2222-22-220000-22-2-200000000-22200002200000000000000000000-2-20000
χ2222222222222-2-222222-2-2-2-2222-22-220000-22-2-200000000-2-2-20000-2-200000000000000000000220000
χ23222222-2-22-2-2222222-222-2-222-2222-20000-2-2-2200000000-2220000-2-2000000000000000000002-20000
χ24222222-2-22-2-2222222-222-2-222-2222-20000-2-2-2200000000-2-2-200002200000000000000000000-220000
χ25222222-2-22-2-2222222-2-2-222-2-2-22-2-22000022-222222-2-2-2-2-200000000000000-2-2220000000000000000
χ26222222-2-22-2-2222222-2-2-222-2-2-22-2-22000022-22-2-2-2-22222-20000000000000022-2-20000000000000000
χ27222222-2-22-2-2-2-22222-222-2-2-2-2-2-2-2220000-222-2000000002000000000022-2-20000-2200000000000000
χ28222222-2-22-2-2-2-22222-222-2-2-2-2-2-2-2220000-222-20000000020000000000-2-22200002-200000000000000
χ2922222-222-2-2-2222-2-22-222222222-2-222222-2-22-200000000-2002-22-200-2-2000000000000000000000000
χ3022222-222-2-2-2222-2-22-222222222-2-22-2-2-2-2-2-22-200000000-200-22-220022000000000000000000000000
χ3122222-222-2-2-2222-2-22-2-2-2-2-2-2-22222-20000222-200000000-20000000000000000000000000000002i−2i2i−2i
χ3222222-222-2-2-2222-2-22-2-2-2-2-2-2-22222-20000222-200000000-2000000000000000000000000000000−2i2i−2i2i
χ3322222-222-2-2-2-2-22-2-22-22222-2-22-22-2-20000-22-22000000002000000000000000000002-22-20000000000
χ3422222-222-2-2-2-2-22-2-22-22222-2-22-22-2-20000-22-2200000000200000000000000000000-22-220000000000
χ3522222-222-2-2-2-2-22-2-22-2-2-2-2-2222-2-22200002-2-220000000020000000000000000000000002-22-2000000
χ3622222-222-2-2-2-2-22-2-22-2-2-2-2-2222-2-22200002-2-22000000002000000000000000000000000-22-22000000
χ3722222-2-2-2-222222-2-22222-2-222-22-2-2-2000022-2-20000000020000000000000000000000002-2-22000000
χ3822222-2-2-2-222222-2-22222-2-222-22-2-2-2000022-2-2000000002000000000000000000000000-222-2000000
χ3922222-2-2-2-222222-2-222-2-222-2-2-222220000-2-2-2-2000000002000000000000000000002-2-220000000000
χ4022222-2-2-2-222222-2-222-2-222-2-2-222220000-2-2-2-200000000200000000000000000000-222-20000000000
χ4122222-2-2-2-222-2-22-2-22222-2-2-2-2-2-22-2200002-22200000000-20000000000000000000000000000002i−2i−2i2i
χ4222222-2-2-2-222-2-22-2-22222-2-2-2-2-2-22-2200002-22200000000-2000000000000000000000000000000−2i2i2i−2i
χ4322222-2-2-2-222-2-22-2-222-2-22222-2-2-22-222-2-2-222200000000-2002-2-2200-22000000000000000000000000
χ4422222-2-2-2-222-2-22-2-222-2-22222-2-2-22-2-2-222-222200000000-200-222-2002-2000000000000000000000000
χ454444444444400-4-4-4-4-4000000-400002222000000000000000-22-2200-2-2000000000000000000000000
χ464444444444400-4-4-4-4-4000000-40000-2-2-2-20000000000000002-22-20022000000000000000000000000
χ47444444-4-44-4-400-4-4-4-440000004000022-2-2000000000000000-222-200-22000000000000000000000000
χ48444444-4-44-4-400-4-4-4-4400000040000-2-2220000000000000002-2-22002-2000000000000000000000000
χ4944444-444-4-4-400-444-44000000-400002222000000000000000-2-2-2-20022000000000000000000000000
χ5044444-444-4-4-400-444-44000000-40000-2-2-2-2000000000000000222200-2-2000000000000000000000000
χ5144444-4-4-4-44400-444-4-40000004000022-2-2000000000000000-2-222002-2000000000000000000000000
χ5244444-4-4-4-44400-444-4-400000040000-2-22200000000000000022-2-200-22000000000000000000000000
χ53444-4-400000044400-404-4004-40-4000000000002i2i−2i−2i2i2i−2i−2i0000000000000002i−2i2i−2i0000000000000000
χ54444-4-400000044400-404-4004-40-400000000000−2i−2i2i2i−2i−2i2i2i000000000000000−2i2i−2i2i0000000000000000
χ55444-4-400000044400-40-4400-440-4000000000002i2i−2i−2i−2i−2i2i2i000000000000000−2i2i2i−2i0000000000000000
χ56444-4-400000044400-40-4400-440-400000000000−2i−2i2i2i2i2i−2i−2i0000000000000002i−2i−2i2i0000000000000000
χ57444-4-4000000-4-4400-404-400-4404000000000002i2i−2i−2i2i2i−2i−2i000000000000000−2i2i−2i2i0000000000000000
χ58444-4-4000000-4-4400-404-400-440400000000000−2i−2i2i2i−2i−2i2i2i0000000000000002i−2i2i−2i0000000000000000
χ59444-4-4000000-4-4400-40-44004-404000000000002i2i−2i−2i−2i−2i2i2i0000000000000002i−2i−2i2i0000000000000000
χ60444-4-4000000-4-4400-40-44004-40400000000000−2i−2i2i2i2i2i−2i−2i000000000000000−2i2i2i−2i0000000000000000
χ6144-44-444-4-44-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i02-200002-2002i−2i2i−2i00000000000000000000
χ6244-44-444-4-44-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i0-220000-2200−2i2i−2i2i00000000000000000000
χ6344-44-444-4-44-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i02-200002-200−2i2i−2i2i00000000000000000000
χ6444-44-444-4-44-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i0-220000-22002i−2i2i−2i00000000000000000000
χ6544-44-44-44-4-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i02-20000-22002i−2i−2i2i00000000000000000000
χ6644-44-44-44-4-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i0-2200002-200−2i2i2i−2i00000000000000000000
χ6744-44-44-44-4-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i02-20000-2200−2i2i2i−2i00000000000000000000
χ6844-44-44-44-4-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i0-2200002-2002i−2i−2i2i00000000000000000000
χ69888-8-800000000-80080008-80000000000000000000000000000000000000000000000000000000000
χ70888-8-800000000-8008000-880000000000000000000000000000000000000000000000000000000000
χ7188-88-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000
χ7288-88-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000
χ7388-8-880000000008-800000000000000000000000004-4-4400000000000000000000000000000000000
χ7488-8-880000000008-80000000000000000000000000-444-400000000000000000000000000000000000
χ7588-8-88000000000-880000000000000000000004-4-44000000000000000000000000000000000000000
χ7688-8-88000000000-88000000000000000000000-444-4000000000000000000000000000000000000000
χ7716-160000000008-800000000000000004-44-400000000000000000000000000000000000000000000000
χ7816-160000000008-80000000000000000-44-4400000000000000000000000000000000000000000000000
χ7916-16000000000-8800000000000000004-4-4400000000000000000000000000000000000000000000000
χ8016-16000000000-880000000000000000-444-400000000000000000000000000000000000000000000000

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