Finite Group Databasebeta

← Group #72241263

Character table — Group #72241263

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222222244444444448888888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1222222222222222222244442222222222444444444444444444444444442444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111-1-11111-1-1111-1-1-1-111-1-11-11111-1-1-1-111-11-1-11111-1-1iiii−i−i−i−i11-1-1-1-1-111-1ii−i−iii−i−iii−i−i
χ1011111-1-11111-1-1111-1-1-1-111-1-11-11111-1-1-1-111-11-1-11111-1-1−i−i−i−iiiii11-1-1-1-1-111-1−i−iii−i−iii−i−iii
χ1111111-1-11111-1-1111-1-1-1-111-1-11-11111-1-1-1-111-11-1-1-1-1-1-111iiii−i−i−i−i11-1-1111-1-11ii−i−i−i−iii−i−iii
χ1211111-1-11111-1-1111-1-1-1-111-1-11-11111-1-1-1-111-11-1-1-1-1-1-111−i−i−i−iiiii11-1-1111-1-11−i−iiiii−i−iii−i−i
χ1311111-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1111111-11-1-111-1-111iiii−i−i−i−i-1-111-1-1-11-11−i−iiiii−i−i−i−iii
χ1411111-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1111111-11-1-111-1-111−i−i−i−iiiii-1-111-1-1-11-11ii−i−i−i−iiiii−i−i
χ1511111-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1111111-11-1-1-1-111-1-1iiii−i−i−i−i-1-111111-11-1−i−iii−i−iiiii−i−i
χ1611111-1-11111-1-1111-1-1-1-111-1-11-1-1-1-1-1111111-11-1-1-1-111-1-1−i−i−i−iiiii-1-111111-11-1ii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-22222222222-2-2-2-2-2-200000000000000-2-2-2-2000000000000000000
χ1822222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000002222000000000000000000
χ1922222222222222-2-222-2-222-2-2-2-200000000-2-2-22220022220000000000000000-2-2000000000000
χ2022222222222222-2-222-2-222-2-2-2-200000000-2-2-222200-2-2-2-2000000000000000022000000000000
χ2122222222222222-2-222-2-2-2-222-2-200000000222-2-2-222000000000000000022-2-200000000000000
χ2222222222222222-2-222-2-2-2-222-2-200000000222-2-2-2-2-20000000000000000-2-22200000000000000
χ2322222-2-22222-2-2222-2-2-2-2-2-2222-22222-2-2-2-2-2-22-22200000000000000-2-222000000000000000000
χ2422222-2-22222-2-2222-2-2-2-2-2-2222-2-2-2-2-22222-2-22-2220000000000000022-2-2000000000000000000
χ2522222-2-22222-2-22-2-2-2-2222222-2200000000-2-222-2-20022-2-20000000000000000-22000000000000
χ2622222-2-22222-2-22-2-2-2-2222222-2200000000-2-222-2-200-2-22200000000000000002-2000000000000
χ2722222-2-22222-2-22-2-2-2-222-2-2-2-2-220000000022-2-222220000000000000000-2-22-200000000000000
χ2822222-2-22222-2-22-2-2-2-222-2-2-2-2-220000000022-2-222-2-2000000000000000022-2200000000000000
χ292222-2222-2-2-2-2-22222-2-2-222-2-2-22000000002-22-2-220000002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ302222-2222-2-2-2-2-22222-2-2-222-2-2-22000000002-22-2-22000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ312222-2222-2-2-2-2-22222-2-2-2-2-222-2200000000-22-222-20000000000000000000000002i−2i2i−2i00000000
χ322222-2222-2-2-2-2-22222-2-2-2-2-222-2200000000-22-222-2000000000000000000000000−2i2i−2i2i00000000
χ332222-2222-2-2-2-2-22-2-22-22222222-200000000-22-2-2-22000000000000000000000000000000002-22-2
χ342222-2222-2-2-2-2-22-2-22-22222222-200000000-22-2-2-2200000000000000000000000000000000-22-22
χ352222-2222-2-2-2-2-22-2-22-222-2-2-2-22-2000000002-2222-200000000000000000000000000002i−2i2i−2i0000
χ362222-2222-2-2-2-2-22-2-22-222-2-2-2-22-2000000002-2222-20000000000000000000000000000−2i2i−2i2i0000
χ372222-2-2-22-2-2-222222-22222222-2-2000000002-2-2-22-200000022-2-2-2-2220000000000000000000000
χ382222-2-2-22-2-2-222222-22222222-2-2000000002-2-2-22-2000000-2-22222-2-20000000000000000000000
χ392222-2-2-22-2-2-222222-2222-2-2-2-2-2-200000000-2222-220000000000000000000000002-2-2200000000
χ402222-2-2-22-2-2-222222-2222-2-2-2-2-2-200000000-2222-22000000000000000000000000-222-200000000
χ412222-2-2-22-2-2-2222-2-2-22-2-222-2-22200000000-222-22-2000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-22-2-2-2222-2-2-22-2-222-2-22200000000-222-22-200000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-22-2-2-2222-2-2-22-2-2-2-22222000000002-2-22-2200000000000000000000000000002-2-220000
χ442222-2-2-22-2-2-2222-2-2-22-2-2-2-22222000000002-2-22-220000000000000000000000000000-222-20000
χ454444444-4-4-4444-400-4-400000000000000000000000000002-22-22-22-20000000000000000000000
χ464444444-4-4-4444-400-4-40000000000000000000000000000-22-22-22-220000000000000000000000
χ4744444-4-4-4-4-44-4-4-4004400000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4844444-4-4-4-4-44-4-4-400440000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ494444-444-444-4-4-4-400-4400000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ504444-444-444-4-4-4-400-440000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ514444-4-4-4-444-444-4004-400000000000000000000000000002-2-22-222-20000000000000000000000
χ524444-4-4-4-444-444-4004-40000000000000000000000000000-222-22-2-220000000000000000000000
χ5344-4-4000400000-400004-44i−4i4i−4i0022-2-222-2-2000000000000000000002i−2i2i−2i000000000000000000
χ5444-4-4000400000-400004-44i−4i4i−4i00-2-222-2-22200000000000000000000−2i2i−2i2i000000000000000000
χ5544-4-4000400000-400004-4−4i4i−4i4i0022-2-222-2-200000000000000000000−2i2i−2i2i000000000000000000
χ5644-4-4000400000-400004-4−4i4i−4i4i00-2-222-2-222000000000000000000002i−2i2i−2i000000000000000000
χ5744-4-4000400000-40000-444i−4i−4i4i0022-2-2-2-222000000000000000000002i−2i−2i2i000000000000000000
χ5844-4-4000400000-40000-444i−4i−4i4i00-2-22222-2-200000000000000000000−2i2i2i−2i000000000000000000
χ5944-4-4000400000-40000-44−4i4i4i−4i0022-2-2-2-22200000000000000000000−2i2i2i−2i000000000000000000
χ6044-4-4000400000-40000-44−4i4i4i−4i00-2-22222-2-2000000000000000000002i−2i−2i2i000000000000000000
χ614-4-44-44-400044-400000000000002-22-22-22-20000002-22-22-20000000000002-20000000000000000
χ624-4-44-44-400044-400000000000002-22-22-22-2000000-22-22-22000000000000-220000000000000000
χ634-4-44-44-400044-40000000000000-22-22-22-220000002-2-22-220000000000002-20000000000000000
χ644-4-44-44-400044-40000000000000-22-22-22-22000000-222-22-2000000000000-220000000000000000
χ654-4-44-4-440004-4400000000000002-22-2-22-220000002-22-2-22000000000000-220000000000000000
χ664-4-44-4-440004-4400000000000002-22-2-22-22000000-22-222-20000000000002-20000000000000000
χ674-4-44-4-440004-440000000000000-22-222-22-20000002-2-222-2000000000000-220000000000000000
χ684-4-44-4-440004-440000000000000-22-222-22-2000000-222-2-220000000000002-20000000000000000
χ6988-8-8000-80000088-8000000000000000000000000000000000000000000000000000000000000
χ7088-8-8000-8000008-88000000000000000000000000000000000000000000000000000000000000
χ718-88-800008-8000000000000000000004-4-44000000000000000000000000000000000000000000
χ728-88-800008-800000000000000000000-444-4000000000000000000000000000000000000000000
χ738-88-80000-8800000000000000004-4-440000000000000000000000000000000000000000000000
χ748-88-80000-880000000000000000-444-40000000000000000000000000000000000000000000000
χ758-8-8888-8000-8-88000000000000000000000000000000000000000000000000000000000000000
χ768-8-888-88000-88-8000000000000000000000000000000000000000000000000000000000000000

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