Finite Group Databasebeta

← Group #72286909

Character table — Group #72286909

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112224444444488816161616161616161616161616161616323232323232323232323232323232323232646464646464646464646464646464646464
order122222244444444422222222224488884444448888888888884444444488888816161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111
χ511111111111111111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ611111111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ911-1-111-111-1-1-1-111-111-1-111-1-11-11-11-1-111-1ii−i−iii−i−iii−i−iii−i−iii−i−i11-1-1i−i1-1i−i11-1-1
χ1011-1-111-111-1-1-1-111-111-1-111-1-11-11-11-1-111-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111−ii1-1−ii-1-111
χ1111-1-111-111-1-1-1-111-111-1-111-1-11-11-11-1-111-1−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111i−i1-1i−i-1-111
χ1211-1-111-111-1-1-1-111-111-1-111-1-11-11-11-1-111-1−i−iii−i−iii−i−iii−i−iii−i−iii11-1-1−ii1-1−ii11-1-1
χ1311-1-111-111-1-1-1-111-111-1-1-1-1111-11-11-1-11-11ii−i−iii−i−iii−i−i−i−iii−i−iii-1-111i−i-11−ii11-1-1
χ1411-1-111-111-1-1-1-111-111-1-1-1-1111-11-11-1-11-11ii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1−ii-11i−i-1-111
χ1511-1-111-111-1-1-1-111-111-1-1-1-1111-11-11-1-11-11−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1i−i-11−ii-1-111
χ1611-1-111-111-1-1-1-111-111-1-1-1-1111-11-11-1-11-11−i−iii−i−iii−i−iiiii−i−iii−i−i-1-111−ii-11i−i11-1-1
χ172222222222222222222-22222-22-2-2-2-2-2-22200000000000000000000000000-2-2000000
χ182222222222222222222-2-2-2-2-2-22-2-2-2-2-2-2-2-20000000000000000000000000022000000
χ192222222222222222-2-2-2200002-222-2-2-2-2000000000000002222000000000000-2-20000
χ202222222222222222-2-2-2200002-222-2-2-2-200000000000000-2-2-2-2000000000000220000
χ212222222222222222-2-2-2-20000-2-2-2-2222200000022220000000000000000-2-200000000
χ222222222222222222-2-2-2-20000-2-2-2-22222000000-2-2-2-200000000000000002200000000
χ2322222-2-2-22222-2-22-22-22200002-2-2-222-2-2002i−2i2i−2i00002i−2i2i−2i0000000000000000000000
χ2422222-2-2-22222-2-22-22-22200002-2-2-222-2-200−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000
χ2522222-2-2-22222-2-22-22-22-20000-2-222-2-2220000000000000000002i−2i2i−2i00000000000000
χ2622222-2-2-22222-2-22-22-22-20000-2-222-2-222000000000000000000−2i2i−2i2i00000000000000
χ2722222-2-2-22222-2-22-2-22-22000022-2-2-2-22200000000000000000000002-22-20000000000
χ2822222-2-2-22222-2-22-2-22-22000022-2-2-2-2220000000000000000000000-22-220000000000
χ2922222-2-2-22222-2-22-2-22-2-20000-222222-2-2000000000000000000000000000000002i−2i2i−2i
χ3022222-2-2-22222-2-22-2-22-2-20000-222222-2-200000000000000000000000000000000−2i2i−2i2i
χ3122-2-222-222-2-2-2-222-222-2222-2-2-2-2-22-222-22-200000000000000000000000000-22000000
χ3222-2-222-222-2-2-2-222-222-22-2-222-2-2-22-222-2-22000000000000000000000000002-2000000
χ3322-2-222-222-2-2-2-222-2-2-2220000-22-222-2-220000002i2i−2i−2i0000000000000000−2i2i00000000
χ3422-2-222-222-2-2-2-222-2-2-2220000-22-222-2-22000000−2i−2i2i2i00000000000000002i−2i00000000
χ3522-2-222-222-2-2-2-222-2-2-22-20000222-2-222-2000000000000002i2i−2i−2i000000000000−2i2i0000
χ3622-2-222-222-2-2-2-222-2-2-22-20000222-2-222-200000000000000−2i−2i2i2i0000000000002i−2i0000
χ3722-2-22-22-22-2-2-22-2222-2-220000-222-2-22-220000000000000000002-2-2200000000000000
χ3822-2-22-22-22-2-2-22-2222-2-220000-222-2-22-22000000000000000000-222-200000000000000
χ3922-2-22-22-22-2-2-22-2222-2-2-2000022-222-22-2002-2-2200002-2-220000000000000000000000
χ4022-2-22-22-22-2-2-22-2222-2-2-2000022-222-22-200-222-20000-222-20000000000000000000000
χ4122-2-22-22-22-2-2-22-222-22220000-2-22-22-22-2000000000000000000000000000000002i−2i−2i2i
χ4222-2-22-22-22-2-2-22-222-22220000-2-22-22-22-200000000000000000000000000000000−2i2i2i−2i
χ4322-2-22-22-22-2-2-22-222-222-200002-2-22-22-2200000000000000000000002-2-220000000000
χ4422-2-22-22-22-2-2-22-222-222-200002-2-22-22-220000000000000000000000-222-20000000000
χ45444444444-4-444-4-4-400000000000000000022220000-2-2-2-20000000000000000000000
χ46444444444-4-444-4-4-4000000000000000000-2-2-2-2000022220000000000000000000000
χ474444444-4-400-4-40000000222200000000-2-200002i−2i2i−2i00002i−2i2i−2i000000000000000000
χ484444444-4-400-4-40000000222200000000-2-20000−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ494444444-4-400-4-40000000-2-2-2-2000000002200002i−2i2i−2i0000−2i2i−2i2i000000000000000000
χ504444444-4-400-4-40000000-2-2-2-200000000220000−2i2i−2i2i00002i−2i2i−2i000000000000000000
χ5144444-4-4-44-4-44-44-440000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000000000
χ5244444-4-4-44-4-44-44-44000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000000000
χ5344-4-444-44444-4-4-4-440000000000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000
χ5444-4-444-44444-4-4-4-44000000000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000
χ5544-4-444-4-4-40044000000022-2-200000000-2200002-2-2200002-2-22000000000000000000
χ5644-4-444-4-4-40044000000022-2-200000000-220000-222-20000-222-2000000000000000000
χ5744-4-444-4-4-400440000000-2-222000000002-200002-2-220000-222-2000000000000000000
χ5844-4-444-4-4-400440000000-2-222000000002-20000-222-200002-2-22000000000000000000
χ5944-4-44-44-4444-444-4-40000000000000000002-2-220000-222-20000000000000000000000
χ6044-4-44-44-4444-444-4-4000000000000000000-222-200002-2-220000000000000000000000
χ6188888-8-88-800-880000000000000000000000000000000000000000000000000000000
χ6288-8-88-888-8008-80000000000000000000000000000000000000000000000000000000
χ63161616-16-16000000000000000000000000000000000000000000000000000000000000000
χ641616-1616-16000000000000000000000000000000000000000000000000000000000000000
χ6516-1600000008-80000000004-44-400000000000000000000000000000000000000000000
χ6616-1600000008-8000000000-44-4400000000000000000000000000000000000000000000
χ6716-160000000-880000000004-4-4400000000000000000000000000000000000000000000
χ6816-160000000-88000000000-444-400000000000000000000000000000000000000000000

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