Finite Group Databasebeta

← Group #72215744

Character table — Group #72215744

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1122244444444888161616161616161616161616161616161616161632323232323232323232323264646464
order1222222444444444222224444444444444884448888888884488
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1
χ3111111111111111111-1-1111-1-111111111111-1-11-1-111111-1-1-1-1-1-1
χ4111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-11-1-11111
χ511111111111111111-11-111-11-1111111111-1-11-1-11-1-1-1-1-1-11-111-1-1
χ611111111111111111-11-111-11-1-1-1-1-1-1-1-1-11-1-11-1-11-11111-11-1-1-111
χ711111111111111111-1-1111-1-11111111111-1-1-11-1-11-1-1-1-1-1-11-1-111
χ811111111111111111-1-1111-1-11-1-1-1-1-1-1-1-11-1-1-11-1-111111-1-1111-1-1
χ911111-1-1111-1-11-11-11111-11111iiii−i−i−i−i-111-1-1-1-1-1ii−i−i-111i−ii−i
χ1011111-1-1111-1-11-11-11111-11111−i−i−i−iiiii-111-1-1-1-1-1−i−iii-111−ii−ii
χ1111111-1-1111-1-11-11-111-1-1-111-1-1iiii−i−i−i−i-11111-111ii−i−i-1-1-1−ii−ii
χ1211111-1-1111-1-11-11-111-1-1-111-1-1−i−i−i−iiiii-11111-111−i−iii-1-1-1i−ii−i
χ1311111-1-1111-1-11-11-11-11-1-11-11-1iiii−i−i−i−i-1-1-1-111-11−i−iii11-1i−i−ii
χ1411111-1-1111-1-11-11-11-11-1-11-11-1−i−i−i−iiiii-1-1-1-111-11ii−i−i11-1−iii−i
χ1511111-1-1111-1-11-11-11-1-11-11-1-11iiii−i−i−i−i-1-1-11-111-1−i−iii1-11−iii−i
χ1611111-1-1111-1-11-11-11-1-11-11-1-11−i−i−i−iiiii-1-1-11-111-1ii−i−i1-11i−i−ii
χ172222222222222222-2200-2-220000000000-2-2-2002000000-2000000
χ182222222222222222-2-200-2-2-20000000000-22200-20000002000000
χ192222222-2-22-2-222-2-220202-202000000000-200200-2000000-200000
χ202222222-2-22-2-222-2-220-202-20-2000000000-200-2002000000200000
χ212222222-2-22-2-222-2-2-2002-22002000000002000200-2000000-20000
χ222222222-2-22-2-222-2-2-200-2-2200-2000000002000-200200000020000
χ2322222-2-2222-2-22-22-2-22002-2200000000002-2-200-20000002000000
χ2422222-2-2222-2-22-22-2-2-2002-2-20000000000222002000000-2000000
χ2522222-2-2-2-22222-2-222020-2-202000000000200-2002000000-200000
χ2622222-2-2-2-22222-2-2220-20-2-20-2000000000200200-2000000200000
χ2722222-2-2-2-22222-2-22-20022200200000000-2000-2002000000-20000
χ2822222-2-2-2-22222-2-22-200-22200-200000000-2000200-200000020000
χ29444444400-400-4-40000000000022-2-222-2-20000000000000000000
χ30444444400-400-4-400000000000-2-222-2-2220000000000000000000
χ3144444-4-400-400-44000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000
χ3244444-4-400-400-4400000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000
χ3344-4-440000444-400-400000000000000000000000002-22-20000000
χ3444-4-440000444-400-40000000000000000000000000-22-220000000
χ3544-4-4400004-4-4-400400000000000000000000000002i−2i−2i2i0000000
χ3644-4-4400004-4-4-40040000000000000000000000000−2i2i2i−2i0000000
χ3744-4-440044-40040-400000000000000000004-40000000000000000
χ3844-4-440044-40040-40000000000000000000-440000000000000000
χ3944-4-4400-4-4-4004040040000-400000000000000000000000000000
χ4044-4-4400-4-4-40040400-40000400000000000000000000000000000
χ41888-8-80000000000000040000-4000000000000000000000000000
χ42888-8-800000000000000-400004000000000000000000000000000
χ4388-88-8000000000000040000-40000000000000000000000000000
χ4488-88-80000000000000-4000040000000000000000000000000000
χ458-80004-44i−4i04i−4i00000000000002-22i−2i2-22i−2i0000000000000000000
χ468-80004-44i−4i04i−4i0000000000000-22−2i2i-22−2i2i0000000000000000000
χ478-80004-4−4i4i0−4i4i00000000000002-2−2i2i2-2−2i2i0000000000000000000
χ488-80004-4−4i4i0−4i4i0000000000000-222i−2i-222i−2i0000000000000000000
χ498-8000-444i−4i0−4i4i00000000000002i−2i-22−2i2i2-20000000000000000000
χ508-8000-444i−4i0−4i4i0000000000000−2i2i2-22i−2i-220000000000000000000
χ518-8000-44−4i4i04i−4i00000000000002i−2i2-2−2i2i-220000000000000000000
χ528-8000-44−4i4i04i−4i0000000000000−2i2i-222i−2i2-20000000000000000000

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