Finite Group Databasebeta

← Group #10901272

Character table — Group #10901272

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222444488888888888888888888881212121216161616161616161616242424242424242424244848
order1222222234444666666612121212244444668888121224242424242424244444441212121212121212224444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1111111-1-1
χ9111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-11111-1-1-1-11111-1-11-1
χ10111111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-111-11
χ11111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-11-1-11111-1-1-1-1-1-111-1-111-11
χ12111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-11111-1-111-1-11-1
χ13111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1-1-1-111-1-1-11
χ14111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1111-1
χ15111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-1111-1
χ16111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-1111111-1-1-11
χ17222222222-2-2-2-22222222-2-2-2-22-20000220000-2-20000000022-2-2000000000000-2200000000
χ18222222222-2-2-2-22222222-2-2-2-22-20000220000-2-200000000-2-2220000000000002-200000000
χ19222222222-2-2-2-22222222-2-2-2-2-220000-2-20000220000000022-2-20000000000002-200000000
χ20222222222-2-2-2-22222222-2-2-2-2-220000-2-200002200000000-2-222000000000000-2200000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1222222-1-1-2-2-2-2-1-1111111110000-2-2-1-111-1-111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-2-2-2-2-1-11111111100002211-1-111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21122-2-211-1-1-1-1111100002-21111-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211-2-222111111-1-1-1-10000-2211-1-1-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221122-2-211-1-1-1-111110000-22-1-1-1-11111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-222111111-1-1-1-100002-2-1-11111-1-1000000000000
χ292-2-2-222-2222-22-22-2-2-22-222-22-200002-200000000000000002-22-2002-20000002-20000000000
χ302-2-2-222-2222-22-22-2-2-22-222-22-200002-20000000000000000-22-22002-2000000-220000000000
χ312-2-2-222-2222-22-22-2-2-22-222-22-20000-2200000000000000002-22-200-22000000-220000000000
χ322-2-2-222-2222-22-22-2-2-22-222-22-20000-220000000000000000-22-2200-220000002-20000000000
χ332-2-2-222-222-22-222-2-2-22-22-22-22002-20000000000000000002-2-220000002-20000002-2000000
χ342-2-2-222-222-22-222-2-2-22-22-22-22002-2000000000000000000-222-20000002-2000000-22000000
χ352-2-2-222-222-22-222-2-2-22-22-22-2200-220000000000000000002-2-22000000-22000000-22000000
χ362-2-2-222-222-22-222-2-2-22-22-22-2200-22000000000000000000-222-2000000-220000002-2000000
χ3744444444-2-4-4-4-4-2-2-2-2-2-2-222224-40000-2-20000220000000000000000000000000000000000
χ3844444444-2-4-4-4-4-2-2-2-2-2-2-22222-440000220000-2-20000000000000000000000000000000000
χ39444-44-4-4-440000444-4-4-4-40000000000000022−220000002222−22−2200000000000000000000000000
χ40444-44-4-4-440000444-4-4-4-400000000000000−2222000000−22−22222200000000000000000000000000
χ41444-44-4-4-4-20000-2-2-222220000000000−2i32i30022−2200i6i6−i6−i6−2−22200000000000000000000000000
χ42444-44-4-4-4-20000-2-2-222220000000000−2i32i300−222200−i6−i6i6i622−2−200000000000000000000000000
χ43444-44-4-4-4-20000-2-2-2222200000000002i3−2i30022−2200−i6−i6i6i6−2−22200000000000000000000000000
χ44444-44-4-4-4-20000-2-2-2222200000000002i3−2i300−222200i6i6−i6−i622−2−200000000000000000000000000
χ4544-44-44-4-4444-4-4-44-44-4-4444-4-4000000000000000000000000000000000000000000000000
χ4644-44-44-4-44-4-444-44-44-4-44-4-444000000000000000000000000000000000000000000000000
χ4744-44-44-4-4-244-4-42-22-222-2-2-22200000000000000000023−2323−2300000000000000000000000000
χ4844-44-44-4-4-244-4-42-22-222-2-2-222000000000000000000−2323−232300000000000000000000000000
χ4944-44-44-4-4-2-4-4442-22-222-222-2-200000000000000−2i32i3−2i32i3000000000000000000000000000000
χ5044-44-44-4-4-2-4-4442-22-222-222-2-2000000000000002i3−2i32i3−2i3000000000000000000000000000000
χ5144-4-4-4-44440000-44-4-444-400000000000022−22000022−22−2222000000000000000000000000000000
χ5244-4-4-4-44440000-44-4-444-4000000000000−22220000−222222−22000000000000000000000000000000
χ5344-4-4-4-444-200002-222-2-2200000000000022−220023−23−222−26−6−6600000000000000000000000000
χ5444-4-4-4-444-200002-222-2-2200000000000022−2200−2323−222−2−666−600000000000000000000000000
χ5544-4-4-4-444-200002-222-2-22000000000000−22220023−232−2−22−666−600000000000000000000000000
χ5644-4-4-4-444-200002-222-2-22000000000000−222200−23232−2−226−6−6600000000000000000000000000
χ574-444-4-4-4440000-4-4444-4-40000000000000000000000000000000000000000000000−2i22i20000
χ584-444-4-4-4440000-4-4444-4-400000000000000000000000000000000000000000000002i2−2i20000
χ594-44-4-444-444-4-44-4-44-4-4444-4-44000000000000000000000000000000000000000000000000
χ604-44-4-444-44-444-4-4-44-4-444-444-4000000000000000000000000000000000000000000000000
χ614-44-4-444-4-24-4-4422-222-2-2-222-20000000000000000000000000000000000−2i32i3000000000000
χ624-44-4-444-4-24-4-4422-222-2-2-222-200000000000000000000000000000000002i3−2i3000000000000
χ634-44-4-444-4-2-444-422-222-2-22-2-22000000000000000000000000000000−2i32i30000000000000000
χ644-44-4-444-4-2-444-422-222-2-22-2-220000000000000000000000000000002i3−2i30000000000000000
χ654-4-444-44-4400004-4-44-44-4000000000000000000000000000000000000000000000000−2i22i200
χ664-4-444-44-4400004-4-44-44-40000000000000000000000000000000000000000000000002i2−2i200
χ674-4-4-444-44-24-44-4-2222-22-2-22-2200004-40000000000000000000000-22000000000000000000
χ684-4-4-444-44-24-44-4-2222-22-2-22-220000-4400000000000000000000002-2000000000000000000
χ694-4-4-444-44-2-44-44-2222-22-22-22-2004-40000000000000000000000000000-2200000000000000
χ704-4-4-444-44-2-44-44-2222-22-22-22-200-4400000000000000000000000000002-200000000000000
χ718-888-8-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000
χ728-8-888-88-8-40000-444-44-440000000000000000000000000000000000000000000000000000

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