Finite Group Databasebeta

← Group #10831777

Character table — Group #10831777

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666664444444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-22222000000002222222200-2-20000-2-20000-2-2-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-200220000-2-2000022220000000000000000000000
χ19222222222-2-2-2-22222222-2-222000022-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-200-220000220000-2-2220000000000000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-222-2-2-2-2-2-2-2-200000000-2-2-2-22222002-2000022000022-2-20000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-111111111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-11111-1-1-1-11111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2-22-222-2-2111111-1-111-1-1-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-222-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-2-2-22-2-22211111111-1-11111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-1-1-1-1111111111111-1-1-1-11111222-2-2-22211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-222-1-1-1-11111111111111111-1-1-1-122-2222-2-211-1-1-1-111-1-1-1-1-1-1111100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2000022221111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-100-2-2000011−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2000022221111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-100-2-2000011i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-21111-1-1-1-1−i3−i3−i3−i3i3i3i3i3111111110022000011−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-21111-1-1-1-1i3i3i3i3−i3−i3−i3−i3111111110022000011i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-211111111−i3−i3−i3−i3i3i3i3i3-1-1-1-1111100-220000-1-1i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-211111111i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100-220000-1-1−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1002-20000-1-1i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1002-20000-1-1−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i300000000000000
χ37222-2-22-2-2222-2-222-2-22-2-2000022-2-2000022-2-2000022-2-222-2-20000000000000000000000000000000000002-2002-2000000
χ38222-2-22-2-2222-2-222-2-22-2-2000022-2-2000022-2-2000022-2-222-2-2000000000000000000000000000000000000-2200-22000000
χ39222-2-22-2-2222-2-222-2-22-2-20000-2-222000022-2-20000-2-222-2-2220000000000000000000000000000000000002-200-22000000
χ40222-2-22-2-2222-2-222-2-22-2-20000-2-222000022-2-20000-2-222-2-222000000000000000000000000000000000000-22002-2000000
χ412-2-2222-2-22-22-22-2-2222-2-200002-22-200002-22-200002-22-22-22-200000000000000000000000000000000002i−2i002i−2i00000000
χ422-2-2222-2-22-22-22-2-2222-2-200002-22-200002-22-200002-22-22-22-20000000000000000000000000000000000−2i2i00−2i2i00000000
χ432-2-2222-2-22-22-22-2-2222-2-20000-22-2200002-22-20000-22-22-22-2200000000000000000000000000000000002i−2i00−2i2i00000000
χ442-2-2222-2-22-22-22-2-2222-2-20000-22-2200002-22-20000-22-22-22-220000000000000000000000000000000000−2i2i002i−2i00000000
χ452-2-2-2-222222-2-22-2-2-2-22222-22-200000000-222-222-2-2000000000000000000002-22-22-2000000002-22-22-22-200000000000000
χ462-2-2-2-222222-2-22-2-2-2-22222-22-200000000-222-222-2-200000000000000000000-22-222-200000000-22-22-22-2200000000000000
χ472-2-2-2-222222-2-22-2-2-2-2222-22-2200000000-222-2-2-222000000000000000000002-2-22-22000000002-22-2-22-2200000000000000
χ482-2-2-2-222222-2-22-2-2-2-2222-22-2200000000-222-2-2-22200000000000000000000-222-2-2200000000-22-222-22-200000000000000
χ492-2-2-2-22222-222-2-2-2-2-22222-2-222-2-2200002-2-2222-2-22-2-222-2-22000000002-2000000-222-22-200000000000000000000000000
χ502-2-2-2-22222-222-2-2-2-2-22222-2-22-222-200002-2-2222-2-2-222-2-222-200000000-22000000-22-22-2200000000000000000000000000
χ512-2-2-2-22222-222-2-2-2-2-2222-222-22-2-2200002-2-22-2-2222-2-222-2-2200000000-220000002-2-22-2200000000000000000000000000
χ522-2-2-2-22222-222-2-2-2-2-2222-222-2-222-200002-2-22-2-222-222-2-222-2000000002-20000002-22-22-200000000000000000000000000
χ532-2-2-2-2222-12-2-221111-1-1-12-22-2000000001-1-11-1-111−i3i3i3−i3i3−i3−i3i3−i3−i3i3i3−i3−i3i3i300002-22-2-11−i3i3i3−i3−i3i3−i3i3-11-11-11-1100000000000000
χ542-2-2-2-2222-12-2-221111-1-1-12-22-2000000001-1-11-1-111−i3i3i3−i3i3−i3−i3i3i3i3−i3−i3i3i3−i3−i30000-22-22-11−i3i3i3−i3i3−i3i3−i31-11-11-11-100000000000000
χ552-2-2-2-2222-12-2-221111-1-1-12-22-2000000001-1-11-1-111i3−i3−i3i3−i3i3i3−i3−i3−i3i3i3−i3−i3i3i30000-22-22-11i3−i3−i3i3−i3i3−i3i31-11-11-11-100000000000000
χ562-2-2-2-2222-12-2-221111-1-1-12-22-2000000001-1-11-1-111i3−i3−i3i3−i3i3i3−i3i3i3−i3−i3i3i3−i3−i300002-22-2-11i3−i3−i3i3i3−i3i3−i3-11-11-11-1100000000000000
χ572-2-2-2-2222-12-2-221111-1-1-1-22-22000000001-1-1111-1-1−i3i3i3−i3i3−i3−i3i3−i3−i3i3i3i3i3−i3−i300002-2-221-1i3−i3−i3i3−i3i3i3−i3-11-111-11-100000000000000
χ582-2-2-2-2222-12-2-221111-1-1-1-22-22000000001-1-1111-1-1−i3i3i3−i3i3−i3−i3i3i3i3−i3−i3−i3−i3i3i30000-222-21-1i3−i3−i3i3i3−i3−i3i31-11-1-11-1100000000000000
χ592-2-2-2-2222-12-2-221111-1-1-1-22-22000000001-1-1111-1-1i3−i3−i3i3−i3i3i3−i3−i3−i3i3i3i3i3−i3−i30000-222-21-1−i3i3i3−i3−i3i3i3−i31-11-1-11-1100000000000000
χ602-2-2-2-2222-12-2-221111-1-1-1-22-22000000001-1-1111-1-1i3−i3−i3i3−i3i3i3−i3i3i3−i3−i3−i3−i3i3i300002-2-221-1−i3i3i3−i3i3−i3−i3i3-11-111-11-100000000000000
χ612-2-2-2-2222-1-222-21111-1-1-12-2-222-2-220000-111-1-1-111-111-1-111-1−i3−i3i3i3−i3−i3i3i32-20000001-1-11-11i3−i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ622-2-2-2-2222-1-222-21111-1-1-12-2-222-2-220000-111-1-1-111-111-1-111-1i3i3−i3−i3i3i3−i3−i32-20000001-1-11-11−i3i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ632-2-2-2-2222-1-222-21111-1-1-12-2-22-222-20000-111-1-1-1111-1-111-1-11−i3−i3i3i3−i3−i3i3i3-220000001-11-11-1i3−i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000
χ642-2-2-2-2222-1-222-21111-1-1-12-2-22-222-20000-111-1-1-1111-1-111-1-11i3i3−i3−i3i3i3−i3−i3-220000001-11-11-1−i3i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000
χ652-2-2-2-2222-1-222-21111-1-1-1-222-22-2-220000-111-111-1-1-111-1-111-1−i3−i3i3i3i3i3−i3−i3-22000000-111-11-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000
χ662-2-2-2-2222-1-222-21111-1-1-1-222-22-2-220000-111-111-1-1-111-1-111-1i3i3−i3−i3−i3−i3i3i3-22000000-111-11-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000
χ672-2-2-2-2222-1-222-21111-1-1-1-222-2-222-20000-111-111-1-11-1-111-1-11−i3−i3i3i3i3i3−i3−i32-2000000-11-11-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000
χ682-2-2-2-2222-1-222-21111-1-1-1-222-2-222-20000-111-111-1-11-1-111-1-11i3i3−i3−i3−i3−i3i3i32-2000000-11-11-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000
χ69444-4-44-4-44-4-44444-4-44-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000000000
χ70444-4-44-4-4-244-4-4-2-222-222000044-4-40000-2-2220000-2-222-2-222000000000000000000000000000000000000000000000000
χ71444-4-44-4-4-244-4-4-2-222-2220000-4-4440000-2-222000022-2-222-2-2000000000000000000000000000000000000000000000000
χ72444-4-44-4-4-2-4-444-2-222-22200000000000022-2-20000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000000000000000000000
χ73444-4-44-4-4-2-4-444-2-222-22200000000000022-2-200002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000000000000000000000
χ7444-44-4-44-4400004-44-4-44-400000000004-4000000000000000000004-44-40000000000000000000000000000000000000000
χ7544-44-4-44-4400004-44-4-44-40000000000-4400000000000000000000-44-440000000000000000000000000000000000000000
χ7644-44-4-44-4-20000-22-222-2200000000004-40000−2i32i3−2i32i300000000−2i32i3−2i32i3-22-220000000000000000000000000000000000000000
χ7744-44-4-44-4-20000-22-222-2200000000004-400002i3−2i32i3−2i3000000002i3−2i32i3−2i3-22-220000000000000000000000000000000000000000
χ7844-44-4-44-4-20000-22-222-220000000000-440000−2i32i3−2i32i3000000002i3−2i32i3−2i32-22-20000000000000000000000000000000000000000
χ7944-44-4-44-4-20000-22-222-220000000000-4400002i3−2i32i3−2i300000000−2i32i3−2i32i32-22-20000000000000000000000000000000000000000
χ8044-4-44-4-44400004-4-44-4-440000000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ8144-4-44-4-44400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ824-444-4-4-4440000-444-4-4-44000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ834-444-4-4-4440000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ844-44-44-44-440000-44-44-44-4000000004-40000000000000000004-4-4400000000000000000000000000000000000000000000
χ854-44-44-44-440000-44-44-44-400000000-44000000000000000000-444-400000000000000000000000000000000000000000000
χ864-44-44-44-4-200002-22-22-22000000004-4000000−2i32i32i3−2i300000000-222-2−2i32i32i3−2i30000000000000000000000000000000000000000
χ874-44-44-44-4-200002-22-22-22000000004-40000002i3−2i3−2i32i300000000-222-22i3−2i3−2i32i30000000000000000000000000000000000000000
χ884-44-44-44-4-200002-22-22-2200000000-44000000−2i32i32i3−2i3000000002-2-222i3−2i3−2i32i30000000000000000000000000000000000000000
χ894-44-44-44-4-200002-22-22-2200000000-440000002i3−2i3−2i32i3000000002-2-22−2i32i32i3−2i30000000000000000000000000000000000000000
χ904-4-4444-4-444-44-4-4-4444-4-4000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-4-24-44-422-2-2-2220000000000002-22-20000−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ924-4-4444-4-4-24-44-422-2-2-2220000000000002-22-200002i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ934-4-4444-4-4-2-44-4422-2-2-22200004-44-40000-22-220000-22-22-22-22000000000000000000000000000000000000000000000000
χ944-4-4444-4-4-2-44-4422-2-2-2220000-44-440000-22-2200002-22-22-22-2000000000000000000000000000000000000000000000000
χ9588-8-88-8-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-8-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000000000

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