Finite Group Databasebeta

← Group #10844607

Character table — Group #10844607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666664444444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ411111111111111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ5111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-11
χ6111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111-1
χ7111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ17222222222-2-2-2-2222222200002222-2-222-2-2-2-222220000000022222222-2-2000000-2-2-2-2000000000000-2-200000000000000
χ18222222222-2-2-2-22222222000022-2-222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-22000000-2-2220000000000002200000000000000
χ19222222222-2-2-2-222222220000-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-2-2-222222-200000022-2-20000000000002200000000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-222-2-2-2-2222200000000-2-2-2-2-2-2-2-2220000002222000000000000-2-200000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111112-2-2-222-2-2-1-1111111-1-1-1-111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-22-2-2-2-22211-1-111111111-1-1-1-11100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-21111-1-1-1-111111111-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222222222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1111111111111-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-111112-222-2-222-1-111-1-1-1-11111-1-1-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-222222-2-211-1-1-1-1-1-1-1-1-1-111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2221111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-1-2-20000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i31100000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2221111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-1-2-20000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i31100000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222-2-211111111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111-2200000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-100000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222-2-211111111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111-2200000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-100000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-211111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-12-2000000-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-100000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-211111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-12-2000000-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-100000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2221111-1-1-1-1−i3−i3−i3−i3i3i3i3i31111111122000000-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i31100000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2221111-1-1-1-1i3i3i3i3−i3−i3−i3−i31111111122000000-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i31100000000000000
χ37222-2-2-2-2222-2-2222-22-2-2-222-2-20000000022-2-2000022-2-222-2-200000000000000000000000000000000002i−2i002i−2i00000000
χ38222-2-2-2-2222-2-2222-22-2-2-222-2-20000000022-2-2000022-2-222-2-20000000000000000000000000000000000−2i2i00−2i2i00000000
χ39222-2-2-2-2222-2-2222-22-2-2-2-2-2220000000022-2-20000-2-222-2-22200000000000000000000000000000000002i−2i00−2i2i00000000
χ40222-2-2-2-2222-2-2222-22-2-2-2-2-2220000000022-2-20000-2-222-2-2220000000000000000000000000000000000−2i2i002i−2i00000000
χ412-2-222-2-2222-22-2-22-2-222-22i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002-20000002i−2i00
χ422-2-222-2-2222-22-2-22-2-222-22i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000-22000000−2i2i00
χ432-2-222-2-2222-22-2-22-2-222-2−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002-2000000−2i2i00
χ442-2-222-2-2222-22-2-22-2-222-2−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000-220000002i−2i00
χ452-2-2-2-2222222-2-2-222-2-2-222i−2i−2i2i00002-22-22-2-2222-2-22i−2i−2i2i2i−2i−2i2i00000000002i−2i000000002i−2i2i−2i000000002-200000000000000
χ462-2-2-2-2222222-2-2-222-2-2-222i−2i−2i2i0000-22-222-2-22-2-2222i−2i−2i2i2i−2i−2i2i0000000000−2i2i00000000−2i2i−2i2i00000000-2200000000000000
χ472-2-2-2-2222222-2-2-222-2-2-22−2i2i2i−2i00002-22-22-2-2222-2-2−2i2i2i−2i−2i2i2i−2i0000000000−2i2i00000000−2i2i−2i2i000000002-200000000000000
χ482-2-2-2-2222222-2-2-222-2-2-22−2i2i2i−2i0000-22-222-2-22-2-222−2i2i2i−2i−2i2i2i−2i00000000002i−2i000000002i−2i2i−2i00000000-2200000000000000
χ492-2-2-2-22222-2-222-222-2-2-22000000002-2-22-222-2-2-222000000000000000000002-22-2000000002-22-22-22-22-200000000000000
χ502-2-2-2-22222-2-222-222-2-2-22000000002-2-22-222-2-2-22200000000000000000000-22-2200000000-22-22-22-222-200000000000000
χ512-2-2-2-22222-2-222-222-2-2-2200000000-222-2-222-222-2-2000000000000000000002-2-22000000002-22-2-22-22-2200000000000000
χ522-2-2-2-22222-2-222-222-2-2-2200000000-222-2-222-222-2-200000000000000000000-222-200000000-22-222-22-2-2200000000000000
χ532-2-2-2-2222-122-2-21-1-1111-12i−2i−2i2i00002-22-2-111-1-1-111−iii−i−iii−i33−3−333−3−3002i−2i00003−33−3−ii−ii−i3i3i3−i3i3−i3−i3i3-1100000000000000
χ542-2-2-2-2222-122-2-21-1-1111-12i−2i−2i2i00002-22-2-111-1-1-111−iii−i−iii−i−3−333−3−333002i−2i0000−33−33−ii−iii3−i3−i3i3−i3i3i3−i3-1100000000000000
χ552-2-2-2-2222-122-2-21-1-1111-12i−2i−2i2i0000-22-22-111-111-1-1−iii−i−iii−i33−3−3−3−33300−2i2i00003−3−33i−ii−i−i3i3i3−i3−i3i3i3−i31-100000000000000
χ562-2-2-2-2222-122-2-21-1-1111-12i−2i−2i2i0000-22-22-111-111-1-1−iii−i−iii−i−3−33333−3−300−2i2i0000−333−3i−ii−ii3−i3−i3i3i3−i3−i3i31-100000000000000
χ572-2-2-2-2222-122-2-21-1-1111-1−2i2i2i−2i00002-22-2-111-1-1-111i−i−iii−i−ii33−3−333−3−300−2i2i00003−33−3i−ii−ii3−i3−i3i3−i3i3i3−i3-1100000000000000
χ582-2-2-2-2222-122-2-21-1-1111-1−2i2i2i−2i00002-22-2-111-1-1-111i−i−iii−i−ii−3−333−3−33300−2i2i0000−33−33i−ii−i−i3i3i3−i3i3−i3−i3i3-1100000000000000
χ592-2-2-2-2222-122-2-21-1-1111-1−2i2i2i−2i0000-22-22-111-111-1-1i−i−iii−i−ii33−3−3−3−333002i−2i00003−3−33−ii−iii3−i3−i3i3i3−i3−i3i31-100000000000000
χ602-2-2-2-2222-122-2-21-1-1111-1−2i2i2i−2i0000-22-22-111-111-1-1i−i−iii−i−ii−3−33333−3−3002i−2i0000−333−3−ii−ii−i3i3i3−i3−i3i3i3−i31-100000000000000
χ612-2-2-2-2222-1-2-2221-1-1111-1000000002-2-221-1-1111-1-13−3−33−333−333−3−3−3−33300002-22-2−333−3−333−3-11-11-11-11-1100000000000000
χ622-2-2-2-2222-1-2-2221-1-1111-1000000002-2-221-1-1111-1-13−3−33−333−3−3−33333−3−30000-22-223−3−33−333−31-11-11-11-1-1100000000000000
χ632-2-2-2-2222-1-2-2221-1-1111-1000000002-2-221-1-1111-1-1−333−33−3−3333−3−3−3−3330000-22-22−333−33−3−331-11-11-11-1-1100000000000000
χ642-2-2-2-2222-1-2-2221-1-1111-1000000002-2-221-1-1111-1-1−333−33−3−33−3−33333−3−300002-22-23−3−333−3−33-11-11-11-11-1100000000000000
χ652-2-2-2-2222-1-2-2221-1-1111-100000000-222-21-1-11-1-1113−3−33−333−333−3−333−3−300002-2-22−33−333−3−33-11-111-11-11-100000000000000
χ662-2-2-2-2222-1-2-2221-1-1111-100000000-222-21-1-11-1-1113−3−33−333−3−3−333−3−3330000-222-23−33−33−3−331-11-1-11-111-100000000000000
χ672-2-2-2-2222-1-2-2221-1-1111-100000000-222-21-1-11-1-111−333−33−3−3333−3−333−3−30000-222-2−33−33−333−31-11-1-11-111-100000000000000
χ682-2-2-2-2222-1-2-2221-1-1111-100000000-222-21-1-11-1-111−333−33−3−33−3−333−3−33300002-2-223−33−3−333−3-11-111-11-11-100000000000000
χ69444-4-4-4-444-444-444-44-4-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-44-24-4-44-2-22-222244-4-400000000-2-2220000-2-222-2-222000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-24-4-44-2-22-2222-4-44400000000-2-222000022-2-222-2-2000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-2-444-4-2-22-222200000000000022-2-20000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-2-444-4-2-22-222200000000000022-2-200002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000000000000000000000000000
χ7444-44-4-44-4400004-44-44-4-400004-400000000000000000000004-44-400000000000000000000000000000000000000000000
χ7544-44-4-44-4400004-44-44-4-40000-440000000000000000000000-44-4400000000000000000000000000000000000000000000
χ7644-44-4-44-4-20000-22-22-22200004-40000000000−2i32i3−2i32i300000000-22-22−2i32i3−2i32i30000000000000000000000000000000000000000
χ7744-44-4-44-4-20000-22-22-22200004-400000000002i3−2i32i3−2i300000000-22-222i3−2i32i3−2i30000000000000000000000000000000000000000
χ7844-44-4-44-4-20000-22-22-2220000-440000000000−2i32i3−2i32i3000000002-22-22i3−2i32i3−2i30000000000000000000000000000000000000000
χ7944-44-4-44-4-20000-22-22-2220000-4400000000002i3−2i32i3−2i3000000002-22-2−2i32i3−2i32i30000000000000000000000000000000000000000
χ8044-4-444-4-4400004-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ8144-4-444-4-4400004-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ824-444-44-4-440000-4-4-444-440000000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ834-444-44-4-440000-4-4-444-4400000000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ844-44-44-44-440000-4-444-44-40000004i−4i0000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ854-44-44-44-440000-4-444-44-4000000−4i4i000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ864-44-44-44-4-2000022-2-22-220000004i−4i00000000−2i32i32i3−2i30000000023−23−2323−2i2i2i−2i0000000000000000000000000000000000000000
χ874-44-44-44-4-2000022-2-22-220000004i−4i000000002i3−2i3−2i32i300000000−232323−23−2i2i2i−2i0000000000000000000000000000000000000000
χ884-44-44-44-4-2000022-2-22-22000000−4i4i00000000−2i32i32i3−2i300000000−232323−232i−2i−2i2i0000000000000000000000000000000000000000
χ894-44-44-44-4-2000022-2-22-22000000−4i4i000000002i3−2i3−2i32i30000000023−23−23232i−2i−2i2i0000000000000000000000000000000000000000
χ904-4-444-4-444-44-44-44-4-444-4000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ914-4-444-4-44-24-44-42-222-2-224i−4i4i−4i00000000-22-220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ924-4-444-4-44-24-44-42-222-2-22−4i4i−4i4i00000000-22-2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ934-4-444-4-44-2-44-442-222-2-220000000000002-22-2000023−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ944-4-444-4-44-2-44-442-222-2-220000000000002-22-20000−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ9588-8-888-8-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000

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