Finite Group Databasebeta

← Group #10844667

Character table — Group #10844667

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666664444444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11-1
χ411111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11
χ5111111111111111111111111-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-11
χ8111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-2222222200002222-2-2-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-2200-20000220000220000-2-2000000000000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2-200000000222222222222-200-20000-2-20000-2-20000-2-2000000000000000000
χ19222222222-2-2-2-222222220000-2-22222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-22222-20020000-2-2000022000022000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-222-2-2-2-200000000-2-2-2-22222-2-2-2-220020000220000-2-2000022000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2222-2-2-2-211-1-1-1-1111111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2-222-2-2111111-1-1111111-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12-2-2-2-2-222-1-1111111-1-1-1-111111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-1-11111-1-11111-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-2-22222211111111-1-1-1-1-1-1-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-222-1-1-1-1111111111111-1-1-1-11111-222-2-2-22211-1-1-1-1-1-1-1-1-1-111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-1-1-1-11111111111111111-1-1-1-1222-222-2-2-1-1-1-1-1-111111111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2-2-21111−i3−i3−i3−i3i3i3i3i3-1-1-1-111111111200-20000-1-1−i3−i3i3i3-1-1−i3−i3i3i311−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2-2-21111i3i3i3i3−i3−i3−i3−i3-1-1-1-111111111200-20000-1-1i3i3−i3−i3-1-1i3i3−i3−i311i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222221111−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-1-1-1-1-1-200-2000011−i3−i3i3i311i3i3−i3−i311i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222221111i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-1-1-1-1-1-200-2000011i3i3−i3−i311−i3−i3i3i311−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-21111−i3−i3−i3−i3i3i3i3i311111111-1-1-1-1-2002000011i3i3−i3−i3-1-1i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-21111i3i3i3i3−i3−i3−i3−i311111111-1-1-1-1-2002000011−i3−i3i3i3-1-1−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2221111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1111120020000-1-1i3i3−i3−i311−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2221111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1111120020000-1-1−i3−i3i3i311i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ37222-2-2-22-222-2-22222-2-2-2-222-2-20000000022-2-222-2-222-2-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ38222-2-2-22-222-2-22222-2-2-2-222-2-20000000022-2-222-2-222-2-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ39222-2-2-22-222-2-22222-2-2-2-2-2-2220000000022-2-2-2-222-2-22200000000000000000000000000000000000000002i−2i−2i2i00000000
χ40222-2-2-22-222-2-22222-2-2-2-2-2-2220000000022-2-2-2-222-2-2220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ412-2-22-222-222-22-2-22-22-2-222i−2i2i−2i000000002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002-200002i−2i000000
χ422-2-22-222-222-22-2-22-22-2-222i−2i2i−2i000000002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-220000−2i2i000000
χ432-2-22-222-222-22-2-22-22-2-22−2i2i−2i2i000000002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002-20000−2i2i000000
χ442-2-22-222-222-22-2-22-22-2-22−2i2i−2i2i000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-2200002i−2i000000
χ452-2-2-22-222222-2-2-22-2-222-22i−2i−2i2i002-2002-22-2-222i−2i−2i2i2i−2i−2i2i000022-2-2000000002i−2i000000002-20000002i−2i2i−2i00000000000000
χ462-2-2-22-222222-2-2-22-2-222-22i−2i−2i2i00-2200-222-2-222i−2i−2i2i2i−2i−2i2i0000-2-22200000000−2i2i00000000-22000000−2i2i−2i2i00000000000000
χ472-2-2-22-222222-2-2-22-2-222-2−2i2i2i−2i002-2002-22-2-22−2i2i2i−2i−2i2i2i−2i000022-2-200000000−2i2i000000002-2000000−2i2i−2i2i00000000000000
χ482-2-2-22-222222-2-2-22-2-222-2−2i2i2i−2i00-2200-222-2-22−2i2i2i−2i−2i2i2i−2i0000-2-222000000002i−2i00000000-220000002i−2i2i−2i00000000000000
χ492-2-2-22-2222-2-222-22-2-222-20000002-200-22-222-2000000000000-2-222000002-20002-2002-22-22-22-22-200000000000000000000
χ502-2-2-22-2222-2-222-22-2-222-20000002-200-22-222-2000000000000-2-22200000-22000-2200-22-222-2-22-2200000000000000000000
χ512-2-2-22-2222-2-222-22-2-222-2000000-22002-2-222-200000000000022-2-2000002-2000-22002-22-2-22-22-2200000000000000000000
χ522-2-2-22-2222-2-222-22-2-222-2000000-22002-2-222-200000000000022-2-200000-220002-200-22-22-222-22-200000000000000000000
χ532-2-2-22-222-122-2-21-111-1-112i−2i−2i2i002-2002-2-111-1−iii−i−iii−i33−3−3-1-11133−3−300002i−2i003−3−i3i3i3−i3-11−i3i3i3−i33−3−ii−ii00000000000000
χ542-2-2-22-222-122-2-21-111-1-112i−2i−2i2i002-2002-2-111-1−iii−i−iii−i−3−333-1-111−3−33300002i−2i00−33i3−i3−i3i3-11i3−i3−i3i3−33−ii−ii00000000000000
χ552-2-2-22-222-122-2-21-111-1-112i−2i−2i2i00-2200-22-111-1−iii−i−iii−i33−3−311-1-1−3−3330000−2i2i00−33−i3i3i3−i31-1i3−i3−i3i33−3i−ii−i00000000000000
χ562-2-2-22-222-122-2-21-111-1-112i−2i−2i2i00-2200-22-111-1−iii−i−iii−i−3−33311-1-133−3−30000−2i2i003−3i3−i3−i3i31-1−i3i3i3−i3−33i−ii−i00000000000000
χ572-2-2-22-222-122-2-21-111-1-11−2i2i2i−2i002-2002-2-111-1i−i−iii−i−ii33−3−3-1-11133−3−30000−2i2i003−3i3−i3−i3i3-11i3−i3−i3i33−3i−ii−i00000000000000
χ582-2-2-22-222-122-2-21-111-1-11−2i2i2i−2i002-2002-2-111-1i−i−iii−i−ii−3−333-1-111−3−3330000−2i2i00−33−i3i3i3−i3-11−i3i3i3−i3−33i−ii−i00000000000000
χ592-2-2-22-222-122-2-21-111-1-11−2i2i2i−2i00-2200-22-111-1i−i−iii−i−ii33−3−311-1-1−3−33300002i−2i00−33i3−i3−i3i31-1−i3i3i3−i33−3−ii−ii00000000000000
χ602-2-2-22-222-122-2-21-111-1-11−2i2i2i−2i00-2200-22-111-1i−i−iii−i−ii−3−33311-1-133−3−300002i−2i003−3−i3i3i3−i31-1i3−i3−i3i3−33−ii−ii00000000000000
χ612-2-2-22-222-1-2-2221-111-1-110000002-200-221-1-113−3−33−333−333−3−311-1-1−3−33302-20002-23−3-11-11-11-11-11−333−3−3300000000000000
χ622-2-2-22-222-1-2-2221-111-1-110000002-200-221-1-113−3−33−333−3−3−33311-1-133−3−30-22000-22−331-11-1-111-11-13−33−3−3300000000000000
χ632-2-2-22-222-1-2-2221-111-1-110000002-200-221-1-11−333−33−3−3333−3−311-1-1−3−3330-22000-223−31-11-1-111-11-1−33−333−300000000000000
χ642-2-2-22-222-1-2-2221-111-1-110000002-200-221-1-11−333−33−3−33−3−33311-1-133−3−302-20002-2−33-11-11-11-11-113−3−333−300000000000000
χ652-2-2-22-222-1-2-2221-111-1-11000000-22002-21-1-113−3−33−333−333−3−3-1-11133−3−302-2000-22−33-11-111-11-11-1−33−333−300000000000000
χ662-2-2-22-222-1-2-2221-111-1-11000000-22002-21-1-113−3−33−333−3−3−333-1-111−3−3330-220002-23−31-11-11-1-11-113−3−333−300000000000000
χ672-2-2-22-222-1-2-2221-111-1-11000000-22002-21-1-11−333−33−3−3333−3−3-1-11133−3−30-220002-2−331-11-11-1-11-11−333−3−3300000000000000
χ682-2-2-22-222-1-2-2221-111-1-11000000-22002-21-1-11−333−33−3−33−3−333-1-111−3−33302-2000-223−3-11-111-11-11-13−33−3−3300000000000000
χ69444-4-4-44-44-444-4444-4-4-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000000000
χ70444-4-4-44-4-24-4-44-2-2-2222244-4-400000000-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ71444-4-4-44-4-24-4-44-2-2-22222-4-44400000000-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ72444-4-4-44-4-2-444-4-2-2-2222200000000000022-2-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ73444-4-4-44-4-2-444-4-2-2-2222200000000000022-2-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ7444-44-4-4-44400004-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7544-44-4-4-44400004-4-444-4-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7644-4-444-4-4400004-4-4-4-44400004i−4i0000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ7744-4-444-4-4400004-4-4-4-4440000−4i4i000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ7844-4-444-4-4-20000-22222-2-200004i−4i000000000000000000−2i2i−2i2i23−2323−23−2i32i3−2i32i30000000000000000000000000000000000000000
χ7944-4-444-4-4-20000-22222-2-200004i−4i000000000000000000−2i2i−2i2i−2323−23232i3−2i32i3−2i30000000000000000000000000000000000000000
χ8044-4-444-4-4-20000-22222-2-20000−4i4i0000000000000000002i−2i2i−2i23−2323−232i3−2i32i3−2i30000000000000000000000000000000000000000
χ8144-4-444-4-4-20000-22222-2-20000−4i4i0000000000000000002i−2i2i−2i−2323−2323−2i32i3−2i32i30000000000000000000000000000000000000000
χ824-4444-4-4-440000-4-444-44-4000000004i−4i00000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ834-4444-4-4-440000-4-444-44-400000000−4i4i0000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ844-4444-4-4-4-2000022-2-22-22000000004i−4i00000000000000−2i32i32i3−2i3−232323−23−2i2i2i−2i0000000000000000000000000000000000000000
χ854-4444-4-4-4-2000022-2-22-22000000004i−4i000000000000002i3−2i3−2i32i323−23−2323−2i2i2i−2i0000000000000000000000000000000000000000
χ864-4444-4-4-4-2000022-2-22-2200000000−4i4i00000000000000−2i32i32i3−2i323−23−23232i−2i−2i2i0000000000000000000000000000000000000000
χ874-4444-4-4-4-2000022-2-22-2200000000−4i4i000000000000002i3−2i3−2i32i3−232323−232i−2i−2i2i0000000000000000000000000000000000000000
χ884-44-4-44-4440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000000022−220000
χ894-44-4-44-4440000-4-44-44-440000000000000000000000000000000000000000000000000000000000000000000000−22220000
χ904-4-44-444-44-44-44-44-44-4-44000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-4-24-44-42-22-222-24i−4i4i−4i00000000-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ924-4-44-444-4-24-44-42-22-222-2−4i4i−4i4i00000000-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ934-4-44-444-4-2-44-442-22-222-20000000000002-22-223−2323−23−2323−23230000000000000000000000000000000000000000000000000000
χ944-4-44-444-4-2-44-442-22-222-20000000000002-22-2−2323−232323−2323−230000000000000000000000000000000000000000000000000000
χ9588-88-8-8-88-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000

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