Finite Group Databasebeta

← Group #10868303

Character table — Group #10868303

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666644444444444412121212121212121212121212121212121212121212121224444444661212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1
χ61111111111111111111111-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-11111-11
χ911111111111111111111-1-111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1
χ1011111111111111111111-1-111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1-1
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ1311111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ1411111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-11111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-11
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-11111-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ17222222222-2-2-2-22222222222222-2-200002222222200000000-2-2-2-22222-20000-200-2-2-2-20000-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-22200002222-2-2-2-200000000-2-2-2-2-2-2-2-220000-20022-2-20000220000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-2222200000000-2-2-2-2-2-2-2-22000020022220000-2-20000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222220000-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000200-2-2220000220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-12-2-2-2-22-2-2-1-1-1-11111-1-11111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-22222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2-222211-1-1-1-1-1-1111111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-11111-222222-2-211-1-1111111-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-22222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-222-2-2-211111111-1-11111-1-1-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-111111111-1-1-1-11111-222-2-2-2221111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-111111111-1-1-1-1111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-12-2-222-222-1-111-1-1-1-1111111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-20000-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-20000-2001111−i3−i3i3i311−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-20000-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-20000-2001111i3i3−i3−i311i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000-1-1-1-11111−i3−i3−i3−i3i3i3i3i31111111120000-200-1-111−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000-1-1-1-11111i3i3i3i3−i3−i3−i3−i31111111120000-200-1-111i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-200001111-1-1-1-1−i3−i3−i3−i3i3i3i3i31111111120000200-1-1-1-1i3i3−i3−i311i3i3−i3−i3−i3−i3i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-200001111-1-1-1-1i3i3i3i3−i3−i3−i3−i31111111120000200-1-1-1-1−i3−i3i3i311−i3−i3i3i3i3i3−i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222000011111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-2000020011-1-1i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222000011111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-2000020011-1-1−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3722-22-22-2-22-22-22-222-2-2-22000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000002i−2i0000002-20000
χ3822-22-22-2-22-22-22-222-2-2-22000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000000−2i2i000000-220000
χ3922-22-22-2-22-22-22-222-2-2-2200000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i22-2-20000000000000000000000000000002i−2i000000-220000
χ4022-22-22-2-22-22-22-222-2-2-2200000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000−2i2i0000002-20000
χ412-222-2-2-22222-2-2-2-2-2-2222000000002-22-2000000002-22-22-22-22-22-2000000000000000000000000000000002i−2i2i−2i00000000
χ422-222-2-2-22222-2-2-2-2-2-2222000000002-22-2000000002-22-22-22-22-22-200000000000000000000000000000000−2i2i−2i2i00000000
χ432-222-2-2-22222-2-2-2-2-2-222200000000-22-2200000000-22-22-22-222-22-2000000000000000000000000000000002i−2i−2i2i00000000
χ442-222-2-2-22222-2-2-2-2-2-222200000000-22-2200000000-22-22-22-222-22-200000000000000000000000000000000−2i2i2i−2i00000000
χ452-2-222-22-222-2-222-2-22-2-22002i−2i002i−2i000000002i2i−2i−2i00000000-222-2000002i−2i0002-200002-22-22i−2i2i−2i2i−2i000000000000000000
χ462-2-222-22-222-2-222-2-22-2-22002i−2i002i−2i000000002i2i−2i−2i00000000-222-200000−2i2i000-220000-22-222i−2i−2i2i−2i2i000000000000000000
χ472-2-222-22-222-2-222-2-22-2-2200−2i2i00−2i2i00000000−2i−2i2i2i00000000-222-2000002i−2i000-220000-22-22−2i2i2i−2i2i−2i000000000000000000
χ482-2-222-22-222-2-222-2-22-2-2200−2i2i00−2i2i00000000−2i−2i2i2i00000000-222-200000−2i2i0002-200002-22-2−2i2i−2i2i−2i2i000000000000000000
χ492-2-222-22-22-222-22-2-22-2-22002i−2i00−2i2i2i−2i−2i2i00002i2i−2i−2i2i−2i−2i2i2i−2i−2i2i2-2-2200000002-200000000000−2i2i00002-22-200000000000000
χ502-2-222-22-22-222-22-2-22-2-22002i−2i00−2i2i−2i2i2i−2i00002i2i−2i−2i−2i2i2i−2i−2i2i2i−2i2-2-220000000-2200000000000−2i2i0000-22-2200000000000000
χ512-2-222-22-22-222-22-2-22-2-2200−2i2i002i−2i2i−2i−2i2i0000−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i2-2-220000000-22000000000002i−2i0000-22-2200000000000000
χ522-2-222-22-22-222-22-2-22-2-2200−2i2i002i−2i−2i2i2i−2i0000−2i−2i2i2i−2i2i2i−2i−2i2i2i−2i2-2-2200000002-2000000000002i−2i00002-22-200000000000000
χ532-2-222-22-2-12-2-22-111-111-1002i−2i002i−2i000033−3−3−i−iii3−3−33−333−31-1-11−i3−i3i3i302i−2i0002-2−i3i33−3-11-11−ii−ii−ii−i3i3i3−i300000000000000
χ542-2-222-22-2-12-2-22-111-111-1002i−2i002i−2i000033−3−3−i−iii−333−33−3−331-1-11−i3−i3i3i30−2i2i000-22−i3i33−31-11-1−iii−ii−ii3−i3−i3i300000000000000
χ552-2-222-22-2-12-2-22-111-111-1002i−2i002i−2i0000−3−333−i−iii3−3−33−333−31-1-11i3i3−i3−i30−2i2i000-22i3−i3−331-11-1−iii−ii−i−i3i3i3−i300000000000000
χ562-2-222-22-2-12-2-22-111-111-1002i−2i002i−2i0000−3−333−i−iii−333−33−3−331-1-11i3i3−i3−i302i−2i0002-2i3−i3−33-11-11−ii−ii−iii3−i3−i3i300000000000000
χ572-2-222-22-2-12-2-22-111-111-100−2i2i00−2i2i000033−3−3ii−i−i3−3−33−333−31-1-11i3i3−i3−i30−2i2i0002-2i3−i33−3-11-11i−ii−ii−ii3−i3−i3i300000000000000
χ582-2-222-22-2-12-2-22-111-111-100−2i2i00−2i2i000033−3−3ii−i−i−333−33−3−331-1-11i3i3−i3−i302i−2i000-22i3−i33−31-11-1i−i−ii−ii−i3i3i3−i300000000000000
χ592-2-222-22-2-12-2-22-111-111-100−2i2i00−2i2i0000−3−333ii−i−i3−3−33−333−31-1-11−i3−i3i3i302i−2i000-22−i3i3−331-11-1i−i−ii−iii3−i3−i3i300000000000000
χ602-2-222-22-2-12-2-22-111-111-100−2i2i00−2i2i0000−3−333ii−i−i−333−33−3−331-1-11−i3−i3i3i30−2i2i0002-2−i3i3−33-11-11i−ii−ii−i−i3i3i3−i300000000000000
χ612-2-222-22-2-1-222-2-111-111-1002i−2i00−2i2i2i−2i−2i2i33−3−3−i−iii−iii−i−iii−i-111-1−i3−i3i3i30002-2000i3−i3−33−i3i3i3−i3i−i3−3−33-11-1100000000000000
χ622-2-222-22-2-1-222-2-111-111-1002i−2i00−2i2i2i−2i−2i2i−3−333−i−iii−iii−i−iii−i-111-1i3i3−i3−i30002-2000−i3i33−3i3−i3−i3i3i−i−333−3-11-1100000000000000
χ632-2-222-22-2-1-222-2-111-111-1002i−2i00−2i2i−2i2i2i−2i33−3−3−i−iiii−i−iii−i−ii-111-1−i3−i3i3i3000-22000i3−i3−33i3−i3−i3i3i−i−333−31-11-100000000000000
χ642-2-222-22-2-1-222-2-111-111-1002i−2i00−2i2i−2i2i2i−2i−3−333−i−iiii−i−iii−i−ii-111-1i3i3−i3−i3000-22000−i3i33−3−i3i3i3−i3i−i3−3−331-11-100000000000000
χ652-2-222-22-2-1-222-2-111-111-100−2i2i002i−2i2i−2i−2i2i33−3−3ii−i−i−iii−i−iii−i-111-1i3i3−i3−i3000-22000−i3i3−33−i3i3i3−i3−ii−333−31-11-100000000000000
χ662-2-222-22-2-1-222-2-111-111-100−2i2i002i−2i2i−2i−2i2i−3−333ii−i−i−iii−i−iii−i-111-1−i3−i3i3i3000-22000i3−i33−3i3−i3−i3i3−ii3−3−331-11-100000000000000
χ672-2-222-22-2-1-222-2-111-111-100−2i2i002i−2i−2i2i2i−2i33−3−3ii−i−ii−i−iii−i−ii-111-1i3i3−i3−i30002-2000−i3i3−33i3−i3−i3i3−ii3−3−33-11-1100000000000000
χ682-2-222-22-2-1-222-2-111-111-100−2i2i002i−2i−2i2i2i−2i−3−333ii−i−ii−i−iii−i−ii-111-1−i3−i3i3i30002-2000i3−i33−3−i3i3i3−i3−ii−333−3-11-1100000000000000
χ69444-44-4-4-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000000000000000022−22000000
χ70444-44-4-4-44000044-4-44-4-400000000000000000000000000000000000000000000000000000000000000000000−2222000000
χ7144-44-44-4-444-44-4-444-4-4-440000000000000000000000000000-4-44400000000000000000000000000000000000000000000
χ7244-44-44-4-4-24-44-42-2-2222-2000000000000000000002323−23−23−23−23232322-2-200000000000000000000000000000000000000000000
χ7344-44-44-4-4-24-44-42-2-2222-200000000000000000000−23−2323232323−23−2322-2-200000000000000000000000000000000000000000000
χ7444-44-44-4-4-2-44-442-2-2222-2000000004i4i−4i−4i00000000−2i−2i2i2i−2i−2i2i2i-2-22200000000000000000000000000000000000000000000
χ7544-44-44-4-4-2-44-442-2-2222-200000000−4i−4i4i4i000000002i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000000000000000000000000000
χ7644-4-4-4-44440000-44-44-44-400004i−4i000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7744-4-4-4-44440000-44-44-44-40000−4i4i00000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7844-4-4-4-444-200002-22-22-2200004i−4i000000−2i32i3−2i32i323−2323−23000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ7944-4-4-4-444-200002-22-22-2200004i−4i0000002i3−2i32i3−2i3−2323−2323000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ8044-4-4-4-444-200002-22-22-220000−4i4i000000−2i32i3−2i32i3−2323−23230000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ8144-4-4-4-444-200002-22-22-220000−4i4i0000002i3−2i32i3−2i323−2323−230000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ824-444-4-4-444-4-444-4-4-4-44440000000000000000000000000000-44-4400000000000000000000000000000000000000000000
χ834-444-4-4-44-244-4-42222-2-2-2000000004-44-400000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ844-444-4-4-44-244-4-42222-2-2-200000000-44-44000000002-22-22-22-2-22-2200000000000000000000000000000000000000000000
χ854-444-4-4-44-2-4-4442222-2-2-200000000000000000000−2i32i3−2i32i32i3−2i32i3−2i32-22-200000000000000000000000000000000000000000000
χ864-444-4-4-44-2-4-4442222-2-2-2000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i32-22-200000000000000000000000000000000000000000000
χ874-44-4-444-440000-4-4444-4-44i−4i00000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ884-44-4-444-440000-4-4444-4-4−4i4i0000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ894-44-4-444-4-2000022-2-2-2224i−4i0000000000−2i2i2i−2i−2i32i32i3−2i3000000000000−232323−230000000000000000000000000000000000000000
χ904-44-4-444-4-2000022-2-2-2224i−4i0000000000−2i2i2i−2i2i3−2i3−2i32i300000000000023−23−23230000000000000000000000000000000000000000
χ914-44-4-444-4-2000022-2-2-222−4i4i00000000002i−2i−2i2i−2i32i32i3−2i300000000000023−23−23230000000000000000000000000000000000000000
χ924-44-4-444-4-2000022-2-2-222−4i4i00000000002i−2i−2i2i2i3−2i3−2i32i3000000000000−232323−230000000000000000000000000000000000000000
χ934-4-4-444-44400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ944-4-4-444-44400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ95888-88-8-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000000000

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