Finite Group Databasebeta

← Group #11714045

Character table — Group #11714045

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order122222222222444444444444366666666666666612121212121212121212121212121212444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-11
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-1
χ511111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ711111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-11-1
χ811111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-11-11
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222000000000000
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-2-222-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-2-2-2-222000000000000
χ1322-222-2-2-2000000002i2i−2i−2i22-2-22222-2-2-200000000-2000000002i2i2i2i−2i−2i−2i−2i00002i−2i000000000000
χ1422-222-2-2-2000000002i2i−2i−2i22-2-2-1-1-1-1111−i3−i3−i3−i3i3i3i3i313333−3−3−3−3−i−i−i−iiiii00002i−2i000000000000
χ1522-222-2-2-2000000002i2i−2i−2i22-2-2-1-1-1-1111i3i3i3i3−i3−i3−i3−i31−3−3−3−33333−i−i−i−iiiii00002i−2i000000000000
χ1622-222-2-2-200000000−2i−2i2i2i22-2-22222-2-2-200000000-200000000−2i−2i−2i−2i2i2i2i2i0000−2i2i000000000000
χ1722-222-2-2-200000000−2i−2i2i2i22-2-2-1-1-1-1111−i3−i3−i3−i3i3i3i3i31−3−3−3−33333iiii−i−i−i−i0000−2i2i000000000000
χ1822-222-2-2-200000000−2i−2i2i2i22-2-2-1-1-1-1111i3i3i3i3−i3−i3−i3−i313333−3−3−3−3iiii−i−i−i−i0000−2i2i000000000000
χ192-222-22-2-200002i2i−2i−2i00002-22-222-2-222-200000000-22i2i−2i−2i2i2i−2i−2i00000000002i−2i00000000000000
χ202-222-22-2-200002i2i−2i−2i00002-22-2-1-111-1-11−i3−i3i3i3−i3−i3i3i31−i−iii−i−iii33−3−333−3−3002i−2i00000000000000
χ212-222-22-2-200002i2i−2i−2i00002-22-2-1-111-1-11i3i3−i3−i3i3i3−i3−i31−i−iii−i−iii−3−333−3−333002i−2i00000000000000
χ222-222-22-2-20000−2i−2i2i2i00002-22-222-2-222-200000000-2−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00000000000000
χ232-222-22-2-20000−2i−2i2i2i00002-22-2-1-111-1-11−i3−i3i3i3−i3−i3i3i31ii−i−iii−i−i−3−333−3−33300−2i2i00000000000000
χ242-222-22-2-20000−2i−2i2i2i00002-22-2-1-111-1-11i3i3−i3−i3i3i3−i3−i31ii−i−iii−i−i33−3−333−3−300−2i2i00000000000000
χ252-2-22-2-22222-2-2000000002-2-2222-2-2-2-2222-2-2-2-222200000000000000002-20000000000000000
χ262-2-22-2-22222-2-2000000002-2-22-1-11111-1-1-11111-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-20000000000000000
χ272-2-22-2-22222-2-2000000002-2-22-1-11111-1-1-11111-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-20000000000000000
χ282-2-22-2-222-2-222000000002-2-2222-2-2-2-22-2-22222-2-220000000000000000-220000000000000000
χ292-2-22-2-222-2-222000000002-2-22-1-11111-111-1-1-1-111-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-220000000000000000
χ302-2-22-2-222-2-222000000002-2-22-1-11111-111-1-1-1-111-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-220000000000000000
χ312-2-2-222-222-22-22-22-22-22-20000-111-11-111-11-11-11-1-11-11-11-11-11-11-11-11-1000000−i2i2−i2i2−i2i2−i2i20000
χ322-2-2-222-222-22-22-22-22-22-20000-111-11-111-11-11-11-1-11-11-11-11-11-11-11-11-1000000i2−i2i2−i2i2−i2i2−i20000
χ332-2-2-222-222-22-2-22-22-22-220000-111-11-111-11-11-11-1-1-11-11-11-11-11-11-11-11000000−i2i2−i2i2i2−i2i2−i20000
χ342-2-2-222-222-22-2-22-22-22-220000-111-11-111-11-11-11-1-1-11-11-11-11-11-11-11-11000000i2−i2i2−i2−i2i2−i2i20000
χ352-2-2-222-22-22-222-22-2-22-220000-111-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11000000−i2i2i2−i2−i2i2i2−i20000
χ362-2-2-222-22-22-222-22-2-22-220000-111-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11000000i2−i2−i2i2i2−i2−i2i20000
χ372-2-2-222-22-22-22-22-222-22-20000-111-11-11-11-11-11-11-1-11-11-11-111-11-11-11-1000000−i2i2i2−i2i2−i2−i2i20000
χ382-2-2-222-22-22-22-22-222-22-20000-111-11-11-11-11-11-11-1-11-11-11-111-11-11-11-1000000i2−i2−i2i2−i2i2i2−i20000
χ3933333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-111111111-1-1-1-1
χ4033333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-111111111-1-1-1-1-111-1
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-1-1-111111-1-11
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-11111-1-111-1-1-1-111
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-1-111-1-11111-1-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-111-1-1-1-111-11-11
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-1-11111-1-11-11-1
χ47444-4-4-4-444-4-440000000000001-11-11-1-1-111-11-1-111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ48444-4-4-4-444-4-440000000000001-11-11-1-1-111-11-1-111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ49444-4-4-4-444-4-44000000000000-22-22-2222-2-22-222-2-20000000000000000000000000000000000
χ50444-4-4-4-44-444-40000000000001-11-11-1-11-1-11-111-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ51444-4-4-4-44-444-40000000000001-11-11-1-11-1-11-111-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ52444-4-4-4-44-444-4000000000000-22-22-222-222-22-2-22-20000000000000000000000000000000000
χ5344-4-4-444-400004i−4i−4i4i000000001-11-1-111−i3i3i3−i3−i3i3i3−i3-1−iii−i−iii−i3−3−333−3−33000000000000000000
χ5444-4-4-444-400004i−4i−4i4i000000001-11-1-111i3−i3−i3i3i3−i3−i3i3-1−iii−i−iii−i−333−3−333−3000000000000000000
χ5544-4-4-444-400004i−4i−4i4i00000000-22-222-2-20000000022i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5644-4-4-444-40000−4i4i4i−4i000000001-11-1-111−i3i3i3−i3−i3i3i3−i3-1i−i−iii−i−ii−333−3−333−3000000000000000000
χ5744-4-4-444-40000−4i4i4i−4i000000001-11-1-111i3−i3−i3i3i3−i3−i3i3-1i−i−iii−i−ii3−3−333−3−33000000000000000000
χ5844-4-4-444-40000−4i4i4i−4i00000000-22-222-2-2000000002−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ594-44-44-44-4000000004i−4i−4i4i00001-1-111-11−i3i3−i3i3i3−i3i3−i3-13−33−3−33−33−ii−iii−ii−i000000000000000000
χ604-44-44-44-4000000004i−4i−4i4i00001-1-111-11i3−i3i3−i3−i3i3−i3i3-1−33−333−33−3−ii−iii−ii−i000000000000000000
χ614-44-44-44-4000000004i−4i−4i4i0000-222-2-22-2000000002000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ624-44-44-44-400000000−4i4i4i−4i00001-1-111-11−i3i3−i3i3i3−i3i3−i3-1−33−333−33−3i−ii−i−ii−ii000000000000000000
χ634-44-44-44-400000000−4i4i4i−4i00001-1-111-11i3−i3i3−i3−i3i3−i3i3-13−33−3−33−33i−ii−i−ii−ii000000000000000000
χ644-44-44-44-400000000−4i4i4i−4i0000-222-2-22-200000000200000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ654-4-4-444-444-44-44-44-44-44-400001-1-11-11-1-11-11-11-111-11-11-11-11-11-11-11-11000000000000000000
χ664-4-4-444-444-44-4-44-44-44-4400001-1-11-11-1-11-11-11-1111-11-11-11-11-11-11-11-1000000000000000000
χ674-4-4-444-44-44-444-44-4-44-4400001-1-11-11-11-11-11-11-11-11-11-11-111-11-11-11-1000000000000000000
χ684-4-4-444-44-44-44-44-444-44-400001-1-11-11-11-11-11-11-111-11-11-11-1-11-11-11-11000000000000000000
χ6966-666-6-6-6000000006i6i−6i−6i-2-222000000000000000000000000000000000000−2i2i000000000000
χ7066-666-6-6-600000000−6i−6i6i6i-2-2220000000000000000000000000000000000002i−2i000000000000
χ716-666-66-6-600006i6i−6i−6i0000-22-220000000000000000000000000000000000−2i2i00000000000000
χ726-666-66-6-60000−6i−6i6i6i0000-22-2200000000000000000000000000000000002i−2i00000000000000
χ736-6-66-6-66666-6-600000000-222-200000000000000000000000000000000-220000000000000000
χ746-6-66-6-666-6-66600000000-222-2000000000000000000000000000000002-20000000000000000

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