Finite Group Databasebeta

← Group #11714049

Character table — Group #11714049

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order12222222444444444444444436666666121212121212121212121212121212121212121212121212224444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-1
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-11
χ511111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ611111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ711111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111-1-11
χ811111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-111-1
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
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-2-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-222-2-2000000000000
χ1322-2-22-22-2000000002i2i−2i−2i22-2-2222-2-22-2-200000000000000002i2i2i2i−2i−2i−2i−2i002i−2i00000000000000
χ1422-2-22-22-2000000002i2i−2i−2i22-2-2-1-1-111-1113333−3−3−3−3−i3−i3−i3−i3i3i3i3i3−i−i−i−iiiii002i−2i00000000000000
χ1522-2-22-22-2000000002i2i−2i−2i22-2-2-1-1-111-111−3−3−3−33333i3i3i3i3−i3−i3−i3−i3−i−i−i−iiiii002i−2i00000000000000
χ1622-2-22-22-200000000−2i−2i2i2i22-2-2222-2-22-2-20000000000000000−2i−2i−2i−2i2i2i2i2i00−2i2i00000000000000
χ1722-2-22-22-200000000−2i−2i2i2i22-2-2-1-1-111-1113333−3−3−3−3i3i3i3i3−i3−i3−i3−i3iiii−i−i−i−i00−2i2i00000000000000
χ1822-2-22-22-200000000−2i−2i2i2i22-2-2-1-1-111-111−3−3−3−33333−i3−i3−i3−i3i3i3i3i3iiii−i−i−i−i00−2i2i00000000000000
χ192-22-22-2-222i2i−2i−2i2i2i−2i−2i2-22-20000-11-11-111-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1000000−i2i22−22−2−i2i20000
χ202-22-22-2-222i2i−2i−2i2i2i−2i−2i2-22-20000-11-11-111-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1000000i2−i2−22−22i2−i20000
χ212-22-22-2-222i2i−2i−2i−2i−2i2i2i-22-220000-11-11-111-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111000000−i2i22−2−22i2−i20000
χ222-22-22-2-222i2i−2i−2i−2i−2i2i2i-22-220000-11-11-111-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111000000i2−i2−222−2−i2i20000
χ232-22-22-2-22−2i−2i2i2i2i2i−2i−2i-22-220000-11-11-111-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111000000−i2i2−222−2i2−i20000
χ242-22-22-2-22−2i−2i2i2i2i2i−2i−2i-22-220000-11-11-111-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111000000i2−i22−2−22−i2i20000
χ252-22-22-2-22−2i−2i2i2i−2i−2i2i2i2-22-20000-11-11-111-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1000000−i2i2−22−22−i2i20000
χ262-22-22-2-22−2i−2i2i2i−2i−2i2i2i2-22-20000-11-11-111-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1000000i2−i22−22−2i2−i20000
χ272-22-2-222-22i−2i2i−2i000000002-22-22-2-2222-2-22i−2i2i−2i2i−2i2i−2i000000000000000000002i−2i000000000000
χ282-22-2-222-22i−2i2i−2i000000002-22-2-111-1-1-111−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i33−33−33−33−300002i−2i000000000000
χ292-22-2-222-22i−2i2i−2i000000002-22-2-111-1-1-111−ii−ii−ii−iii3−i3i3−i3i3−i3i3−i3−33−33−33−3300002i−2i000000000000
χ302-22-2-222-2−2i2i−2i2i000000002-22-22-2-2222-2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000−2i2i000000000000
χ312-22-2-222-2−2i2i−2i2i000000002-22-2-111-1-1-111i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i3−33−33−33−330000−2i2i000000000000
χ322-22-2-222-2−2i2i−2i2i000000002-22-2-111-1-1-111i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i33−33−33−33−30000−2i2i000000000000
χ332-2-22-2-22200002-22-200002-2-222-2-2-2-2222000000002-22-2-22-22000000002-20000000000000000
χ342-2-22-2-22200002-22-200002-2-22-11111-1-1-1−i3i3−i3i3i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i32-20000000000000000
χ352-2-22-2-22200002-22-200002-2-22-11111-1-1-1i3−i3i3−i3−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i32-20000000000000000
χ362-2-22-2-2220000-22-2200002-2-222-2-2-2-222200000000-22-222-22-200000000-220000000000000000
χ372-2-22-2-2220000-22-2200002-2-22-11111-1-1-1−i3i3−i3i3i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i3-220000000000000000
χ382-2-22-2-2220000-22-2200002-2-22-11111-1-1-1i3−i3i3−i3−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i3-220000000000000000
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
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-11111-1-1-1-1-11-11
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-1-1-1-1-111111-11-1
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-100000000000000000000000000000000-1-1111111-1-111-1-1-1-111
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-111-1-11111-1-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-10000000000000000000000000000000011-1-11111-1-1-1-111-111-1
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-10000000000000000000000000000000011-1-111-1-11111-1-11-1-11
χ474444-4-4-4-44-4-4400000000000011-1-11-11-1-111-1-111-13−3−333−3−33−333−3−333−3000000000000000000
χ484444-4-4-4-44-4-4400000000000011-1-11-11-1-111-1-111-1−333−3−333−33−3−333−3−33000000000000000000
χ494444-4-4-4-44-4-44000000000000-2-222-22-222-2-222-2-220000000000000000000000000000000000
χ504444-4-4-4-4-444-400000000000011-1-11-11-11-1-111-1-113−3−333−3−333−3−333−3−33000000000000000000
χ514444-4-4-4-4-444-400000000000011-1-11-11-11-1-111-1-11−333−3−333−3−333−3−333−3000000000000000000
χ524444-4-4-4-4-444-4000000000000-2-222-22-22-222-2-222-20000000000000000000000000000000000
χ5344-4-4-44-4400004i−4i−4i4i0000000011-11-1-1-113−3−33−333−3−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i3000000000000000000
χ5444-4-4-44-4400004i−4i−4i4i0000000011-11-1-1-11−333−33−3−33−iii−ii−i−iii3−i3−i3i3−i3i3i3−i3000000000000000000
χ5544-4-4-44-4400004i−4i−4i4i00000000-2-22-2222-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5644-4-4-44-440000−4i4i4i−4i0000000011-11-1-1-113−3−33−333−3i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i3000000000000000000
χ5744-4-4-44-440000−4i4i4i−4i0000000011-11-1-1-11−333−33−3−33i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i3000000000000000000
χ5844-4-4-44-440000−4i4i4i−4i00000000-2-22-2222-200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ594-44-44-4-444i4i−4i−4i4i4i−4i−4i4-44-400001-11-11-1-11−i−iii−i−iii−i−iii−i−iii-1-111-1-111000000000000000000
χ604-44-44-4-444i4i−4i−4i−4i−4i4i4i-44-4400001-11-11-1-11−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1000000000000000000
χ614-44-44-4-44−4i−4i4i4i4i4i−4i−4i-44-4400001-11-11-1-11ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1000000000000000000
χ624-44-44-4-44−4i−4i4i4i−4i−4i4i4i4-44-400001-11-11-1-11ii−i−iii−i−iii−i−iii−i−i-1-111-1-111000000000000000000
χ634-4-4444-4-4000000004i−4i−4i4i00001-111-1-11-1−i3−i3i3i3i3i3−i3−i3−3−33333−3−3−i−iiiii−i−i000000000000000000
χ644-4-4444-4-4000000004i−4i−4i4i00001-111-1-11-1i3i3−i3−i3−i3−i3i3i333−3−3−3−333−i−iiiii−i−i000000000000000000
χ654-4-4444-4-4000000004i−4i−4i4i0000-22-2-222-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ664-4-4444-4-400000000−4i4i4i−4i00001-111-1-11-1−i3−i3i3i3i3i3−i3−i333−3−3−3−333ii−i−i−i−iii000000000000000000
χ674-4-4444-4-400000000−4i4i4i−4i00001-111-1-11-1i3i3−i3−i3−i3−i3i3i3−3−33333−3−3ii−i−i−i−iii000000000000000000
χ684-4-4444-4-400000000−4i4i4i−4i0000-22-2-222-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ6966-6-66-66-6000000006i6i−6i−6i-2-2220000000000000000000000000000000000−2i2i00000000000000
χ7066-6-66-66-600000000−6i−6i6i6i-2-22200000000000000000000000000000000002i−2i00000000000000
χ716-66-6-666-66i−6i6i−6i00000000-22-22000000000000000000000000000000000000−2i2i000000000000
χ726-66-6-666-6−6i6i−6i6i00000000-22-220000000000000000000000000000000000002i−2i000000000000
χ736-6-66-6-66600006-66-60000-222-200000000000000000000000000000000-220000000000000000
χ746-6-66-6-6660000-66-660000-222-2000000000000000000000000000000002-20000000000000000

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