Finite Group Databasebeta

← Group #11714058

Character table — Group #11714058

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order12222222444444444444444436666666121212121212121212121212121212121212121212121212444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ511111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ611111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11
χ711111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-11
χ811111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-111-1
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
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-222-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-2-2-222000000000000
χ1322-22-2-22-200002i2i−2i−2i00002-22-2222-2-22-2-2000000002i2i2i2i−2i−2i−2i−2i00000000002i−2i00000000000000
χ1422-22-2-22-200002i2i−2i−2i00002-22-2-1-1-111-111−i3−i3−i3−i3i3i3i3i3−i−i−i−iiiii3333−3−3−3−3002i−2i00000000000000
χ1522-22-2-22-200002i2i−2i−2i00002-22-2-1-1-111-111i3i3i3i3−i3−i3−i3−i3−i−i−i−iiiii−3−3−3−33333002i−2i00000000000000
χ1622-22-2-22-20000−2i−2i2i2i00002-22-2222-2-22-2-200000000−2i−2i−2i−2i2i2i2i2i0000000000−2i2i00000000000000
χ1722-22-2-22-20000−2i−2i2i2i00002-22-2-1-1-111-111−i3−i3−i3−i3i3i3i3i3iiii−i−i−i−i−3−3−3−3333300−2i2i00000000000000
χ1822-22-2-22-20000−2i−2i2i2i00002-22-2-1-1-111-111i3i3i3i3−i3−i3−i3−i3iiii−i−i−i−i3333−3−3−3−300−2i2i00000000000000
χ192-222-2-2-222i2i−2i−2i2-22-22i2i−2i−2i0000-11-11-111-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i000000−i2i22−2−i2i22−20000
χ202-222-2-2-222i2i−2i−2i2-22-22i2i−2i−2i0000-11-11-111-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i000000i2−i2−22i2−i2−220000
χ212-222-2-2-222i2i−2i−2i-22-22−2i−2i2i2i0000-11-11-111-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii000000−i2i22−2i2−i2−220000
χ222-222-2-2-222i2i−2i−2i-22-22−2i−2i2i2i0000-11-11-111-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii000000i2−i2−22−i2i22−20000
χ232-222-2-2-22−2i−2i2i2i2-22-2−2i−2i2i2i0000-11-11-111-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii000000−i2i2−22−i2i2−220000
χ242-222-2-2-22−2i−2i2i2i2-22-2−2i−2i2i2i0000-11-11-111-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii000000i2−i22−2i2−i22−20000
χ252-222-2-2-22−2i−2i2i2i-22-222i2i−2i−2i0000-11-11-111-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i000000−i2i2−22i2−i22−20000
χ262-222-2-2-22−2i−2i2i2i-22-222i2i−2i−2i0000-11-11-111-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i000000i2−i22−2−i2i2−220000
χ272-22-22-22-22i−2i2i−2i00000000-222-222-22-2-2-222i−2i2i−2i2i−2i2i−2i00000000000000002i−2i0000000000000000
χ282-22-22-22-22i−2i2i−2i00000000-222-2-1-11-1111-1−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i33−33−33−33−32i−2i0000000000000000
χ292-22-22-22-22i−2i2i−2i00000000-222-2-1-11-1111-1−ii−ii−ii−iii3−i3i3−i3i3−i3i3−i3−33−33−33−332i−2i0000000000000000
χ302-22-22-22-2−2i2i−2i2i00000000-222-222-22-2-2-22−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i0000000000000000
χ312-22-22-22-2−2i2i−2i2i00000000-222-2-1-11-1111-1i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i3−33−33−33−33−2i2i0000000000000000
χ322-22-22-22-2−2i2i−2i2i00000000-222-2-1-11-1111-1i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i33−33−33−33−3−2i2i0000000000000000
χ332-2-2-2-2222000000002-22-2-2-22222-2-22-22-200000000000000002-22-2-22-2200002-2000000000000
χ342-2-2-2-2222000000002-22-2-2-222-1-111-11-113−33−3−33−33−33−333−33−3-11-111-11-100002-2000000000000
χ352-2-2-2-2222000000002-22-2-2-222-1-111-11-11−33−333−33−33−33−3−33−33-11-111-11-100002-2000000000000
χ362-2-2-2-222200000000-22-22-2-22222-2-22-22-20000000000000000-22-222-22-20000-22000000000000
χ372-2-2-2-222200000000-22-22-2-222-1-111-11-113−33−3−33−333−33−3−33−331-11-1-11-110000-22000000000000
χ382-2-2-2-222200000000-22-22-2-222-1-111-11-11−33−333−33−3−33−333−33−31-11-1-11-110000-22000000000000
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
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-111111111-1-1-1-1-1-111
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-1-1-1111111-1-1
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-11111-1-111-1-1-11-11
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-1-111-1-1111-11-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-111-1-1-1-111-111-1
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-1-11111-1-11-1-11
χ47444-4-44-4-44-4-440000000000001-1-1-1-1111-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ48444-4-44-4-44-4-440000000000001-1-1-1-1111-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ49444-4-44-4-44-4-44000000000000-22222-2-2-22-2-222-2-220000000000000000000000000000000000
χ50444-4-44-4-4-444-40000000000001-1-1-1-11111-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ51444-4-44-4-4-444-40000000000001-1-1-1-11111-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ52444-4-44-4-4-444-4000000000000-22222-2-2-2-222-2-222-20000000000000000000000000000000000
χ5344-4-44-4-44000000004i−4i−4i4i00001-1-1111-1-1−i3i3i3−i3i3−i3−i3i33−3−33−333−3−iii−ii−i−ii000000000000000000
χ5444-4-44-4-44000000004i−4i−4i4i00001-1-1111-1-1i3−i3−i3i3−i3i3i3−i3−333−33−3−33−iii−ii−i−ii000000000000000000
χ5544-4-44-4-44000000004i−4i−4i4i0000-222-2-2-22200000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5644-4-44-4-4400000000−4i4i4i−4i00001-1-1111-1-1−i3i3i3−i3i3−i3−i3i3−333−33−3−33i−i−ii−iii−i000000000000000000
χ5744-4-44-4-4400000000−4i4i4i−4i00001-1-1111-1-1i3−i3−i3i3−i3i3i3−i33−3−33−333−3i−i−ii−iii−i000000000000000000
χ5844-4-44-4-4400000000−4i4i4i−4i0000-222-2-2-2220000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ594-444-4-4-444i4i−4i−4i4-44-44i4i−4i−4i00001-11-11-1-11−i−iii−i−iii-1-111-1-111−i−iii−i−iii000000000000000000
χ604-444-4-4-444i4i−4i−4i-44-44−4i−4i4i4i00001-11-11-1-11−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i000000000000000000
χ614-444-4-4-44−4i−4i4i4i4-44-4−4i−4i4i4i00001-11-11-1-11ii−i−iii−i−i-1-111-1-111ii−i−iii−i−i000000000000000000
χ624-444-4-4-44−4i−4i4i4i-44-444i4i−4i−4i00001-11-11-1-11ii−i−iii−i−i11-1-111-1-1−i−iii−i−iii000000000000000000
χ634-4-4444-4-400004i−4i−4i4i000000001-111-1-11-133−3−3−3−333−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3000000000000000000
χ644-4-4444-4-400004i−4i−4i4i000000001-111-1-11-1−3−33333−3−3−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000000000
χ654-4-4444-4-400004i−4i−4i4i00000000-22-2-222-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ664-4-4444-4-40000−4i4i4i−4i000000001-111-1-11-133−3−3−3−333ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3000000000000000000
χ674-4-4444-4-40000−4i4i4i−4i000000001-111-1-11-1−3−33333−3−3ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000000000
χ684-4-4444-4-40000−4i4i4i−4i00000000-22-2-222-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ6966-66-6-66-600006i6i−6i−6i0000-22-220000000000000000000000000000000000−2i2i00000000000000
χ7066-66-6-66-60000−6i−6i6i6i0000-22-2200000000000000000000000000000000002i−2i00000000000000
χ716-66-66-66-66i−6i6i−6i000000002-2-2200000000000000000000000000000000−2i2i0000000000000000
χ726-66-66-66-6−6i6i−6i6i000000002-2-22000000000000000000000000000000002i−2i0000000000000000
χ736-6-6-6-6666000000006-66-622-2-2000000000000000000000000000000000000-22000000000000
χ746-6-6-6-666600000000-66-6622-2-20000000000000000000000000000000000002-2000000000000

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