Finite Group Databasebeta

← Group #11712883

Character table — Group #11712883

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222244446666666688888888121212121212121212121212161616161616161616161616242424242424242424242424
order12222222444444444444444436666666444488888888121212121212121212121212444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111-1-1-1-111-1-111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ611111111-1-1-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ711111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ811111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ91-111-1-1-11ii−i−ii−i1-11-1ii−i−i1-1111-1-11-1-11-1i−i11-1-1ii−i−iii−i−iii−i−i11-1-1i−ii−i1-11-1i−i1-1
χ101-111-1-1-11ii−i−ii−i1-11-1ii−i−i1-1111-1-11-1-11-1i−i-1-111−i−iiiii−i−iii−i−i11-1-1−ii−ii-11-11−ii-11
χ111-111-1-1-11ii−i−i−ii-111-1ii−i−i1-1111-1-11-1-1-11−ii11-1-1ii−i−iii−i−i−i−iii-1-111−iii−i1-1-11−ii-11
χ121-111-1-1-11ii−i−i−ii-111-1ii−i−i1-1111-1-11-1-1-11−ii-1-111−i−iiiii−i−i−i−iii-1-111i−i−ii-111-1i−i1-1
χ131-111-1-1-11−i−iiii−i-111-1−i−iii1-1111-1-11-1-1-11i−i11-1-1−i−iii−i−iiiii−i−i-1-111i−i−ii1-1-11i−i-11
χ141-111-1-1-11−i−iiii−i-111-1−i−iii1-1111-1-11-1-1-11i−i-1-111ii−i−i−i−iiiii−i−i-1-111−iii−i-111-1−ii1-1
χ151-111-1-1-11−i−iii−ii1-11-1−i−iii1-1111-1-11-1-11-1−ii11-1-1−i−iii−i−iii−i−iii11-1-1−ii−ii1-11-1−ii1-1
χ161-111-1-1-11−i−iii−ii1-11-1−i−iii1-1111-1-11-1-11-1−ii-1-111ii−i−i−i−iii−i−iii11-1-1i−ii−i-11-11i−i-11
χ17222222222222222222222222-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222222222-2-2-2-222222222-1-1-1-1-1-1-1-1-2-2-2-200000000-1-1-1-111111111000000000000
χ1922222222-2-2-2-222-2-222-2-2-2-222-1-1-1-1-1-1-1-1-2-222000000001111-1-1-1-11111000000000000
χ2022222222-2-2-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-122-2-20000000011111111-1-1-1-1000000000000
χ21222-22-2-2-22-22-20000222-22-2-2-222-22-2-22-20000000000002-22-200000000000000000000
χ22222-22-2-2-22-22-20000222-22-2-2-2-1-11-111-11000000000000-11-113−33−33−33−3000000000000
χ23222-22-2-2-22-22-20000222-22-2-2-2-1-11-111-11000000000000-11-11−33−33−33−33000000000000
χ24222-22-2-2-2-22-22000022-22-22-2-222-22-2-22-2000000000000-22-2200000000000000000000
χ25222-22-2-2-2-22-22000022-22-22-2-2-1-11-111-110000000000001-11-13−33−3−33−33000000000000
χ26222-22-2-2-2-22-22000022-22-22-2-2-1-11-111-110000000000001-11-1−33−333−33−3000000000000
χ272-222-2-2-222i2i−2i−2i2i−2i2-22-22i2i−2i−2i2-2-1-1-111-1112-22i−2i00000000−i−iii−i−iii-1-111000000000000
χ282-222-2-2-222i2i−2i−2i−2i2i-222-22i2i−2i−2i2-2-1-1-111-111-22−2i2i00000000−i−iiiii−i−i11-1-1000000000000
χ292-222-2-2-22−2i−2i2i2i2i−2i-222-2−2i−2i2i2i2-2-1-1-111-111-222i−2i00000000ii−i−i−i−iii11-1-1000000000000
χ302-222-2-2-22−2i−2i2i2i−2i2i2-22-2−2i−2i2i2i2-2-1-1-111-1112-2−2i2i00000000ii−i−iii−i−i-1-111000000000000
χ312-22-2-222-22i−2i−2i2i00002-22i−2i−2i2i-2222-2-22-2-220000000000002i−2i−2i2i00000000000000000000
χ322-22-2-222-22i−2i−2i2i00002-22i−2i−2i2i-22-1-111-111-1000000000000−iii−i−i3i3i3−i3−333−3000000000000
χ332-22-2-222-22i−2i−2i2i00002-22i−2i−2i2i-22-1-111-111-1000000000000−iii−ii3−i3−i3i33−3−33000000000000
χ342-22-2-222-2−2i2i2i−2i00002-2−2i2i2i−2i-2222-2-22-2-22000000000000−2i2i2i−2i00000000000000000000
χ352-22-2-222-2−2i2i2i−2i00002-2−2i2i2i−2i-22-1-111-111-1000000000000i−i−ii−i3i3i3−i33−3−33000000000000
χ362-22-2-222-2−2i2i2i−2i00002-2−2i2i2i−2i-22-1-111-111-1000000000000i−i−iii3−i3−i3i3−333−3000000000000
χ373333333333333333-1-1-1-1-1-1-1-100000000-1-1-1-111111111000000000000-1-1-1-1-1-1-1-11111
χ383333333333333333-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000011111111-1-1-1-1
χ39333333333333-3-3-3-3-1-1-1-1-1-1-1-10000000011111111111100000000000011-1-1-1-111-1-1-1-1
χ40333333333333-3-3-3-3-1-1-1-1-1-1-1-1000000001111-1-1-1-1-1-1-1-1000000000000-1-11111-1-11111
χ4133333333-3-3-3-333-3-3-1-11111-1-10000000011-1-11111-1-1-1-1000000000000-1-111-1-11111-1-1
χ4233333333-3-3-3-333-3-3-1-11111-1-10000000011-1-1-1-1-1-1111100000000000011-1-111-1-1-1-111
χ4333333333-3-3-3-3-3-333-1-11111-1-100000000-1-1111111-1-1-1-10000000000001111-1-1-1-1-1-111
χ4433333333-3-3-3-3-3-333-1-11111-1-100000000-1-111-1-1-1-11111000000000000-1-1-1-1111111-1-1
χ453-333-3-3-333i3i−3i−3i3i−3i3-3-11−i−iii-1100000000-11−ii11-1-1ii−i−i000000000000−ii−ii-11-11i−i1-1
χ463-333-3-3-333i3i−3i−3i3i−3i3-3-11−i−iii-1100000000-11−ii-1-111−i−iii000000000000i−ii−i1-11-1−ii-11
χ473-333-3-3-333i3i−3i−3i−3i3i-33-11−i−iii-11000000001-1i−i11-1-1ii−i−i000000000000i−i−ii-111-1−ii-11
χ483-333-3-3-333i3i−3i−3i−3i3i-33-11−i−iii-11000000001-1i−i-1-111−i−iii000000000000−iii−i1-1-11i−i1-1
χ493-333-3-3-33−3i−3i3i3i3i−3i-33-11ii−i−i-11000000001-1−ii11-1-1−i−iii000000000000−iii−i-111-1i−i-11
χ503-333-3-3-33−3i−3i3i3i3i−3i-33-11ii−i−i-11000000001-1−ii-1-111ii−i−i000000000000i−i−ii1-1-11−ii1-1
χ513-333-3-3-33−3i−3i3i3i−3i3i3-3-11ii−i−i-1100000000-11i−i11-1-1−i−iii000000000000i−ii−i-11-11−ii1-1
χ523-333-3-3-33−3i−3i3i3i−3i3i3-3-11ii−i−i-1100000000-11i−i-1-111ii−i−i000000000000−ii−ii1-11-1i−i-11
χ5344-44-44-4-40000000000000000-22-2222-2-20000000022−2222−22000000000000000000000000
χ5444-44-44-4-40000000000000000-22-2222-2-200000000−2222−2222000000000000000000000000
χ5544-4-4-4-4440000000000000000-2222-2-2-220000−2i22i2−2i22i20000000000000000000000000000
χ5644-4-4-4-4440000000000000000-2222-2-2-2200002i2−2i22i2−2i20000000000000000000000000000
χ574-4-444-44-40000000000000000-22-2-2-222200000000−2i22i22i2−2i2000000000000000000000000
χ584-4-444-44-40000000000000000-22-2-2-2222000000002i2−2i2−2i22i2000000000000000000000000
χ594-4-4-444-440000000000000000-222-22-22-20000−2i22i22i2−2i20000000000000000000000000000
χ604-4-4-444-440000000000000000-222-22-22-200002i2−2i2−2i22i20000000000000000000000000000
χ61666-66-6-6-66-66-60000-2-2-22-222200000000000000000000000000000000000000000000
χ62666-66-6-6-6-66-660000-2-22-22-22200000000000000000000000000000000000000000000
χ636-66-6-666-66i−6i−6i6i0000-22−2i2i2i−2i2-200000000000000000000000000000000000000000000
χ646-66-6-666-6−6i6i6i−6i0000-222i−2i−2i2i2-200000000000000000000000000000000000000000000
χ6588-88-88-8-800000000000000002-22-2-2-222000000000000000000000000000000000000
χ6688-8-8-8-88800000000000000002-2-2-2222-2000000000000000000000000000000000000
χ678-8-888-88-800000000000000002-2222-2-2-2000000000000000000000000000000000000
χ688-8-8-888-8800000000000000002-2-22-22-22000000000000000000000000000000000000

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