Finite Group Databasebeta

← Group #11712886

Character table — Group #11712886

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222244446666666688888888121212121212121212121212161616161616161616161616242424242424242424242424
order122244448888448822448888366612121212444444888888121212122424242424242424444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-11111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ511111111-1-1-1-111-1-11111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ811111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ91111-1-1-1-1ii−i−i1-1i−i-1-111ii−i−i1111-1-1-1-11-1ii−i−ii−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−ii−i1-1
χ101111-1-1-1-1ii−i−i1-1i−i-1-111ii−i−i1111-1-1-1-11-1−i−iiii−i-1-11111-1-1ii−i−iii−i−i-11-11−ii−ii−ii-11
χ111111-1-1-1-1ii−i−i-11−ii-1-111ii−i−i1111-1-1-1-1-11ii−i−i−ii11-1-1-1-111ii−i−i−i−iii1-1-11−iii−i−ii-11
χ121111-1-1-1-1ii−i−i-11−ii-1-111ii−i−i1111-1-1-1-1-11−i−iii−ii-1-111-1-111ii−i−i−i−iii-111-1i−i−iii−i1-1
χ131111-1-1-1-1−i−iii1-1−ii-1-111−i−iii1111-1-1-1-11-1ii−i−i−ii-1-11111-1-1−i−iii−i−iii-11-11i−ii−ii−i-11
χ141111-1-1-1-1−i−iii1-1−ii-1-111−i−iii1111-1-1-1-11-1−i−iii−ii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii−ii1-1
χ151111-1-1-1-1−i−iii-11i−i-1-111−i−iii1111-1-1-1-1-11ii−i−ii−i-1-111-1-111−i−iiiii−i−i-111-1−iii−i−ii1-1
χ161111-1-1-1-1−i−iii-11i−i-1-111−i−iii1111-1-1-1-1-11−i−iiii−i11-1-1-1-111−i−iiiii−i−i1-1-11i−i−iii−i-11
χ17222222222222222222222222-1-1-1-1-1-1-1-1220000220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222222222-2-2-2-222222222-1-1-1-1-1-1-1-1-2-20000-2-200001111-1-1-1-11111000000000000
χ1922222222-2-2-2-222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1220000-2-20000-1-1-1-111111111000000000000
χ2022222222-2-2-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-2-2000022000011111111-1-1-1-1000000000000
χ212222-2-2-2-22i2i−2i−2i2-22i−2i-2-2222i2i−2i−2i-1-1-1-111112-200002i−2i0000-1-111−i−iii−i−iii000000000000
χ222222-2-2-2-22i2i−2i−2i-22−2i2i-2-2222i2i−2i−2i-1-1-1-11111-220000−2i2i000011-1-1−i−iiiii−i−i000000000000
χ232222-2-2-2-2−2i−2i2i2i2-2−2i2i-2-222−2i−2i2i2i-1-1-1-111112-20000−2i2i0000-1-111ii−i−iii−i−i000000000000
χ242222-2-2-2-2−2i−2i2i2i-222i−2i-2-222−2i−2i2i2i-1-1-1-11111-2200002i−2i000011-1-1ii−i−i−i−iii000000000000
χ2522-2-222-2-22-22-200002-22-22-22-222-2-222-2-200000000000000002-22-20000000000000000
χ2622-2-222-2-22-22-200002-22-22-22-2-1-111-1-1110000000000003−33−3-11-113−33−3000000000000
χ2722-2-222-2-22-22-200002-22-22-22-2-1-111-1-111000000000000−33−33-11-11−33−33000000000000
χ2822-2-222-2-2-22-2200002-22-2-22-2222-2-222-2-20000000000000000-22-220000000000000000
χ2922-2-222-2-2-22-2200002-22-2-22-22-1-111-1-1110000000000003−33−31-11-1−33−33000000000000
χ3022-2-222-2-2-22-2200002-22-2-22-22-1-111-1-111000000000000−33−331-11-13−33−3000000000000
χ3122-2-2-2-2222i−2i−2i2i0000-222-22i−2i−2i2i22-2-2-2-22200000000000000002i−2i−2i2i0000000000000000
χ3222-2-2-2-2222i−2i−2i2i0000-222-22i−2i−2i2i-1-11111-1-10000000000003−3−33−iii−ii3−i3−i3i3000000000000
χ3322-2-2-2-2222i−2i−2i2i0000-222-22i−2i−2i2i-1-11111-1-1000000000000−333−3−iii−i−i3i3i3−i3000000000000
χ3422-2-2-2-222−2i2i2i−2i0000-222-2−2i2i2i−2i22-2-2-2-2220000000000000000−2i2i2i−2i0000000000000000
χ3522-2-2-2-222−2i2i2i−2i0000-222-2−2i2i2i−2i-1-11111-1-10000000000003−3−33i−i−ii−i3i3i3−i3000000000000
χ3622-2-2-2-222−2i2i2i−2i0000-222-2−2i2i2i−2i-1-11111-1-1000000000000−333−3i−i−iii3−i3−i3i3000000000000
χ373333333333333333-1-1-1-1-1-1-1-100000000-1-11111-1-11111000000000000-1-1-1-111-1-1-1-111
χ383333333333333333-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-10000000000001111-1-11111-1-1
χ39333333333333-3-3-3-3-1-1-1-1-1-1-1-100000000111111111111000000000000-1-111-1-1-1-111-1-1
χ40333333333333-3-3-3-3-1-1-1-1-1-1-1-10000000011-1-1-1-111-1-1-1-100000000000011-1-11111-1-111
χ4133333333-3-3-3-333-3-3-1-1-1-1111100000000-1-1111111-1-1-1-1000000000000111111-1-1-1-1-1-1
χ4233333333-3-3-3-333-3-3-1-1-1-1111100000000-1-1-1-1-1-1111111000000000000-1-1-1-1-1-1111111
χ4333333333-3-3-3-3-3-333-1-1-1-1111100000000111111-1-1-1-1-1-100000000000011-1-1-1-1-1-11111
χ4433333333-3-3-3-3-3-333-1-1-1-111110000000011-1-1-1-1-1-11111000000000000-1-1111111-1-1-1-1
χ453333-3-3-3-33i3i−3i−3i3-33i−3i11-1-1−i−iii00000000-11ii−i−i−ii11-1-1000000000000-11-11i−i−ii−ii1-1
χ463333-3-3-3-33i3i−3i−3i3-33i−3i11-1-1−i−iii00000000-11−i−iii−ii-1-1110000000000001-11-1−iii−ii−i-11
χ473333-3-3-3-33i3i−3i−3i-33−3i3i11-1-1−i−iii000000001-1ii−i−ii−i11-1-1000000000000-111-1−ii−iii−i-11
χ483333-3-3-3-33i3i−3i−3i-33−3i3i11-1-1−i−iii000000001-1−i−iiii−i-1-1110000000000001-1-11i−ii−i−ii1-1
χ493333-3-3-3-3−3i−3i3i3i3-3−3i3i11-1-1ii−i−i00000000-11ii−i−ii−i-1-1110000000000001-11-1i−i−ii−ii-11
χ503333-3-3-3-3−3i−3i3i3i3-3−3i3i11-1-1ii−i−i00000000-11−i−iiii−i11-1-1000000000000-11-11−iii−ii−i1-1
χ513333-3-3-3-3−3i−3i3i3i-333i−3i11-1-1ii−i−i000000001-1ii−i−i−ii-1-1110000000000001-1-11−ii−iii−i1-1
χ523333-3-3-3-3−3i−3i3i3i-333i−3i11-1-1ii−i−i000000001-1−i−iii−ii11-1-1000000000000-111-1i−ii−i−ii-11
χ534-44-44i−4i4i−4i0000000000000000-222-22i−2i2i−2i0000000022−22−2i22i2000000000000000000000000
χ544-44-44i−4i4i−4i0000000000000000-222-22i−2i2i−2i00000000−22222i2−2i2000000000000000000000000
χ554-44-4−4i4i−4i4i0000000000000000-222-2−2i2i−2i2i0000000022−222i2−2i2000000000000000000000000
χ564-44-4−4i4i−4i4i0000000000000000-222-2−2i2i−2i2i00000000−2222−2i22i2000000000000000000000000
χ574-4-444i−4i−4i4i0000000000000000-22-222i−2i−2i2i002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ584-4-444i−4i−4i4i0000000000000000-22-222i−2i−2i2i00−2+2i2−2i−2−2i2+2i000000000000000000000000000000
χ594-4-44−4i4i4i−4i0000000000000000-22-22−2i2i2i−2i002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ604-4-44−4i4i4i−4i0000000000000000-22-22−2i2i2i−2i00−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ6166-6-666-6-66-66-60000-22-22-22-2200000000000000000000000000000000000000000000
χ6266-6-666-6-6-66-660000-22-222-22-200000000000000000000000000000000000000000000
χ6366-6-6-6-6666i−6i−6i6i00002-2-22−2i2i2i−2i00000000000000000000000000000000000000000000
χ6466-6-6-6-666−6i6i6i−6i00002-2-222i−2i−2i2i00000000000000000000000000000000000000000000
χ658-88-88i−8i8i−8i00000000000000002-2-22−2i2i−2i2i000000000000000000000000000000000000
χ668-88-8−8i8i−8i8i00000000000000002-2-222i−2i2i−2i000000000000000000000000000000000000
χ678-8-888i−8i−8i8i00000000000000002-22-2−2i2i2i−2i000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i00000000000000002-22-22i−2i−2i2i000000000000000000000000000000000000

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