Finite Group Databasebeta

← Group #11797941

Character table — Group #11797941

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1122244444444444444888888888824242424242424242424242424242424363636364848484872727272
order12244336666881212242424246121212242424242424244444668812122424242444881212121216161616
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1
χ611111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111
χ711111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-111-1-111
χ811111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-111-1-1
χ911-1-1111-11-11i−i-1-1ii−i−i-111-1i−iii−i−i1-11-1i−i11i−i-1-1ii−i−ii−i1-1i−i1-11-1i−i
χ1011-1-1111-11-11i−i-1-1ii−i−i-111-1i−iii−i−i1-1-11−ii11i−i-1-1ii−i−ii−i1-1−ii-11-11−ii
χ1111-1-1111-11-11i−i-1-1ii−i−i-111-1i−iii−i−i-111-1i−i-1-1−ii11−i−iiii−i1-1i−i1-1-11−ii
χ1211-1-1111-11-11i−i-1-1ii−i−i-111-1i−iii−i−i-11-11−ii-1-1−ii11−i−iiii−i1-1−ii-111-1i−i
χ1311-1-1111-11-11−ii-1-1−i−iii-111-1−ii−i−iii1-11-1−ii11−ii-1-1−i−iii−ii1-1−ii1-11-1−ii
χ1411-1-1111-11-11−ii-1-1−i−iii-111-1−ii−i−iii1-1-11i−i11−ii-1-1−i−iii−ii1-1i−i-11-11i−i
χ1511-1-1111-11-11−ii-1-1−i−iii-111-1−ii−i−iii-111-1−ii-1-1i−i11ii−i−i−ii1-1−ii1-1-11i−i
χ1611-1-1111-11-11−ii-1-1−i−iii-111-1−ii−i−iii-11-11i−i-1-1i−i11ii−i−i−ii1-1i−i-111-1−ii
χ17222222222222222222222222222220000000000000000-2-2-2-200000000
χ1822222222222-2-222-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-200000000
χ1922-2-2222-22-222i−2i-2-22i2i−2i−2i-222-22i−2i2i2i−2i−2i0000000000000000−2i2i-2200000000
χ2022-2-2222-22-22−2i2i-2-2−2i−2i2i2i-222-2−2i2i−2i−2i2i2i00000000000000002i−2i-2200000000
χ21444441-21-21144-2-2-2-2-2-2-2-211-2-2111100222200000000000000-1-1-1-10000
χ22444441-21-21144-2-2-2-2-2-2-2-211-2-2111100-2-2-2-20000000000000011110000
χ23444441-21-211-4-4-2-22222-2-21122-1-1-1-10022-2-20000000000000011-1-10000
χ24444441-21-211-4-4-2-22222-2-21122-1-1-1-100-2-22200000000000000-1-1110000
χ2544444-21-21-2-24411111111-2-211-2-2-2-2220000-1-122-1-1-1-1-1-1000000000000
χ2644444-21-21-2-24411111111-2-211-2-2-2-2-2-2000011-2-2111111000000000000
χ2744444-21-21-2-2-4-411-1-1-1-111-2-2-1-12222220000-1-1-2-2-1-11111000000000000
χ2844444-21-21-2-2-4-411-1-1-1-111-2-2-1-12222-2-20000112211-1-1-1-1000000000000
χ29444-4-444444400-4-400004-4-4-40000000000000000000000000000000000
χ30444-4-4-21-21-2-200-1-13i3i−3i−3i1-122−3i3i0000000000−i3i300−i3i33−33−3000000000000
χ31444-4-4-21-21-2-200-1-13i3i−3i−3i1-122−3i3i0000000000i3−i300i3−i3−33−33000000000000
χ32444-4-4-21-21-2-200-1-1−3i−3i3i3i1-1223i−3i0000000000−i3i300−i3i3−33−33000000000000
χ33444-4-4-21-21-2-200-1-1−3i−3i3i3i1-1223i−3i0000000000i3−i300i3−i33−33−3000000000000
χ3444-44-444-44-4400440000-4-4-440000000000000000000000000000000000
χ3544-44-4-21212-200113333-1-12-2-3-30000000000−i3i300i3−i3−i3i3i3−i3000000000000
χ3644-44-4-21212-200113333-1-12-2-3-30000000000i3−i300−i3i3i3−i3−i3i3000000000000
χ3744-44-4-21212-20011-3-3-3-3-1-12-2330000000000−i3i300i3−i3i3−i3−i3i3000000000000
χ3844-44-4-21212-20011-3-3-3-3-1-12-2330000000000i3−i300−i3i3−i3i3i3−i3000000000000
χ3944-4-441-2-1-2-114i−4i22−2i−2i2i2i2-21-1−2i2iii−i−i002-22i−2i00000000000000−ii-110000
χ4044-4-441-2-1-2-114i−4i22−2i−2i2i2i2-21-1−2i2iii−i−i00-22−2i2i00000000000000i−i1-10000
χ4144-4-441-2-1-2-11−4i4i222i2i−2i−2i2-21-12i−2i−i−iii002-2−2i2i00000000000000i−i-110000
χ4244-4-441-2-1-2-11−4i4i222i2i−2i−2i2-21-12i−2i−i−iii00-222i−2i00000000000000−ii1-10000
χ4344-4-44-21212-24i−4i-1-1ii−i−i-11-22i−i−2i−2i2i2i2-20000-1-12i−2i11−i−iii000000000000
χ4444-4-44-21212-24i−4i-1-1ii−i−i-11-22i−i−2i−2i2i2i-22000011−2i2i-1-1ii−i−i000000000000
χ4544-4-44-21212-2−4i4i-1-1−i−iii-11-22−ii2i2i−2i−2i2-20000-1-1−2i2i11ii−i−i000000000000
χ4644-4-44-21212-2−4i4i-1-1−i−iii-11-22−ii2i2i−2i−2i-220000112i−2i-1-1−i−iii000000000000
χ47888-8-82-42-42200440000-44-2-20000000000000000000000000000000000
χ4888-88-82-4-2-4-2200-4-4000044-220000000000000000000000000000000000
χ498-80002-464-6-2000026−2626−260000006−66−60000000000000000000000000000
χ508-80002-464-6-20000−2626−2626000000−66−660000000000000000000000000000
χ518-80002-4-646-200002i6−2i6−2i62i6000000i6−i6−i6i60000000000000000000000000000
χ528-80002-4-646-20000−2i62i62i6−2i6000000−i6i6i6−i60000000000000000000000000000
χ538-8000880-80-80000000000000000000000000000000000000000000000
χ548-8000-420-204006i−6i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ558-8000-420-204006i−6i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ568-8000-420-20400−6i6i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ578-8000-420-20400−6i6i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.