Finite Group Databasebeta

← Group #11771777

Character table — Group #11771777

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1122244444444444444888888888824242424242424242424242436364848484848487272727272
order1224433666688121224242424612121224242424242416161616484848484848484824441212121288888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ511111111111-1-111-1-1-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-11-1-1-1111ii−i−i
χ611111111111-1-111-1-1-1-11111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1111-1-11−i−iii
χ711111111111-1-111-1-1-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-11-1-1-1111−i−iii
χ811111111111-1-111-1-1-1-11111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1111-1-11ii−i−i
χ922222222222222222222222222222000000000000-2-2000000-20000
χ1022222222222-2-222-2-2-2-22222-2-2-2-2-2-200000000000022000000-20000
χ11222-2-222222200-2-200002-2-2-20000002−22−222−2−222−2−2-2200000000000
χ12222-2-222222200-2-200002-2-2-2000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22-200000000000
χ13222-2-222222200-2-200002-2-2-2000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22-200000000000
χ14222-2-222222200-2-200002-2-2-2000000−22−22−2−222−2−222-2200000000000
χ1522-22-222-22-222i−2i-2-22i2i−2i−2i-222-22i−2i2i2i−2i−2i0000000000000000000001+i−1−i1−i−1+i
χ1622-22-222-22-222i−2i-2-22i2i−2i−2i-222-22i−2i2i2i−2i−2i000000000000000000000−1−i1+i−1+i1−i
χ1722-22-222-22-22−2i2i-2-2−2i−2i2i2i-222-2−2i2i−2i−2i2i2i0000000000000000000001−i−1+i1+i−1−i
χ1822-22-222-22-22−2i2i-2-2−2i−2i2i2i-222-2−2i2i−2i−2i2i2i000000000000000000000−1+i1−i−1−i1+i
χ19444441-21-21144-2-2-2-2-2-2-2-211-2-211110000000000000022-1-1-1-100000
χ20444441-21-21144-2-2-2-2-2-2-2-211-2-2111100000000000000-2-2111100000
χ21444441-21-211-4-4-2-22222-2-21122-1-1-1-1000000000000002-211-1-100000
χ22444441-21-211-4-4-2-22222-2-21122-1-1-1-100000000000000-22-1-11100000
χ2344444-21-21-2-24411111111-2-211-2-2-2-22222-1-1-1-1-1-1-1-10000000000000
χ2444444-21-21-2-24411111111-2-211-2-2-2-2-2-2-2-2111111110000000000000
χ2544444-21-21-2-2-4-411-1-1-1-111-2-2-1-122222i2i−2i−2i−i−i−i−iiiii0000000000000
χ2644444-21-21-2-2-4-411-1-1-1-111-2-2-1-12222−2i−2i2i2iiiii−i−i−i−i0000000000000
χ27444-4-4-21-21-2-200-1-13i3i−3i−3i1-122−3i3i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000000000000
χ28444-4-4-21-21-2-200-1-13i3i−3i−3i1-122−3i3i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000000000000
χ29444-4-4-21-21-2-200-1-1−3i−3i3i3i1-1223i−3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000000000000
χ30444-4-4-21-21-2-200-1-1−3i−3i3i3i1-1223i−3i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000000000000
χ3144-44-41-2-1-2-114i−4i22−2i−2i2i2i2-21-1−2i2iii−i−i00000000000000003−3−i3i300000
χ3244-44-41-2-1-2-114i−4i22−2i−2i2i2i2-21-1−2i2iii−i−i0000000000000000−33i3−i300000
χ3344-44-41-2-1-2-11−4i4i222i2i−2i−2i2-21-12i−2i−i−iii00000000000000003−3i3−i300000
χ3444-44-41-2-1-2-11−4i4i222i2i−2i−2i2-21-12i−2i−i−iii0000000000000000−33−i3i300000
χ3544-44-4-21212-24i−4i-1-1ii−i−i-11-22i−i−2i−2i2i2i0000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ3644-44-4-21212-24i−4i-1-1ii−i−i-11-22i−i−2i−2i2i2i0000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ3744-44-4-21212-2−4i4i-1-1−i−iii-11-22−ii2i2i−2i−2i0000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ3844-44-4-21212-2−4i4i-1-1−i−iii-11-22−ii2i2i−2i−2i0000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ3944-4-4444-44-4400440000-4-4-440000000000000000000000000000000
χ4044-4-44-21212-200113333-1-12-2-3-3000000003−3−333−3−330000000000000
χ4144-4-44-21212-200113333-1-12-2-3-300000000−333−3−333−30000000000000
χ4244-4-44-21212-20011-3-3-3-3-1-12-23300000000−i3i3i3−i3i3−i3−i3i30000000000000
χ4344-4-44-21212-20011-3-3-3-3-1-12-23300000000i3−i3−i3i3−i3i3i3−i30000000000000
χ44888-8-82-42-42200440000-44-2-20000000000000000000000000000000
χ4588-8-882-4-2-4-2200-4-4000044-220000000000000000000000000000000
χ468-80002-464-6-2000026−2626−260000006−66−60000000000000000000000000
χ478-80002-464-6-20000−2626−2626000000−66−660000000000000000000000000
χ488-80002-4-646-200002i6−2i6−2i62i6000000i6−i6−i6i60000000000000000000000000
χ498-80002-4-646-20000−2i62i62i6−2i6000000−i6i6i6−i60000000000000000000000000
χ508-8000880-80-80000000000000000000000000000000000000000000
χ518-8000-420-204006i−6i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000
χ528-8000-420-204006i−6i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000
χ538-8000-420-20400−6i6i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000
χ548-8000-420-20400−6i6i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000

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