Finite Group Databasebeta

← Group #11788830

Character table — Group #11788830

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244444444444444888888888812121212121212121818181824242424242424242424242436364848484872727272
order12244334466661212121212126121212121212121212444444442244248812121212121212124461224244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ61111111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-111
χ71111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ81111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ911-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i11-1-1ii−i−i-111-11-1i−i11-1-1ii−i−ii−i1-1i−i1-1i−i
χ1011-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i11-1-1ii−i−i-111-1-11−ii11-1-1ii−i−ii−i-11−ii-11−ii
χ1111-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i-1-111−i−iii-111-11-1i−i-1-111−i−iiii−i1-1i−i-11−ii
χ1211-11-111i−i-111-1ii−i−i-1-1-111-1i−iii−i−i-1-111−i−iii-111-1-11−ii-1-111−i−iiii−i-11−ii1-1i−i
χ1311-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii11-1-1−i−iii-111-11-1−ii11-1-1−i−iii−ii1-1−ii1-1−ii
χ1411-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii11-1-1−i−iii-111-1-11i−i11-1-1−i−iii−ii-11i−i-11i−i
χ1511-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii-1-111ii−i−i-111-11-1−ii-1-111ii−i−i−ii1-1−ii-11i−i
χ1611-11-111−ii-111-1−i−iii-1-1-111-1−ii−i−iii-1-111ii−i−i-111-1-11i−i-1-111ii−i−i−ii-11i−i1-1−ii
χ172222222222222222222222222222200000000-2-2-2-2000000000000-2-200000000
χ182222222-2-22222-2-2-2-2222222-2-2-2-2-2-200000000-2-2-2-20000000000002200000000
χ19222-2-2220022220000-2-22-2-2-200000000002-22-2-2-222000000002-22-20000000000
χ20222-2-2220022220000-2-22-2-2-20000000000-22-22-2-22200000000-22-220000000000
χ21222-2-2220022220000-2-22-2-2-20000002-22-2000022-2-200002-22-200000000000000
χ22222-2-2220022220000-2-22-2-2-2000000-22-22000022-2-20000-22-2200000000000000
χ2322-22-2222i−2i-222-22i2i−2i−2i-2-2-222-22i−2i2i2i−2i−2i000000002-2-22000000000000−2i2i00000000
χ2422-22-222−2i2i-222-2−2i−2i2i2i-2-2-222-2−2i2i−2i−2i2i2i000000002-2-220000000000002i−2i00000000
χ2522-2-222200-222-2000022-2-2-2200000000002i−2i−2i2i2-22-2000000002i−2i−2i2i0000000000
χ2622-2-222200-222-2000022-2-2-220000000000−2i2i2i−2i2-22-200000000−2i2i2i−2i0000000000
χ2722-2-222200-222-2000022-2-2-220000002-2-220000-22-2200002-2-2200000000000000
χ2822-2-222200-222-2000022-2-2-22000000-222-20000-22-220000-222-200000000000000
χ29444441-2441-2111111-2-2-2-21111-2-2-2-22222222200000000-1-1-1-1-1-1-1-10000000000
χ30444441-2441-2111111-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-200000000111111110000000000
χ31444441-2-4-41-211-1-1-1-1-2-2-2-211-1-122222222-2-2-2-200000000-1-1-1-111110000000000
χ32444441-2-4-41-211-1-1-1-1-2-2-2-211-1-12222-2-2-2-22222000000001111-1-1-1-10000000000
χ3344444-2144-21-2-2-2-2-2-21111-2-2-2-2111100000000000022220000000000-1-1-1-10000
χ3444444-2144-21-2-2-2-2-2-21111-2-2-2-21111000000000000-2-2-2-2000000000011110000
χ3544444-21-4-4-21-2-222221111-2-222-1-1-1-100000000000022-2-20000000000-1-1110000
χ3644444-21-4-4-21-2-222221111-2-222-1-1-1-1000000000000-2-222000000000011-1-10000
χ37444-4-41-2001-211333322-22-1-1-3-300002-22-22-22-200000000-11-11-11-110000000000
χ38444-4-41-2001-211333322-22-1-1-3-30000-22-22-22-22000000001-11-11-11-10000000000
χ39444-4-41-2001-211-3-3-3-322-22-1-13300002-22-2-22-2200000000-11-111-11-10000000000
χ40444-4-41-2001-211-3-3-3-322-22-1-1330000-22-222-22-2000000001-11-1-11-110000000000
χ4144-44-41-24i−4i-1-21-1ii−i−i222-21-1i−i−2i−2i2i2i22-2-22i2i−2i−2i00000000-1-111−i−iii0000000000
χ4244-44-41-24i−4i-1-21-1ii−i−i222-21-1i−i−2i−2i2i2i-2-222−2i−2i2i2i0000000011-1-1ii−i−i0000000000
χ4344-44-41-2−4i4i-1-21-1−i−iii222-21-1−ii2i2i−2i−2i22-2-2−2i−2i2i2i00000000-1-111ii−i−i0000000000
χ4444-44-41-2−4i4i-1-21-1−i−iii222-21-1−ii2i2i−2i−2i-2-2222i2i−2i−2i0000000011-1-1−i−iii0000000000
χ4544-44-4-214i−4i21-22−2i−2i2i2i-1-1-11-22−2i2iii−i−i0000000000002-22i−2i0000000000-11−ii0000
χ4644-44-4-214i−4i21-22−2i−2i2i2i-1-1-11-22−2i2iii−i−i000000000000-22−2i2i00000000001-1i−i0000
χ4744-44-4-21−4i4i21-222i2i−2i−2i-1-1-11-222i−2i−i−iii0000000000002-2−2i2i0000000000-11i−i0000
χ4844-44-4-21−4i4i21-222i2i−2i−2i-1-1-11-222i−2i−i−iii000000000000-222i−2i00000000001-1−ii0000
χ4944-4-441-200-1-21-13i3i−3i−3i-2-222-11−3i3i00002-2-222i−2i−2i2i00000000-111-1−iii−i0000000000
χ5044-4-441-200-1-21-13i3i−3i−3i-2-222-11−3i3i0000-222-2−2i2i2i−2i000000001-1-11i−i−ii0000000000
χ5144-4-441-200-1-21-1−3i−3i3i3i-2-222-113i−3i00002-2-22−2i2i2i−2i00000000-111-1i−i−ii0000000000
χ5244-4-441-200-1-21-1−3i−3i3i3i-2-222-113i−3i0000-222-22i−2i−2i2i000000001-1-11−iii−i0000000000
χ53888-8-8-4200-42-4-40000-2-22-2440000000000000000000000000000000000000000
χ5488-8-88-420042-44000022-2-24-40000000000000000000000000000000000000000
χ558-80002-40064-2-623−2323−230000000023−2323−230000000000000000000000000000000000
χ568-80002-40064-2-6−2323−232300000000−2323−23230000000000000000000000000000000000
χ578-80002-400-64-26−2i32i32i3−2i300000000−2i32i32i3−2i30000000000000000000000000000000000
χ588-80002-400-64-262i3−2i3−2i32i3000000002i3−2i3−2i32i30000000000000000000000000000000000
χ598-800088000-8-8000000000000000000000000000000000000000000000000000
χ608-8000-42000-240−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ116i−6i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000000000000000
χ618-8000-42000-240−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11−6i6i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000000000000000
χ628-8000-42000-2402ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−6i6i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000000000000000
χ638-8000-42000-2402ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ116i−6i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.