Finite Group Databasebeta

← Group #11788764

Character table — Group #11788764

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244444444444444888888888812121212121212121818181824242424242424242424242436364848484872727272
order12244336666881212242424246121212242424242424224488882244224466121224242424886612124444
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
χ511111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ611111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-111
χ711111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ811111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ911-11-111-111-1i−i-1-1ii−i−i-111-1i−iii−i−i11-1-1ii−i−i1-11-11-1i−i11-1-1ii−i−ii−i1-1i−i1-1i−i
χ1011-11-111-111-1i−i-1-1ii−i−i-111-1i−iii−i−i11-1-1ii−i−i1-11-1-11−ii11-1-1ii−i−ii−i-11−ii-11−ii
χ1111-11-111-111-1i−i-1-1ii−i−i-111-1i−iii−i−i-1-111−i−iii1-11-11-1i−i-1-111−i−iiii−i1-1i−i-11−ii
χ1211-11-111-111-1i−i-1-1ii−i−i-111-1i−iii−i−i-1-111−i−iii1-11-1-11−ii-1-111−i−iiii−i-11−ii1-1i−i
χ1311-11-111-111-1−ii-1-1−i−iii-111-1−ii−i−iii11-1-1−i−iii1-11-11-1−ii11-1-1−i−iii−ii1-1−ii1-1−ii
χ1411-11-111-111-1−ii-1-1−i−iii-111-1−ii−i−iii11-1-1−i−iii1-11-1-11i−i11-1-1−i−iii−ii-11i−i-11i−i
χ1511-11-111-111-1−ii-1-1−i−iii-111-1−ii−i−iii-1-111ii−i−i1-11-11-1−ii-1-111ii−i−i−ii1-1−ii-11i−i
χ1611-11-111-111-1−ii-1-1−i−iii-111-1−ii−i−iii-1-111ii−i−i1-11-1-11i−i-1-111ii−i−i−ii-11i−i1-1−ii
χ172222222222222222222222222222200000000-2-2-2-2000000000000-2-200000000
χ1822222222222-2-222-2-2-2-22222-2-2-2-2-2-200000000-2-2-2-20000000000002200000000
χ19222-2-222222200-2-200002-2-2-200000000002i−2i2i−2i-2-222000000002i−2i2i−2i0000000000
χ20222-2-222222200-2-200002-2-2-20000000000−2i2i−2i2i-2-22200000000−2i2i−2i2i0000000000
χ21222-2-222222200-2-200002-2-2-20000002-22-2000022-2-200002-22-200000000000000
χ22222-2-222222200-2-200002-2-2-2000000-22-22000022-2-20000-22-2200000000000000
χ2322-22-222-222-22i−2i-2-22i2i−2i−2i-222-22i−2i2i2i−2i−2i00000000-22-22000000000000−2i2i00000000
χ2422-22-222-222-2−2i2i-2-2−2i−2i2i2i-222-2−2i2i−2i−2i2i2i00000000-22-220000000000002i−2i00000000
χ2522-2-2222-222-200220000-2-2-2200000000002-2-22-222-2000000002-2-220000000000
χ2622-2-2222-222-200220000-2-2-220000000000-222-2-222-200000000-222-20000000000
χ2722-2-2222-222-200220000-2-2-220000002-2-2200002-2-2200002-2-2200000000000000
χ2822-2-2222-222-200220000-2-2-22000000-222-200002-2-220000-222-200000000000000
χ29444441-2-2-21-2441111111-21-211-2-2-2-22222222200000000-1-1-1-1-1-1-1-10000000000
χ30444441-2-2-21-2441111111-21-211-2-2-2-2-2-2-2-2-2-2-2-200000000111111110000000000
χ31444441-2-2-21-2-4-411-1-1-1-11-21-2-1-122222222-2-2-2-200000000-1-1-1-111110000000000
χ32444441-2-2-21-2-4-411-1-1-1-11-21-2-1-12222-2-2-2-22222000000001111-1-1-1-10000000000
χ3344444-2111-2144-2-2-2-2-2-2-21-21-2-2111100000000000022220000000000-1-1-1-10000
χ3444444-2111-2144-2-2-2-2-2-2-21-21-2-21111000000000000-2-2-2-2000000000011110000
χ3544444-2111-21-4-4-2-22222-21-2122-1-1-1-100000000000022-2-20000000000-1-1110000
χ3644444-2111-21-4-4-2-22222-21-2122-1-1-1-1000000000000-2-222000000000011-1-10000
χ37444-4-41-2-2-21-200-1-13i3i−3i−3i12-12−3i3i00002-22-22i−2i2i−2i00000000-11-11−ii−ii0000000000
χ38444-4-41-2-2-21-200-1-13i3i−3i−3i12-12−3i3i0000-22-22−2i2i−2i2i000000001-11-1i−ii−i0000000000
χ39444-4-41-2-2-21-200-1-1−3i−3i3i3i12-123i−3i00002-22-2−2i2i−2i2i00000000-11-11i−ii−i0000000000
χ40444-4-41-2-2-21-200-1-1−3i−3i3i3i12-123i−3i0000-22-222i−2i2i−2i000000001-11-1−ii−ii0000000000
χ4144-44-41-22-2124i−4i-1-1ii−i−i-1-212i−i−2i−2i2i2i22-2-22i2i−2i−2i00000000-1-111−i−iii0000000000
χ4244-44-41-22-2124i−4i-1-1ii−i−i-1-212i−i−2i−2i2i2i-2-222−2i−2i2i2i0000000011-1-1ii−i−i0000000000
χ4344-44-41-22-212−4i4i-1-1−i−iii-1-212−ii2i2i−2i−2i22-2-2−2i−2i2i2i00000000-1-111ii−i−i0000000000
χ4444-44-41-22-212−4i4i-1-1−i−iii-1-212−ii2i2i−2i−2i-2-2222i2i−2i−2i0000000011-1-1−i−iii0000000000
χ4544-44-4-21-11-2-14i−4i22−2i−2i2i2i21-2-1−2i2iii−i−i0000000000002-22i−2i0000000000-11−ii0000
χ4644-44-4-21-11-2-14i−4i22−2i−2i2i2i21-2-1−2i2iii−i−i000000000000-22−2i2i00000000001-1i−i0000
χ4744-44-4-21-11-2-1−4i4i222i2i−2i−2i21-2-12i−2i−i−iii0000000000002-2−2i2i0000000000-11i−i0000
χ4844-44-4-21-11-2-1−4i4i222i2i−2i−2i21-2-12i−2i−i−iii000000000000-222i−2i00000000001-1−ii0000
χ4944-4-441-22-21200113333-12-1-2-3-300002-2-222-2-2200000000-111-1-111-10000000000
χ5044-4-441-22-21200113333-12-1-2-3-30000-222-2-222-2000000001-1-111-1-110000000000
χ5144-4-441-22-2120011-3-3-3-3-12-1-23300002-2-22-222-200000000-111-11-1-110000000000
χ5244-4-441-22-2120011-3-3-3-3-12-1-2330000-222-22-2-22000000001-1-11-111-10000000000
χ53888-8-8-4222-4200440000-4-24-20000000000000000000000000000000000000000
χ5488-8-88-42-22-4-200-4-400004-2420000000000000000000000000000000000000000
χ558-80002-404-20006i−6i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000
χ568-80002-404-20006i−6i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000
χ578-80002-404-2000−6i6i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000
χ588-80002-404-2000−6i6i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000
χ598-8000880-8-800000000000000000000000000000000000000000000000000000
χ608-8000-426-24-600002i6−2i6−2i62i6000000−i6i6i6−i60000000000000000000000000000000000
χ618-8000-426-24-60000−2i62i62i6−2i6000000i6−i6−i6i60000000000000000000000000000000000
χ628-8000-42-6-246000026−2626−26000000−66−660000000000000000000000000000000000
χ638-8000-42-6-2460000−2626−26260000006−66−60000000000000000000000000000000000

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