Finite Group Databasebeta

← Group #10692777

Character table — Group #10692777

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order122234444446662444121212121212444461212128888888888881212121224242424242424248888888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ911111-1-1-1-1-1-1111-1111-1-1-1-1-1-11-11-1-1111ii−i−iii−i−ii−ii−i11-1-1ii−i−iii−i−ii−ii−i11-1-11-1
χ1011111-1-1-1-1-1-1111-1111-1-1-1-1-1-11-11-1-1111ii−i−iii−i−i−ii−ii11-1-1−i−iii−i−iiii−ii−i-1-111-11
χ1111111-1-1-1-1-1-1111-1111-1-1-1-1-1-11-11-1-1111−i−iii−i−iiii−ii−i11-1-1ii−i−iii−i−i−ii−ii-1-111-11
χ1211111-1-1-1-1-1-1111-1111-1-1-1-1-1-11-11-1-1111−i−iii−i−iii−ii−ii11-1-1−i−iii−i−iii−ii−ii11-1-11-1
χ1311111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-11-11-1111ii−i−i−i−iiii−i−ii-1-111ii−i−i−i−iiii−i−ii11-1-1-11
χ1411111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-11-11-1111ii−i−i−i−iii−iii−i-1-111−i−iiiii−i−ii−i−ii-1-1111-1
χ1511111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-11-11-1111−i−iiiii−i−ii−i−ii-1-111ii−i−i−i−iii−iii−i-1-1111-1
χ1611111-1-1-1-1-1-1111-1111-1-1-1-1-1-1-11-11-1111−i−iiiii−i−i−iii−i-1-111−i−iiiii−i−i−iii−i11-1-1-11
χ17222222222-2-2222-2-2-22-2-2222222-2-2-22-2-20000000000002-22-2000000000000000000
χ18222222222-2-2222-2-2-22-2-22222-2-222-22-2-2000000000000-22-22000000000000000000
χ19222222-22-222222-2-22-2222-22-20000-2-22-200002222000000000000000000-2-2000000
χ20222222-22-222222-2-22-2222-22-20000-2-22-20000-2-2-2-200000000000000000022000000
χ21222222-22-2-2-222222-2-2-2-22-22-200002-2-222i2i−2i−2i00000000000000000000−2i2i00000000
χ22222222-22-2-2-222222-2-2-2-22-22-200002-2-22−2i−2i2i2i000000000000000000002i−2i00000000
χ2322222-22-2222222-22-2-222-22-220000-2-2-22222200000000000000000000-2-200000000
χ2422222-22-2222222-22-2-222-22-220000-2-2-22-2-2-2-2000000000000000000002200000000
χ2522222-22-22-2-22222-22-2-2-2-22-2200002-22-200002i2i−2i−2i000000000000000000−2i2i000000
χ2622222-22-22-2-22222-22-2-2-2-22-2200002-22-20000−2i−2i2i2i0000000000000000002i−2i000000
χ2722222-2-2-2-2222222-2-2222-2-2-2-22-2-2222-2-20000000000002-2-22000000000000000000
χ2822222-2-2-2-2222222-2-2222-2-2-2-2-222-222-2-2000000000000-222-2000000000000000000
χ292222-1222222-1-1-12222-1-1-1-1-1-12222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-1-1-1-1111111110000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-21111-1-1-1-111110000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-22211111111-1-1-1-10000000000
χ332222-12222-2-2-1-1-1-2-2-2211-1-1-1-122-2-21-111000000000000-11-11−i3i3−i3i3−i3i3−i3i30000000000
χ342222-12222-2-2-1-1-1-2-2-2211-1-1-1-122-2-21-111000000000000-11-11i3−i3i3−i3i3−i3i3−i30000000000
χ352222-12222-2-2-1-1-1-2-2-2211-1-1-1-1-2-2221-1110000000000001-11-1−i3i3−i3i3i3−i3i3−i30000000000
χ362222-12222-2-2-1-1-1-2-2-2211-1-1-1-1-2-2221-1110000000000001-11-1i3−i3i3−i3−i3i3−i3i30000000000
χ372222-1-2-2-2-222-1-1-12-2-22-1-111112-2-22-1-111000000000000-111-13−3−333−3−330000000000
χ382222-1-2-2-2-222-1-1-12-2-22-1-111112-2-22-1-111000000000000-111-1−333−3−333−30000000000
χ392222-1-2-2-2-222-1-1-12-2-22-1-11111-222-2-1-1110000000000001-1-113−3−33−333−30000000000
χ402222-1-2-2-2-222-1-1-12-2-22-1-11111-222-2-1-1110000000000001-1-11−333−33−3−330000000000
χ412222-1-2-2-2-2-2-2-1-1-1-22221111112-22-21-1-1-1000000002i−2i2i−2i-1-111−i−iii−i−iii0000000000
χ422222-1-2-2-2-2-2-2-1-1-1-22221111112-22-21-1-1-100000000−2i2i−2i2i-1-111ii−i−iii−i−i0000000000
χ432222-1-2-2-2-2-2-2-1-1-1-2222111111-22-221-1-1-1000000002i−2i−2i2i11-1-1−i−iiiii−i−i0000000000
χ442222-1-2-2-2-2-2-2-1-1-1-2222111111-22-221-1-1-100000000−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000
χ454444-24-44-444-2-2-2-4-44-4-2-2-22-22000022-220000000000000000000000000000000000
χ464444-24-44-4-4-4-2-2-244-4-422-22-220000-222-20000000000000000000000000000000000
χ474444-2-44-4444-2-2-2-44-4-4-2-22-22-20000222-20000000000000000000000000000000000
χ484444-2-44-44-4-4-2-2-24-44-4222-22-20000-22-220000000000000000000000000000000000
χ4944-4-4400004-44-4-400004-400000000000000000000000000000000000000002-22-200
χ5044-4-4400004-44-4-400004-40000000000000000000000000000000000000000-22-2200
χ5144-4-440000-444-4-40000-4400000000000000000000000000000000000000002-2-2200
χ5244-4-440000-444-4-40000-440000000000000000000000000000000000000000-222-200
χ534-44-4440-4000-44-400000040-4000000000000022−2222−2200000000000000000000000000
χ544-44-4440-4000-44-400000040-40000000000000−2222−222200000000000000000000000000
χ554-44-44-404000-44-4000000-4040000000000000−2i22i22i2−2i200000000000000000000000000
χ564-44-44-404000-44-4000000-40400000000000002i2−2i2−2i22i200000000000000000000000000
χ574-4-444040-400-4-44000000040-400000000−2i22i2−2i22i2000000000000000000000000000000
χ584-4-444040-400-4-44000000040-4000000002i2−2i22i2−2i2000000000000000000000000000000
χ594-4-4440-40400-4-440000000-4040000000022−22−2222000000000000000000000000000000
χ604-4-4440-40400-4-440000000-40400000000−222222−22000000000000000000000000000000
χ6188-8-8-400008-8-4440000-440000000000000000000000000000000000000000000000
χ6288-8-8-40000-88-44400004-40000000000000000000000000000000000000000000000
χ638-88-8-480-80004-44000000-4040000000000000000000000000000000000000000000
χ648-88-8-4-8080004-4400000040-40000000000000000000000000000000000000000000
χ658-8-88-4080-80044-40000000-404000000000000000000000000000000000000000000
χ668-8-88-40-8080044-4000000040-4000000000000000000000000000000000000000000

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