Finite Group Databasebeta

← Group #10692770

Character table — Group #10692770

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order1222344444466624441212121212122244612121288888888668888121224242424242424248888888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1
χ911111-1-1-1-1-1-1111-1111-1-1-1-1-1-11-11-1-1111ii−i−iii−i−i1-1i−ii−i1-1ii−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−i1-1−ii−ii1-1−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−iii1-1i−ii−i1-1ii−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−iii1-1−ii−ii1-1−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−iii-11i−i−ii-11ii−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-11−iii−i-11−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−i-11i−i−ii-11ii−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-11−iii−i-11−i−iiiii−i−i−iii−i11-1-1-11
χ17222222222-2-2222-2-2-2222-2-22222-2-2-2-2-2200000000220000-2-2000000000000000000
χ18222222222-2-2222-2-2-2222-2-222-2-222-2-2-2200000000-2-2000022000000000000000000
χ19222222-22-222222-2-22-22-2222-20000-22-2-200002222000000000000000000-2-2000000
χ20222222-22-222222-2-22-22-2222-20000-22-2-20000-2-2-2-200000000000000000022000000
χ21222222-22-2-2-222222-2-22-2-2-22-200002-22-22i2i−2i−2i00000000000000000000−2i2i00000000
χ22222222-22-2-2-222222-2-22-2-2-22-200002-22-2−2i−2i2i2i000000000000000000002i−2i00000000
χ2322222-22-2222222-22-2-2-2222-220000-2-22-2222200000000000000000000-2-200000000
χ2422222-22-2222222-22-2-2-2222-220000-2-22-2-2-2-2-2000000000000000000002200000000
χ2522222-22-22-2-22222-22-2-22-2-2-22000022-2-200002i2i−2i−2i000000000000000000−2i2i000000
χ2622222-22-22-2-22222-22-2-22-2-2-22000022-2-20000−2i−2i2i2i0000000000000000002i−2i000000
χ2722222-2-2-2-2222222-2-22-2-222-2-22-2-222-2-22000000002-20000-22000000000000000000
χ2822222-2-2-2-2222222-2-22-2-222-2-2-222-22-2-2200000000-2200002-2000000000000000000
χ292222-1222222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-1-12222-1-1-1-1-1-1-1-1-1-10000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-12222-1-1-1-100000000-1-1-2-2-2-2-1-1111111110000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000000001122-2-211-1-1-1-111110000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000011-2-222111111-1-1-1-10000000000
χ332222-12222-2-2-1-1-1-2-2-22-1-111-1-122-2-2111-100000000-1-1000011−i3i3−i3i3−i3i3−i3i30000000000
χ342222-12222-2-2-1-1-1-2-2-22-1-111-1-122-2-2111-100000000-1-1000011i3−i3i3−i3i3−i3i3−i30000000000
χ352222-12222-2-2-1-1-1-2-2-22-1-111-1-1-2-222111-100000000110000-1-1−i3i3−i3i3i3−i3i3−i30000000000
χ362222-12222-2-2-1-1-1-2-2-22-1-111-1-1-2-222111-100000000110000-1-1i3−i3i3−i3−i3i3−i3i30000000000
χ372222-1-2-2-2-222-1-1-12-2-2211-1-1112-2-22-111-100000000-1100001-13−3−333−3−330000000000
χ382222-1-2-2-2-222-1-1-12-2-2211-1-1112-2-22-111-100000000-1100001-1−333−3−333−30000000000
χ392222-1-2-2-2-222-1-1-12-2-2211-1-111-222-2-111-1000000001-10000-113−3−33−333−30000000000
χ402222-1-2-2-2-222-1-1-12-2-2211-1-111-222-2-111-1000000001-10000-11−333−33−3−330000000000
χ412222-1-2-2-2-2-2-2-1-1-1-22221111112-22-21-1-1-100000000-112i−2i2i−2i-11−i−iii−i−iii0000000000
χ422222-1-2-2-2-2-2-2-1-1-1-22221111112-22-21-1-1-100000000-11−2i2i−2i2i-11ii−i−iii−i−i0000000000
χ432222-1-2-2-2-2-2-2-1-1-1-2222111111-22-221-1-1-1000000001-12i−2i−2i2i1-1−i−iiiii−i−i0000000000
χ442222-1-2-2-2-2-2-2-1-1-1-2222111111-22-221-1-1-1000000001-1−2i2i2i−2i1-1ii−i−i−i−iii0000000000
χ454444-24-44-444-2-2-2-4-44-4-22-2-2-2200002-2220000000000000000000000000000000000
χ464444-24-44-4-4-4-2-2-244-4-4-2222-220000-22-220000000000000000000000000000000000
χ474444-2-44-4444-2-2-2-44-4-42-2-2-22-2000022-220000000000000000000000000000000000
χ484444-2-44-44-4-4-2-2-24-44-42-2222-20000-2-2220000000000000000000000000000000000
χ4944-4-4440-40004-4-400004000-4000000000000022−2222−2200000000000000000000000000
χ5044-4-4440-40004-4-400004000-40000000000000−2222−222200000000000000000000000000
χ5144-4-44-4040004-4-40000-400040000000000000−2i22i22i2−2i200000000000000000000000000
χ5244-4-44-4040004-4-40000-4000400000000000002i2−2i2−2i22i200000000000000000000000000
χ534-44-4400004-4-4-440000004-4000000000000000000000000000000000000002i−2i2i−2i00
χ544-44-4400004-4-4-440000004-400000000000000000000000000000000000000−2i2i−2i2i00
χ554-44-440000-44-4-44000000-44000000000000000000000000000000000000002i−2i−2i2i00
χ564-44-440000-44-4-44000000-4400000000000000000000000000000000000000−2i2i2i−2i00
χ574-4-444040-400-44-4000004000-400000000−2i22i2−2i22i2000000000000000000000000000000
χ584-4-444040-400-44-4000004000-4000000002i2−2i22i2−2i2000000000000000000000000000000
χ594-4-4440-40400-44-400000-400040000000022−22−2222000000000000000000000000000000
χ604-4-4440-40400-44-400000-4000400000000−222222−22000000000000000000000000000000
χ6188-8-8-480-8000-4440000-400040000000000000000000000000000000000000000000
χ6288-8-8-4-808000-44400004000-40000000000000000000000000000000000000000000
χ638-88-8-400008-844-4000000-4400000000000000000000000000000000000000000000
χ648-88-8-40000-8844-40000004-400000000000000000000000000000000000000000000
χ658-8-88-4080-8004-4400000-40004000000000000000000000000000000000000000000
χ668-8-88-40-808004-44000004000-4000000000000000000000000000000000000000000

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