Finite Group Databasebeta

← Group #10692782

Character table — Group #10692782

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order12223444444666244466888812121212121212128812122424242424242424888844881212121224242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1
χ811111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ911111-1-1-1-1-1-1111-1111-1-1ii−i−i-1-111-1-1-1-1i−i11iiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−i1-11-1i−i11-1-1i−i
χ1011111-1-1-1-1-1-1111-1111-1-1ii−i−i-1-111-1-1-1-1i−i11iiii−i−i−i−iii−i−i-11−ii-1-111−i−iii1-11-1i−i-1-111−ii
χ1111111-1-1-1-1-1-1111-1111-1-1ii−i−i-1-111-1-1-1-1i−i11iiii−i−i−i−i−i−iii1-1i−i11-1-1ii−i−i-11-11−ii-1-111−ii
χ1211111-1-1-1-1-1-1111-1111-1-1ii−i−i-1-111-1-1-1-1i−i11iiii−i−i−i−i−i−iii-11−ii-1-111−i−iii-11-11−ii11-1-1i−i
χ1311111-1-1-1-1-1-1111-1111-1-1−i−iii-1-111-1-1-1-1−ii11−i−i−i−iiiiiii−i−i1-1−ii11-1-1−i−iii-11-11i−i-1-111i−i
χ1411111-1-1-1-1-1-1111-1111-1-1−i−iii-1-111-1-1-1-1−ii11−i−i−i−iiiiiii−i−i-11i−i-1-111ii−i−i-11-11i−i11-1-1−ii
χ1511111-1-1-1-1-1-1111-1111-1-1−i−iii-1-111-1-1-1-1−ii11−i−i−i−iiiii−i−iii1-1−ii11-1-1−i−iii1-11-1−ii11-1-1−ii
χ1611111-1-1-1-1-1-1111-1111-1-1−i−iii-1-111-1-1-1-1−ii11−i−i−i−iiiii−i−iii-11i−i-1-111ii−i−i1-11-1−ii-1-111i−i
χ1722222222-2-22222-2-2-22-2-2000022-2-22-2-22002-200000000000000000000000022-2-200000000
χ1822222222-2-22222-2-2-22-2-2000022-2-22-2-22002-2000000000000000000000000-2-22200000000
χ19222222-2-2222222-2-22-2-2-200002222-222-200-2-20000000022220000000000000000-2-2000000
χ20222222-2-2222222-2-22-2-2-200002222-222-200-2-200000000-2-2-2-2000000000000000022000000
χ21222222-2-2-2-2222222-2-2222i2i−2i−2i22-2-2-2-2-2-2−2i2i-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ22222222-2-2-2-2222222-2-222−2i−2i2i2i22-2-2-2-2-2-22i−2i-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2322222-22222-2222-22-2-2-2-22222-2-2-2-22222-2-2-2222-2-2-2-2220000000000000000000000000000
χ2422222-22222-2222-22-2-2-2-2-2-2-2-2-2-2-2-2222222-22-2-22222-2-20000000000000000000000000000
χ2522222-222-2-2-22222-22-2220000-2-2222-2-2200-2-2000000002i2i−2i−2i0000000000000000−2i2i000000
χ2622222-222-2-2-22222-22-2220000-2-2222-2-2200-2-200000000−2i−2i2i2i00000000000000002i−2i000000
χ2722222-2-2-222-22222-2-22220000-2-2-2-2-222-2002-20000000000000000000000002-2-2200000000
χ2822222-2-2-222-22222-2-22220000-2-2-2-2-222-2002-2000000000000000000000000-222-200000000
χ292222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ312222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-11111000000000000
χ322222-1222222-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-1000000000000
χ332222-12-2-2-2-22-1-1-122-2-2-1-12i2i−2i−2i-1-1111111−2i2i1-1−i−iii−i−iii00000000−i3i3−i3i33−33−3000000000000
χ342222-12-2-2-2-22-1-1-122-2-2-1-12i2i−2i−2i-1-1111111−2i2i1-1−i−iii−i−iii00000000i3−i3i3−i3−33−33000000000000
χ352222-12-2-2-2-22-1-1-122-2-2-1-1−2i−2i2i2i-1-11111112i−2i1-1ii−i−iii−i−i00000000−i3i3−i3i3−33−33000000000000
χ362222-12-2-2-2-22-1-1-122-2-2-1-1−2i−2i2i2i-1-11111112i−2i1-1ii−i−iii−i−i00000000i3−i3i3−i33−33−3000000000000
χ372222-1-22222-2-1-1-1-22-2-21122221111-1-1-1-1-2-21-1-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-1-22222-2-1-1-1-22-2-21122221111-1-1-1-1-2-21-1-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-1-22222-2-1-1-1-22-2-211-2-2-2-21111-1-1-1-1221-111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-1-22222-2-1-1-1-22-2-211-2-2-2-21111-1-1-1-1221-111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-2-2-1-1-1-2222112i2i−2i−2i11-1-111112i−2i-1-1−i−i−i−iiiii00002-22i−2i-1-111−i−iii000000000000
χ422222-1-2-2-2-2-2-2-1-1-1-2222112i2i−2i−2i11-1-111112i−2i-1-1−i−i−i−iiiii0000-22−2i2i11-1-1ii−i−i000000000000
χ432222-1-2-2-2-2-2-2-1-1-1-222211−2i−2i2i2i11-1-11111−2i2i-1-1iiii−i−i−i−i00002-2−2i2i-1-111ii−i−i000000000000
χ442222-1-2-2-2-2-2-2-1-1-1-222211−2i−2i2i2i11-1-11111−2i2i-1-1iiii−i−i−i−i0000-222i−2i11-1-1−i−iii000000000000
χ454444-2444-4-44-2-2-2-4-4-44220000-2-222-222-200-22000000000000000000000000000000000000
χ464444-24-4-4444-2-2-2-4-44-4220000-2-2-2-22-2-220022000000000000000000000000000000000000
χ474444-2-444-4-4-4-2-2-24-44-4-2-2000022-2-2-222-20022000000000000000000000000000000000000
χ484444-2-4-4-444-4-2-2-24-4-44-2-2000022222-2-2200-22000000000000000000000000000000000000
χ4944-4-440004-404-4-40000000000000004-4000000000000000000000000000000000002-22-200
χ5044-4-440004-404-4-40000000000000004-400000000000000000000000000000000000-22-2200
χ5144-4-44000-4404-4-4000000000000000-44000000000000000000000000000000000002-2-2200
χ5244-4-44000-4404-4-4000000000000000-4400000000000000000000000000000000000-222-200
χ534-44-4440000-4-44-400000000004-400000000000000000022−2222−22000000000000000000000000
χ544-44-4440000-4-44-400000000004-4000000000000000000−2222−2222000000000000000000000000
χ554-44-44-400004-44-40000000000-44000000000000000000−2i22i22i2−2i2000000000000000000000000
χ564-44-44-400004-44-40000000000-440000000000000000002i2−2i2−2i22i2000000000000000000000000
χ574-4-44404-4000-4-44000000−2i22i2−2i22i20000400-40000−2i22i20000−2i22i20000000000000000000000000000
χ584-4-44404-4000-4-440000002i2−2i22i2−2i20000400-400002i2−2i200002i2−2i20000000000000000000000000000
χ594-4-4440-44000-4-4400000022−22−22220000-4004000022−220000−22220000000000000000000000000000
χ604-4-4440-44000-4-44000000−222222−220000-40040000−2222000022−220000000000000000000000000000
χ614-4-44-204-400022-20000−2i32i3−2i22i2−2i22i200−2i32i3-20020000i2−i26−66−6i2−i20000000000000000000000000000
χ624-4-44-204-400022-20000−2i32i32i2−2i22i2−2i200−2i32i3-20020000−i2i2−66−66−i2i20000000000000000000000000000
χ634-4-44-204-400022-200002i3−2i3−2i22i2−2i22i2002i3−2i3-20020000i2−i2−66−66i2−i20000000000000000000000000000
χ644-4-44-204-400022-200002i3−2i32i2−2i22i2−2i2002i3−2i3-20020000−i2i26−66−6−i2i20000000000000000000000000000
χ654-4-44-20-4400022-20000−2i32i322−22−2222002i3−2i3200-20000−22−i6i6i6−i62−20000000000000000000000000000
χ664-4-44-20-4400022-20000−2i32i3−222222−22002i3−2i3200-200002−2i6−i6−i6i6−220000000000000000000000000000
χ674-4-44-20-4400022-200002i3−2i322−22−222200−2i32i3200-20000−22i6−i6−i6i62−20000000000000000000000000000
χ684-4-44-20-4400022-200002i3−2i3−222222−2200−2i32i3200-200002−2−i6i6i6−i6−220000000000000000000000000000
χ6988-8-8-40008-80-444000000000000000-4400000000000000000000000000000000000000000
χ7088-8-8-4000-880-4440000000000000004-400000000000000000000000000000000000000000
χ718-88-8-480000-84-440000000000-440000000000000000000000000000000000000000000000
χ728-88-8-4-8000084-4400000000004-40000000000000000000000000000000000000000000000

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