Finite Group Databasebeta

← Group #10692308

Character table — Group #10692308

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212161616161616161616161616242424242424242424244848
order122234444446662224444466121212121212121244661212121212121212888844881212121224242424888888888888
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
χ5111111111111111-1-11-1-1111111111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111-1-11-1-1111111111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ7111111111111111-1-11-1-1111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1
χ8111111111111111-1-11-1-1111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ9111111-11-1-1-11111111-1-1-1-111111-1-1-1-111-111-111-1-1-1-1-1ii−i−i1-11-111-1-111-1-1i−iii−i−iii−i−ii−i
χ10111111-11-1-1-11111111-1-1-1-111111-1-1-1-111-111-111-1-1-1-1-1ii−i−i-11-11-1-111-1-111i−iii−i−i−i−iii−ii
χ11111111-11-1-1-11111111-1-1-1-111111-1-1-1-111-111-111-1-1-1-1-1−i−iii1-11-111-1-111-1-1−ii−i−iii−i−iii−ii
χ12111111-11-1-1-11111111-1-1-1-111111-1-1-1-111-111-111-1-1-1-1-1−i−iii-11-11-1-111-1-111−ii−i−iiiii−i−ii−i
χ13111111-11-1-1-11111-1-1111-1-111111-1-1-1-11-11-1-1-1-1-111-111ii−i−i1-1-1111-1-1-1-111i−i−i−iii−i−iiii−i
χ14111111-11-1-1-11111-1-1111-1-111111-1-1-1-11-11-1-1-1-1-111-111ii−i−i-111-1-1-11111-1-1i−i−i−iiiii−i−i−ii
χ15111111-11-1-1-11111-1-1111-1-111111-1-1-1-11-11-1-1-1-1-111-111−i−iii1-1-1111-1-1-1-111−iiii−i−iii−i−i−ii
χ16111111-11-1-1-11111-1-1111-1-111111-1-1-1-11-11-1-1-1-1-111-111−i−iii-111-1-1-11111-1-1−iiii−i−i−i−iiii−i
χ1722222222-22-2222-222-2-2-2-22-2-22-2-2-2-2222-22222-2-2-2-2-2220000000000000000000000000000
χ1822222222-22-2222-2-2-2-222-22-2-22-2-2-2-22222-2-2-222222-2-2-20000000000000000000000000000
χ19222222-222-22222-222-2222-2-2-22-2-222-2-22-2-222-2-2-2222-2-20000000000000000000000000000
χ20222222-222-22222-2-2-2-2-2-22-2-2-22-2-222-2-2222-2-2-222-2-22220000000000000000000000000000
χ2122222-22-2222222-200200-2-2-2-2-2222222-20000-20000-2002222000000000000-2-20000000000
χ2222222-22-2222222-200200-2-2-2-2-2222222-20000-20000-200-2-2-2-2000000000000220000000000
χ2322222-22-2-22-2222200-2002-222-2-2-2-2-222-20000-200002000000000000000000002i−2i2i−2i000000
χ2422222-22-2-22-2222200-2002-222-2-2-2-2-222-20000-20000200000000000000000000−2i2i−2i2i000000
χ2522222-2-2-22-22222200-200-2222-2-2-222-2-2-2000020000-2000000000000000000002-2-22000000
χ2622222-2-2-22-22222200-200-2222-2-2-222-2-2-2000020000-200000000000000000000-222-2000000
χ2722222-2-2-2-2-2-2222-20020022-2-2-222-2-2-2-2-20000200002002i2i−2i−2i000000000000−2i2i0000000000
χ2822222-2-2-2-2-2-2222-20020022-2-2-222-2-2-2-2-2000020000200−2i−2i2i2i0000000000002i−2i0000000000
χ292222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ312222-1222222-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-1-1-2-211-11111-111000022-2-2-1-1-1-11111000000000000
χ322222-1222222-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-1-1-2-211-11111-1110000-2-2221111-1-1-1-1000000000000
χ332222-1222-22-2-1-1-1-222-2-2-2-2211-11111-1-1-1-22-1-1-111111-1-100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ342222-1222-22-2-1-1-1-222-2-2-2-2211-11111-1-1-1-22-1-1-111111-1-100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ352222-1222-22-2-1-1-1-2-2-2-222-2211-11111-1-1-12-211-1-1-1-1-111100000000−i3i3−i3i3i3−i3i3−i3000000000000
χ362222-1222-22-2-1-1-1-2-2-2-222-2211-11111-1-1-12-211-1-1-1-1-111100000000i3−i3i3−i3−i3i3−i3i3000000000000
χ372222-12-222-22-1-1-1-222-2222-211-111-1-111-1-2-2-1-1111-1-1-11100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ382222-12-222-22-1-1-1-222-2222-211-111-1-111-1-2-2-1-1111-1-1-11100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ392222-12-222-22-1-1-1-2-2-2-2-2-22-211-111-1-111-122111-1-111-1-1-100000000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-12-222-22-1-1-1-2-2-2-2-2-22-211-111-1-111-122111-1-111-1-1-100000000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-12-22-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-11111-12-2-1-11-1-11111100002-22-2-1-111-1-111000000000000
χ422222-12-22-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-11111-12-2-1-11-1-1111110000-22-2211-1-111-1-1000000000000
χ432222-12-22-2-2-2-1-1-12-2-2222-2-2-1-1-1-1-11111-1-2211111-1-11-1-100002-2-22-1-11111-1-1000000000000
χ442222-12-22-2-2-2-1-1-12-2-2222-2-2-1-1-1-1-11111-1-2211111-1-11-1-10000-222-211-1-1-1-111000000000000
χ454444-2-44-4444-2-2-2-400400-4-4222-2-2-2-2-2-220000200002000000000000000000000000000000
χ464444-2-44-4-44-4-2-2-2400-4004-4-2-222222-2-22000020000-2000000000000000000000000000000
χ474444-2-4-4-44-44-2-2-2400-400-44-2-2222-2-22220000-200002000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-40040044222-2-2222220000-20000-2000000000000000000000000000000
χ4944-4-4400040-44-4-400000000000004-400000000000000000000000000000000000002-22-200
χ5044-4-4400040-44-4-400000000000004-40000000000000000000000000000000000000-22-2200
χ5144-4-44000-4044-4-40000000000000-4400000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-44000-4044-4-40000000000000-440000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-4440-4000-44-404-400000004000000-4004-4000000000000000000000000000000000000
χ544-44-4440-4000-44-40-4400000004000000-400-44000000000000000000000000000000000000
χ554-44-44-404000-44-400004i−4i0000-4000000400000004i−4i0000000000000000000000000000000
χ564-44-44-404000-44-40000−4i4i0000-400000040000000−4i4i0000000000000000000000000000000
χ574-44-4-240-40002-2204-400000−2i32i3-2−2i32i30000200-220−2i32i3000000000000000000000000000000000
χ584-44-4-240-40002-2204-4000002i3−2i3-22i3−2i30000200-2202i3−2i3000000000000000000000000000000000
χ594-44-4-240-40002-220-4400000−2i32i3-2−2i32i300002002-202i3−2i3000000000000000000000000000000000
χ604-44-4-240-40002-220-44000002i3−2i3-22i3−2i300002002-20−2i32i3000000000000000000000000000000000
χ614-44-4-2-4040002-2200004i−4i00−2i32i322i3−2i30000-20000000−2i2i023−230000000000000000000000000000
χ624-44-4-2-4040002-2200004i−4i002i3−2i32−2i32i30000-20000000−2i2i0−23230000000000000000000000000000
χ634-44-4-2-4040002-220000−4i4i00−2i32i322i3−2i30000-200000002i−2i0−23230000000000000000000000000000
χ644-44-4-2-4040002-220000−4i4i002i3−2i32−2i32i30000-200000002i−2i023−230000000000000000000000000000
χ654-4-4440400-40-4-440000000000000004-40000000000000−2i22i2−2i22i2000000000000000000000000
χ664-4-4440400-40-4-440000000000000004-400000000000002i2−2i22i2−2i2000000000000000000000000
χ674-4-4440-40040-4-44000000000000000-44000000000000022−22−2222000000000000000000000000
χ684-4-4440-40040-4-44000000000000000-440000000000000−222222−22000000000000000000000000
χ6988-8-8-400080-8-4440000000000000-440000000000000000000000000000000000000000000
χ7088-8-8-4000-808-44400000000000004-40000000000000000000000000000000000000000000
χ718-8-88-40800-8044-4000000000000000-4400000000000000000000000000000000000000000
χ728-8-88-40-8008044-40000000000000004-400000000000000000000000000000000000000000

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