Finite Group Databasebeta

← Group #10693271

Character table — Group #10693271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12223444466624444661212121212121212444444441212121212121212121288888812121212242424248888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111-1-111-1-1111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1
χ911111-1-1-1-11111-111-111-1-1-1-1-1-111111-1-1-11-1-111111-1-1-1-1ii−i−i1-11-11-111-1-1i−iii−i−ii−ii−i
χ1011111-1-1-1-11111-111-111-1-1-1-1-1-111111-1-1-11-1-111111-1-1-1-1−i−iii1-11-11-111-1-1−ii−i−iii−ii−ii
χ1111111-1-1-1-11111-111-111-1-1-1-1-1-11111-11-1-1-11-111111-1-1-1-1ii−i−i-11-11-11-1-111i−i−i−iiii−i−ii
χ1211111-1-1-1-11111-111-111-1-1-1-1-1-11111-11-1-1-11-111111-1-1-1-1−i−iii-11-11-11-1-111−iiii−i−i−iii−i
χ1311111-1-1-1-11111-111-111-1-1-1-1-1-111-1-11-1111-1-1-1-1-1-111111ii−i−i-111-11-1-1-111i−iii−i−i−ii−ii
χ1411111-1-1-1-11111-111-111-1-1-1-1-1-111-1-11-1111-1-1-1-1-1-111111−i−iii-111-11-1-1-111−ii−i−iiii−ii−i
χ1511111-1-1-1-11111-111-111-1-1-1-1-1-111-1-1-1111-11-1-1-1-1-111111ii−i−i1-1-11-1111-1-1i−i−i−iii−iii−i
χ1611111-1-1-1-11111-111-111-1-1-1-1-1-111-1-1-1111-11-1-1-1-1-111111−i−iii1-1-11-1111-1-1−iiii−i−ii−i−ii
χ17222222222222-2-22-2-2-2-22222-2-2-2-200000000-200002000022220000000000-2-200000000
χ18222222222222-2-22-2-2-2-22222-2-2-2-200000000-2000020000-2-2-2-200000000002200000000
χ192222222-2-222222-2-2-22222-2-222-2-200000000-20000-2000000000000000000002i−2i2i−2i0000
χ202222222-2-222222-2-2-22222-2-222-2-200000000-20000-200000000000000000000−2i2i−2i2i0000
χ212222222-2-2222-2-2-222-2-222-2-2-2-222002200-2-220000-2000000000022-2-200000000000000
χ222222222-2-2222-2-2-222-2-222-2-2-2-22200-2-2002220000-20000000000-2-22200000000000000
χ2322222-2-2222222-2-2-2222-2-222-2-2-2-20000000020000-2000000000000000000002-2-220000
χ2422222-2-2222222-2-2-2222-2-222-2-2-2-20000000020000-200000000000000000000-222-20000
χ2522222-2-222222-22-22-2-2-2-2-2222222002-200-22-20000-200000000002-2-2200000000000000
χ2622222-2-222222-22-22-2-2-2-2-222222200-22002-2-20000-20000000000-222-200000000000000
χ2722222-2-2-2-2222-222-22-2-2-2-2-2-222-2-20000000020000200002i2i−2i−2i0000000000−2i2i00000000
χ2822222-2-2-2-2222-222-22-2-2-2-2-2-222-2-2000000002000020000−2i−2i2i2i00000000002i−2i00000000
χ292222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-222-2-222-11111-111110000-2-2-1-1-1-111110000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-111110000221111-1-1-1-10000000000
χ332222-122-2-2-1-1-1-2-2-22211-1-11111-1-1002200-2-2-1−i3−i3i3i31−i3−i3i3i3000000-1-111−i3i3−i3i30000000000
χ342222-122-2-2-1-1-1-2-2-22211-1-11111-1-1002200-2-2-1i3i3−i3−i31i3i3−i3−i3000000-1-111i3−i3i3−i30000000000
χ352222-122-2-2-1-1-1-2-2-22211-1-11111-1-100-2-20022-1−i3−i3i3i31−i3−i3i3i300000011-1-1i3−i3i3−i30000000000
χ362222-122-2-2-1-1-1-2-2-22211-1-11111-1-100-2-20022-1i3i3−i3−i31i3i3−i3−i300000011-1-1−i3i3−i3i30000000000
χ372222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-1002-200-221−i3−i3i3i31i3i3−i3−i3000000-111-1−i3i3i3−i30000000000
χ382222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-1002-200-221i3i3−i3−i31−i3−i3i3i3000000-111-1i3−i3−i3i30000000000
χ392222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-100-22002-21−i3−i3i3i31i3i3−i3−i30000001-1-11i3−i3−i3i30000000000
χ402222-1-2-222-1-1-1-22-22-21111-1-1-1-1-1-100-22002-21i3i3−i3−i31−i3−i3i3i30000001-1-11−i3i3i3−i30000000000
χ412222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-1222-2-2-22-21-1-1-1-1-1111100002-2-11-11-1-1110000000000
χ422222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-122-22-2-2-221-1-1-1-1-111110000-221-11-111-1-10000000000
χ432222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-1-2-22-2222-211111-1-1-1-1-10000-22-11-1111-1-10000000000
χ442222-1-2-2-2-2-1-1-12-222-2-1-1111111-1-1-2-2-2222-2211111-1-1-1-1-100002-21-11-1-1-1110000000000
χ454444-24444-2-2-2-4-44-4-422-2-2-2-222220000000020000-20000000000000000000000000000
χ464444-244-4-4-2-2-244-4-4-4-2-2-2-222-2-222000000002000020000000000000000000000000000
χ474444-2-4-444-2-2-24-4-4-44-2-222-2-2222200000000-2000020000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-444-44222222-2-22200000000-20000-20000000000000000000000000000
χ4944-4-444-4004-4-400000004-400000000000000000000000022−2222−2200000000000000000000
χ5044-4-444-4004-4-400000004-4000000000000000000000000−2222−222200000000000000000000
χ5144-4-44-44004-4-40000000-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-4-44-44004-4-40000000-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ534-4-444004i−4i-4-440000000004i−4i00002i−2i002-20002i−2i2i−2i02-22-2000000000000000000000000
χ544-4-444004i−4i-4-440000000004i−4i0000−2i2i00-22000−2i2i−2i2i0-22-22000000000000000000000000
χ554-4-44400−4i4i-4-44000000000−4i4i00002i−2i00-220002i−2i2i−2i0-22-22000000000000000000000000
χ564-4-44400−4i4i-4-44000000000−4i4i0000−2i2i002-2000−2i2i−2i2i02-22-2000000000000000000000000
χ574-4-44-2004i−4i22-2000000000−2i2i23−23−2i32i32i−2i002-20002ζ14−2ζ142ζ22−2ζ220−1−i31+i3−1+i31−i3000000000000000000000000
χ584-4-44-2004i−4i22-2000000000−2i2i23−23−2i32i3−2i2i00-22000−2ζ142ζ14−2ζ222ζ2201+i3−1−i31−i3−1+i3000000000000000000000000
χ594-4-44-2004i−4i22-2000000000−2i2i−23232i3−2i32i−2i002-20002ζ22−2ζ222ζ14−2ζ140−1+i31−i3−1−i31+i3000000000000000000000000
χ604-4-44-2004i−4i22-2000000000−2i2i−23232i3−2i3−2i2i00-22000−2ζ222ζ22−2ζ142ζ1401−i3−1+i31+i3−1−i3000000000000000000000000
χ614-4-44-200−4i4i22-20000000002i−2i23−232i3−2i32i−2i00-220002ζ22−2ζ222ζ14−2ζ1401−i3−1+i31+i3−1−i3000000000000000000000000
χ624-4-44-200−4i4i22-20000000002i−2i23−232i3−2i3−2i2i002-2000−2ζ222ζ22−2ζ142ζ140−1+i31−i3−1−i31+i3000000000000000000000000
χ634-4-44-200−4i4i22-20000000002i−2i−2323−2i32i32i−2i00-220002ζ14−2ζ142ζ22−2ζ2201+i3−1−i31−i3−1+i3000000000000000000000000
χ644-4-44-200−4i4i22-20000000002i−2i−2323−2i32i3−2i2i002-2000−2ζ142ζ14−2ζ222ζ220−1−i31+i3−1+i31−i3000000000000000000000000
χ6588-8-8-48-800-4440000000-44000000000000000000000000000000000000000000000000
χ6688-8-8-4-8800-44400000004-4000000000000000000000000000000000000000000000000
χ678-88-880000-88-8000000000000000000000000000000000000000000000000000000000
χ688-88-8-400004-4400000−4i34i300000000000000000000000000000000000000000000000000
χ698-88-8-400004-44000004i3−4i300000000000000000000000000000000000000000000000000

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