Finite Group Databasebeta

← Group #10693272

Character table — Group #10693272

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12223444466624444661212121212121212444488881212121212121212121288888824242424242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ911111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1ii−i−i111111-1-1-1-1ii−i−ii−iii−i−iii−i−i1-11-1i−ii−i1-1
χ1011111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1ii−i−i111111-1-1-1-1−i−iiii−iii−i−iii−i−i-11-11−ii−ii-11
χ1111111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1−i−iii111111-1-1-1-1ii−i−i−ii−i−iii−i−iii-11-11i−ii−i-11
χ1211111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-1−i−iii111111-1-1-1-1−i−iii−ii−i−iii−i−iii1-11-1−ii−ii1-1
χ1311111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111ii−i−i11-1-1-1-11111ii−i−i−iiii−i−i−i−iii1-11-1i−i−ii-11
χ1411111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111ii−i−i11-1-1-1-11111−i−iii−iiii−i−i−i−iii-11-11−iii−i1-1
χ1511111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111−i−iii11-1-1-1-11111ii−i−ii−i−i−iiiii−i−i-11-11i−i−ii1-1
χ1611111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111−i−iii11-1-1-1-11111−i−iiii−i−i−iiiii−i−i1-11-1−iii−i-11
χ17222222222222-2-22-2-2-2-222-2-222-2-2000000002-200000000222200000000000000-2-20000
χ18222222222222-2-22-2-2-2-222-2-222-2-2000000002-200000000-2-2-2-200000000000000220000
χ19222222-2-2222222-2-2-2222222-2-2-2-200002i−2i2i−2i-2-2000000000000002i−2i2i−2i00000000000000
χ20222222-2-2222222-2-2-2222222-2-2-2-20000−2i2i−2i2i-2-200000000000000−2i2i−2i2i00000000000000
χ21222222-2-22222-2-2-222-2-222-2-2-2-22200000000-22000000000000000000000022-2-2000000
χ22222222-2-22222-2-2-222-2-222-2-2-2-22200000000-220000000000000000000000-2-222000000
χ2322222-222-22222-2-22-222-2-2-2-2222200002-2-22-2-2000000000000002-2-2200000000000000
χ2422222-222-22222-2-22-222-2-2-2-222220000-222-2-2-200000000000000-222-200000000000000
χ2522222-222-2222-22-2-22-2-2-2-22222-2-200000000-2200000000000000000000002-2-22000000
χ2622222-222-2222-22-2-22-2-2-2-22222-2-200000000-220000000000000000000000-222-2000000
χ2722222-2-2-2-2222-2222-2-2-2-2-222-2-222000000002-2000000002i2i−2i−2i00000000000000−2i2i0000
χ2822222-2-2-2-2222-2222-2-2-2-2-222-2-222000000002-200000000−2i−2i2i2i000000000000002i−2i0000
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
χ302222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ332222-12-2-22-1-1-122-2-2-2-1-1-1-1-1-1111100002i−2i2i−2i11−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−30000000000
χ342222-12-2-22-1-1-122-2-2-2-1-1-1-1-1-1111100002i−2i2i−2i11i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−330000000000
χ352222-12-2-22-1-1-122-2-2-2-1-1-1-1-1-111110000−2i2i−2i2i11−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−330000000000
χ362222-12-2-22-1-1-122-2-2-2-1-1-1-1-1-111110000−2i2i−2i2i11i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−30000000000
χ372222-1-222-2-1-1-12-2-22-2-1-11111-1-1-1-100002-2-2211−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i30000000000
χ382222-1-222-2-1-1-12-2-22-2-1-11111-1-1-1-100002-2-2211i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i30000000000
χ392222-1-222-2-1-1-12-2-22-2-1-11111-1-1-1-10000-222-211−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i30000000000
χ402222-1-222-2-1-1-12-2-22-2-1-11111-1-1-1-10000-222-211i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i30000000000
χ412222-1-2-2-2-2-1-1-12-22-22-1-11111111122-2-22i2i−2i−2i-1-1-1-1-1-1111100002i−2i−i−iii−i−iii0000000000
χ422222-1-2-2-2-2-1-1-12-22-22-1-11111111122-2-2−2i−2i2i2i-1-1-1-1-1-111110000−2i2iii−i−iii−i−i0000000000
χ432222-1-2-2-2-2-1-1-12-22-22-1-111111111-2-2222i2i−2i−2i-1-11111-1-1-1-10000−2i2i−i−iiiii−i−i0000000000
χ442222-1-2-2-2-2-1-1-12-22-22-1-111111111-2-222−2i−2i2i2i-1-11111-1-1-1-100002i−2iii−i−i−i−iii0000000000
χ454444-24444-2-2-2-4-44-4-422-2-222-2-22200000000-2200000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-44422-2-22222-2-2000000002-200000000000000000000000000000000
χ474444-2-444-4-2-2-2-44-4-442222-2-2-2-222000000002-200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-4444-42222-2-222-2-200000000-2200000000000000000000000000000000
χ494-44-44400-44-4-400000004-400000000000000000000000022−2222−2200000000000000000000
χ504-44-44400-44-4-400000004-4000000000000000000000000−2222−222200000000000000000000
χ514-44-44-40044-4-40000000-44000000000000000000000000−2i22i22i2−2i200000000000000000000
χ524-44-44-40044-4-40000000-440000000000000000000000002i2−2i2−2i22i200000000000000000000
χ534-4-44404i−4i0-44-4000000000004i−4i002i−2i2-20000002i−2i2i−2i2-22-2000000000000000000000000
χ544-4-44404i−4i0-44-4000000000004i−4i00−2i2i-22000000−2i2i−2i2i-22-22000000000000000000000000
χ554-4-4440−4i4i0-44-400000000000−4i4i002i−2i-220000002i−2i2i−2i-22-22000000000000000000000000
χ564-4-4440−4i4i0-44-400000000000−4i4i00−2i2i2-2000000−2i2i−2i2i2-22-2000000000000000000000000
χ574-4-44-204i−4i02-2200000−2i32i30000−2i2i23−232i−2i2-20000002ζ14−2ζ142ζ22−2ζ22−1−i31+i3−1+i31−i3000000000000000000000000
χ584-4-44-204i−4i02-2200000−2i32i30000−2i2i23−23−2i2i-22000000−2ζ142ζ14−2ζ222ζ221+i3−1−i31−i3−1+i3000000000000000000000000
χ594-4-44-204i−4i02-22000002i3−2i30000−2i2i−23232i−2i2-20000002ζ22−2ζ222ζ14−2ζ14−1+i31−i3−1−i31+i3000000000000000000000000
χ604-4-44-204i−4i02-22000002i3−2i30000−2i2i−2323−2i2i-22000000−2ζ222ζ22−2ζ142ζ141−i3−1+i31+i3−1−i3000000000000000000000000
χ614-4-44-20−4i4i02-2200000−2i32i300002i−2i−23232i−2i-220000002ζ14−2ζ142ζ22−2ζ221+i3−1−i31−i3−1+i3000000000000000000000000
χ624-4-44-20−4i4i02-2200000−2i32i300002i−2i−2323−2i2i2-2000000−2ζ142ζ14−2ζ222ζ22−1−i31+i3−1+i31−i3000000000000000000000000
χ634-4-44-20−4i4i02-22000002i3−2i300002i−2i23−232i−2i-220000002ζ22−2ζ222ζ14−2ζ141−i3−1+i31+i3−1−i3000000000000000000000000
χ644-4-44-20−4i4i02-22000002i3−2i300002i−2i23−23−2i2i2-2000000−2ζ222ζ22−2ζ142ζ14−1+i31−i3−1−i31+i3000000000000000000000000
χ6588-8-880000-8-88000000000000000000000000000000000000000000000000000000000
χ6688-8-8-4000044-400000000043−430000000000000000000000000000000000000000000000
χ6788-8-8-4000044-4000000000−43430000000000000000000000000000000000000000000000
χ688-88-8-4800-8-4440000000-44000000000000000000000000000000000000000000000000
χ698-88-8-4-8008-44400000004-4000000000000000000000000000000000000000000000000

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