Finite Group Databasebeta

← Group #10693266

Character table — Group #10693266

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order12223444466612121212244446688881212121212124444881212121212121212121224242424242424248824242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-1-1-1111-1-1-1-11-11-1111ii−i−i-1-111-1-111-1-1i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1i−i
χ1011111-1-1-1-1111-1-1-1-11-11-1111ii−i−i-1-111-1-111-1-1i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i-11-11−i−iii-11−ii
χ1111111-1-1-1-1111-1-1-1-11-11-1111ii−i−i-1-111-1-1-1-111i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii1-11-1ii−i−i-11−ii
χ1211111-1-1-1-1111-1-1-1-11-11-1111ii−i−i-1-111-1-1-1-111i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii-11-11−i−iii1-1i−i
χ1311111-1-1-1-1111-1-1-1-11-11-1111−i−iii-1-111-1-111-1-1−ii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1−ii
χ1411111-1-1-1-1111-1-1-1-11-11-1111−i−iii-1-111-1-111-1-1−ii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii-11-11ii−i−i-11i−i
χ1511111-1-1-1-1111-1-1-1-11-11-1111−i−iii-1-111-1-1-1-111−ii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i1-11-1−i−iii-11i−i
χ1611111-1-1-1-1111-1-1-1-11-11-1111−i−iii-1-111-1-1-1-111−ii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i-11-11ii−i−i1-1−ii
χ172222222222222222-2-22-2-2-2-22222-2-222220000-2-2-2-20000000022-2-222-2-2000000000000000000
χ182222222222222222-2-22-2-2-2-2-2-2-2-2-2-22222000022-2-200000000-2-222-2-222000000000000000000
χ192222222-2-2222222222-2-2-222000022-2-2-2-2000000-2-2000000000000000000000000002i−2i2i−2i0000
χ202222222-2-2222222222-2-2-222000022-2-2-2-2000000-2-200000000000000000000000000−2i2i−2i2i0000
χ212222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-200000022000000000000000000000022-2-200000000
χ222222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-2000000220000000000000000000000-2-22200000000
χ2322222-2-222222-2-2-2-22-2-22-2220000-2-2-2-222000000-22000000000000000000000000002-2-220000
χ2422222-2-222222-2-2-2-22-2-22-2220000-2-2-2-222000000-2200000000000000000000000000-222-20000
χ2522222-2-222222-2-2-2-2-22-2-22-2-2000022-2-2220000002-200000000000000000000002-2-2200000000
χ2622222-2-222222-2-2-2-2-22-2-22-2-2000022-2-2220000002-20000000000000000000000-222-200000000
χ2722222-2-2-2-2222-2-2-2-2-2222-2-2-22i2i−2i−2i2222-2-20000−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-2-2222-2-2-2−2i−2i2i2i2222-2-200002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ302222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ312222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ322222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ332222-12222-1-1-1-1-1-1-1-2-22-2-211222211-1-1-1-10000-2-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-12222-1-1-1-1-1-1-1-2-22-2-211222211-1-1-1-10000-2-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-12222-1-1-1-1-1-1-1-2-22-2-211-2-2-2-211-1-1-1-100002211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-12222-1-1-1-1-1-1-1-2-22-2-211-2-2-2-211-1-1-1-100002211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-1-2-2-2-2-1-1-111112-22-22-1-12i2i−2i−2i11-1-11122-2-22i−2i-11-1-1-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ382222-1-2-2-2-2-1-1-111112-22-22-1-12i2i−2i−2i11-1-111-2-2222i−2i-111111-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ392222-1-2-2-2-2-1-1-111112-22-22-1-1−2i−2i2i2i11-1-11122-2-2−2i2i-11-1-1-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ402222-1-2-2-2-2-1-1-111112-22-22-1-1−2i−2i2i2i11-1-111-2-222−2i2i-111111-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ412222-1-2-2-2-2-1-1-11111-2222-2112i2i−2i−2i-1-1-1-1110000−2i2i1-1−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-1-2-2-2-2-1-1-11111-2222-2112i2i−2i−2i-1-1-1-1110000−2i2i1-1i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ432222-1-2-2-2-2-1-1-11111-2222-211−2i−2i2i2i-1-1-1-11100002i−2i1-1−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ442222-1-2-2-2-2-1-1-11111-2222-211−2i−2i2i2i-1-1-1-11100002i−2i1-1i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ454444-244-4-4-2-2-2-2-2-2-244-4-4-4-2-20000-2-22222000000220000000000000000000000000000000000
χ464444-244-4-4-2-2-2-2-2-2-2-4-4-444220000222222000000-2-20000000000000000000000000000000000
χ474444-2-4-444-2-2-222224-4-44-4-2-200002222-2-20000002-20000000000000000000000000000000000
χ484444-2-4-444-2-2-22222-44-4-44220000-2-222-2-2000000-220000000000000000000000000000000000
χ494-44-444-4004-4-444-4-4000000022−2222−22000000000000000000000022−220022−2200000000000000000000
χ504-44-444-4004-4-444-4-40000000−2222−22220000000000000000000000−222200−222200000000000000000000
χ514-44-44-44004-4-4-4-4440000000−2i22i22i2−2i20000000000000000000000−2i22i2002i2−2i200000000000000000000
χ524-44-44-44004-4-4-4-44400000002i2−2i2−2i22i200000000000000000000002i2−2i200−2i22i200000000000000000000
χ534-44-4-24-400-222-2-22200000−2i32i322−2222−22−2i32i300000000000000000000−22i6−i6−22i6−i6000000000000000000
χ544-44-4-24-400-222-2-22200000−2i32i3−2222−2222−2i32i3000000000000000000002−2−i6i62−2−i6i6000000000000000000
χ554-44-4-24-400-222-2-222000002i3−2i322−2222−222i3−2i300000000000000000000−22−i6i6−22−i6i6000000000000000000
χ564-44-4-24-400-222-2-222000002i3−2i3−2222−22222i3−2i3000000000000000000002−2i6−i62−2i6−i6000000000000000000
χ574-44-4-2-4400-22222-2-200000−2i32i3−2i22i22i2−2i22i3−2i300000000000000000000i2−i26−6−i2i2−66000000000000000000
χ584-44-4-2-4400-22222-2-200000−2i32i32i2−2i2−2i22i22i3−2i300000000000000000000−i2i2−66i2−i26−6000000000000000000
χ594-44-4-2-4400-22222-2-2000002i3−2i3−2i22i22i2−2i2−2i32i300000000000000000000i2−i2−66−i2i26−6000000000000000000
χ604-44-4-2-4400-22222-2-2000002i3−2i32i2−2i2−2i22i2−2i32i300000000000000000000−i2i26−6i2−i2−66000000000000000000
χ614-4-444004i−4i-44-400000000000000000004i−4i2i−2i2-200002i−2i2i−2i2-22-200000000000000000000000000
χ624-4-444004i−4i-44-400000000000000000004i−4i−2i2i-220000−2i2i−2i2i-22-2200000000000000000000000000
χ634-4-44400−4i4i-44-40000000000000000000−4i4i2i−2i-2200002i−2i2i−2i-22-2200000000000000000000000000
χ644-4-44400−4i4i-44-40000000000000000000−4i4i−2i2i2-20000−2i2i−2i2i2-22-200000000000000000000000000
χ654-4-44-2004i−4i2-2223−2323−230000000000000−2i32i3−2i2i2i−2i2-200002ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ664-4-44-2004i−4i2-2223−2323−230000000000000−2i32i3−2i2i−2i2i-220000−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ674-4-44-2004i−4i2-22−2323−232300000000000002i3−2i3−2i2i2i−2i2-200002ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ684-4-44-2004i−4i2-22−2323−232300000000000002i3−2i3−2i2i−2i2i-220000−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ694-4-44-200−4i4i2-2223−2323−2300000000000002i3−2i32i−2i2i−2i-2200002ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ704-4-44-200−4i4i2-2223−2323−2300000000000002i3−2i32i−2i−2i2i2-20000−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ714-4-44-200−4i4i2-22−2323−23230000000000000−2i32i32i−2i2i−2i-2200002ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ724-4-44-200−4i4i2-22−2323−23230000000000000−2i32i32i−2i−2i2i2-20000−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ7388-8-880000-8-88000000000000000000000000000000000000000000000000000000000000000
χ7488-8-8-4000044-443−43−434300000000000000000000000000000000000000000000000000000000000
χ7588-8-8-4000044-4−434343−4300000000000000000000000000000000000000000000000000000000000

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