Finite Group Databasebeta

← Group #10693280

Character table — Group #10693280

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order1222344446661212121224444668888121212121212224466668812121212121224242424242424248824242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-1-1-1111-1-1-1-111-1-1111ii−i−i11-1-1-1-111-1-11111i−i1-1-1-1-1-1iiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1i−i
χ1011111-1-1-1-1111-1-1-1-111-1-1111ii−i−i11-1-1-1-111-1-11111i−i1-1-1-1-1-1iiii−i−i−i−ii−iii−i−i-11-11−i−iii-11−ii
χ1111111-1-1-1-1111-1-1-1-111-1-1111ii−i−i11-1-1-1-1-1-111-1-1-1-1i−i1-11111iiii−i−i−i−i−ii−i−iii1-11-1ii−i−i-11−ii
χ1211111-1-1-1-1111-1-1-1-111-1-1111ii−i−i11-1-1-1-1-1-111-1-1-1-1i−i1-11111iiii−i−i−i−i−ii−i−iii-11-11−i−iii1-1i−i
χ1311111-1-1-1-1111-1-1-1-111-1-1111−i−iii11-1-1-1-111-1-11111−ii1-1-1-1-1-1−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1−ii
χ1411111-1-1-1-1111-1-1-1-111-1-1111−i−iii11-1-1-1-111-1-11111−ii1-1-1-1-1-1−i−i−i−iiiii−ii−i−iii-11-11ii−i−i-11i−i
χ1511111-1-1-1-1111-1-1-1-111-1-1111−i−iii11-1-1-1-1-1-111-1-1-1-1−ii1-11111−i−i−i−iiiiii−iii−i−i1-11-1−i−iii-11i−i
χ1611111-1-1-1-1111-1-1-1-111-1-1111−i−iii11-1-1-1-1-1-111-1-1-1-1−ii1-11111−i−i−i−iiiiii−iii−i−i-11-11ii−i−i1-1−ii
χ172222222222222222-22-2-2-2-2-2222222-2-22200000000-2-2-2-2000022-2-222-2-2000000000000000000
χ182222222222222222-22-2-2-2-2-2-2-2-2-222-2-2220000000022-2-20000-2-222-2-222000000000000000000
χ192222222-2-222222222-22-2-2220000-2-222-2-20000000000-2-200000000000000000000002i−2i2i−2i0000
χ202222222-2-222222222-22-2-2220000-2-222-2-20000000000-2-20000000000000000000000−2i2i−2i2i0000
χ212222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-200000000002200000000000000000022-2-200000000
χ222222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-2000000000022000000000000000000-2-22200000000
χ2322222-2-222222-2-2-2-22-2-22-2220000-2-2-2-2220000000000-2200000000000000000000002-2-220000
χ2422222-2-222222-2-2-2-22-2-22-2220000-2-2-2-2220000000000-220000000000000000000000-222-20000
χ2522222-2-222222-2-2-2-2-2-22-22-2-20000-2-2222200000000002-20000000000000000002-2-2200000000
χ2622222-2-222222-2-2-2-2-2-22-22-2-20000-2-2222200000000002-2000000000000000000-222-200000000
χ2722222-2-2-2-2222-2-2-2-2-2222-2-2-22i2i−2i−2i2222-2-200000000−2i2i-2200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-2-2222-2-2-2−2i−2i2i2i2222-2-2000000002i−2i-220000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ302222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-1-2-21111000000000000
χ312222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-1-1-1-111111111-2-21111000000000000
χ322222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-21111-2-2-1-111111111111122-1-1-1-1000000000000
χ332222-12222-1-1-1-1-1-1-1-22-2-2-2112222-1-111-1-10000−i3−i3i3i3-2-211−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-12222-1-1-1-1-1-1-1-22-2-2-2112222-1-111-1-10000i3i3−i3−i3-2-211i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-12222-1-1-1-1-1-1-1-22-2-2-211-2-2-2-2-1-111-1-10000−i3−i3i3i32211−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-12222-1-1-1-1-1-1-1-22-2-2-211-2-2-2-2-1-111-1-10000i3i3−i3−i32211i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-1-2-2-2-2-1-1-1111122-2-22-1-12i2i−2i−2i-1-1111122-2-2-1-1-1-12i−2i-111111−i−i−i−iiiii2i−2i−i−iii000000000000
χ382222-1-2-2-2-2-1-1-1111122-2-22-1-12i2i−2i−2i-1-11111-2-22211112i−2i-11-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ392222-1-2-2-2-2-1-1-1111122-2-22-1-1−2i−2i2i2i-1-1111122-2-2-1-1-1-1−2i2i-111111iiii−i−i−i−i−2i2iii−i−i000000000000
χ402222-1-2-2-2-2-1-1-1111122-2-22-1-1−2i−2i2i2i-1-11111-2-2221111−2i2i-11-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ412222-1-2-2-2-2-1-1-11111-2222-2112i2i−2i−2i-1-1-1-1110000−i3−i3i3i3−2i2i1-1i3i3−i3−i3−i−iiiii−i−i003−3−33000000000000
χ422222-1-2-2-2-2-1-1-11111-2222-2112i2i−2i−2i-1-1-1-1110000i3i3−i3−i3−2i2i1-1−i3−i3i3i3−i−iiiii−i−i00−333−3000000000000
χ432222-1-2-2-2-2-1-1-11111-2222-211−2i−2i2i2i-1-1-1-1110000−i3−i3i3i32i−2i1-1i3i3−i3−i3ii−i−i−i−iii00−333−3000000000000
χ442222-1-2-2-2-2-1-1-11111-2222-211−2i−2i2i2i-1-1-1-1110000i3i3−i3−i32i−2i1-1−i3−i3i3i3ii−i−i−i−iii003−3−33000000000000
χ454444-244-4-4-2-2-2-2-2-2-24-44-4-4-2-2000022-2-222000000000022000000000000000000000000000000
χ464444-244-4-4-2-2-2-2-2-2-2-4-4-4442200002222220000000000-2-2000000000000000000000000000000
χ474444-2-4-444-2-2-222224-4-44-4-2-200002222-2-200000000002-2000000000000000000000000000000
χ484444-2-4-444-2-2-22222-4-44-4422000022-2-2-2-20000000000-22000000000000000000000000000000
χ494-44-44004i−4i4-4-400000000000000000004i−4i2-22i−2i2-22-200002i−2i2i−2i00000000000000000000000000
χ504-44-44004i−4i4-4-400000000000000000004i−4i-22−2i2i-22-220000−2i2i−2i2i00000000000000000000000000
χ514-44-4400−4i4i4-4-40000000000000000000−4i4i2-2−2i2i2-22-20000−2i2i−2i2i00000000000000000000000000
χ524-44-4400−4i4i4-4-40000000000000000000−4i4i-222i−2i-22-2200002i−2i2i−2i00000000000000000000000000
χ534-44-4-2004i−4i-22223−2323−2300000000000−2i32i300−2i2i2-22i−2i−1−i31+i3−1+i31−i300002ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ544-44-4-2004i−4i-22223−2323−2300000000000−2i32i300−2i2i-22−2i2i1+i3−1−i31−i3−1+i30000−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ554-44-4-2004i−4i-222−2323−2323000000000002i3−2i300−2i2i2-22i−2i−1+i31−i3−1−i31+i300002ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ564-44-4-2004i−4i-222−2323−2323000000000002i3−2i300−2i2i-22−2i2i1−i3−1+i31+i3−1−i30000−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ574-44-4-200−4i4i-22223−2323−23000000000002i3−2i3002i−2i2-2−2i2i−1+i31−i3−1−i31+i30000−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ584-44-4-200−4i4i-22223−2323−23000000000002i3−2i3002i−2i-222i−2i1−i3−1+i31+i3−1−i300002ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ594-44-4-200−4i4i-222−2323−232300000000000−2i32i3002i−2i2-2−2i2i−1−i31+i3−1+i31−i30000−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ604-44-4-200−4i4i-222−2323−232300000000000−2i32i3002i−2i-222i−2i1+i3−1−i31−i3−1+i300002ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ614-4-4444-400-4-4444-4-40000000−2i22i2−2i22i20000000000000000000000−2i22i200−2i22i200000000000000000000
χ624-4-4444-400-4-4444-4-400000002i2−2i22i2−2i200000000000000000000002i2−2i2002i2−2i200000000000000000000
χ634-4-444-4400-4-44-4-444000000022−22−2222000000000000000000000022−2200−222200000000000000000000
χ644-4-444-4400-4-44-4-4440000000−222222−220000000000000000000000−22220022−2200000000000000000000
χ654-4-44-24-40022-2-2-22200000−2i32i3−2i22i2−2i22i200−2i32i3000000000000000000i2−i26−6i2−i26−6000000000000000000
χ664-4-44-24-40022-2-2-22200000−2i32i32i2−2i22i2−2i200−2i32i3000000000000000000−i2i2−66−i2i2−66000000000000000000
χ674-4-44-24-40022-2-2-222000002i3−2i3−2i22i2−2i22i2002i3−2i3000000000000000000i2−i2−66i2−i2−66000000000000000000
χ684-4-44-24-40022-2-2-222000002i3−2i32i2−2i22i2−2i2002i3−2i3000000000000000000−i2i26−6−i2i26−6000000000000000000
χ694-4-44-2-440022-222-2-200000−2i32i322−22−2222002i3−2i3000000000000000000−22i6−i62−2−i6i6000000000000000000
χ704-4-44-2-440022-222-2-200000−2i32i3−222222−22002i3−2i30000000000000000002−2−i6i6−22i6−i6000000000000000000
χ714-4-44-2-440022-222-2-2000002i3−2i322−22−222200−2i32i3000000000000000000−22−i6i62−2i6−i6000000000000000000
χ724-4-44-2-440022-222-2-2000002i3−2i3−222222−2200−2i32i30000000000000000002−2i6−i6−22−i6i6000000000000000000
χ7388-8-880000-88-8000000000000000000000000000000000000000000000000000000000000000
χ7488-8-8-400004-4443−43−434300000000000000000000000000000000000000000000000000000000000
χ7588-8-8-400004-44−434343−4300000000000000000000000000000000000000000000000000000000000

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