Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ #2121 |
280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(6,13)(9,17)(12,18)(14,19);(1,2,3)(4,6)(5,9)(7,14)(8,13)(10,12)(11,17)(15,18)(16,19);(4,5)(6,12)(7,15,16,10)(8,11)(9,14,17,19)(13,18)Polycyclic presentation:
2^7,3|a^2=e,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^c=h^2,e^d=eg36 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2121, C2×#69135, #10947927, … |
| maximal normal subgroup of | D3×#2121, C2×#69135, #10947927, … |
| maximal quotient of | #10704274, #10704363, #10704444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1711);