Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#365 ⋊ C2 |
| Sylow | C3 ⋊ AGL(1,ℤ/16) |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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:
(1,2)(4,6,14,17,8,15,7,13)(5,10,12,9,11,19,16,18);(2,3)(4,5)(6,10)(7,16)(8,11)(9,17)(12,14)(13,18)(15,19);(5,9,11,18)(6,13)(7,14)(10,16,19,12)(15,17)Polycyclic presentation:
2^7,3|a^2=e,c^2=efg,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,d^b=dfg,e^b=eg,f^b=fg,h^b=h^2,d^c=dg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,ℤ/16), C2×#69310, #10948632, … |
| maximal normal subgroup of | D3×AGL(1,ℤ/16), C2×#69310, #10948632, … |
| maximal quotient of | #10707059, #10707071, #10707137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1886);