Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#518 ⋊ C2 |
| Sylow | C3 ⋊ #1904 |
346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(1,2,3)(5,11)(7,8)(10,14)(12,13)(15,16)(18,19);(4,6)(5,10,13,18)(7,15)(8,16)(9,17)(11,14,12,19);(2,3)(4,5,8,11,9,13,7,12)(6,14,16,18,17,19,15,10)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,e^b=eg,d^c=dg,e^c=eg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1904, C2×#71651, #10797081, … |
| maximal normal subgroup of | D3×#1904, C2×#71651, #10797081, … |
| maximal quotient of | #10690598, #10690612, #10690626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4227);