Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#458 ⋊ C2 |
| Sylow | C3 ⋊ #2197 |
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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:
(4,12)(10,16)(18,19);(1,3,5,11)(2,6,8,13)(4,10,12,16)(7,9,14,15)(17,18,19);(1,2)(3,9)(4,7)(5,8)(6,10)(11,15)(12,14)(13,16)Polycyclic presentation:
2^7,3|b^2=g,b^a=bd,c^a=ce,f^a=fg,e^b=efg,d^c=df,h^c=h^2,e^d=eg36 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2197, C2×#71000, #10949206, … |
| maximal normal subgroup of | D3×#2197, C2×#71000, #10949206, … |
| maximal quotient of | #10707219, #10707225, #10707260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3576);