Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#352 ⋊ C2 |
| Sylow | C3 ⋊ #2198 |
246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 246 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:
(1,4,6,3)(2,8,10,11)(5,12,14,13)(7,9,15,16)(17,18,19);(1,3,6,4)(2,7,10,15)(5,12,14,13)(8,9,11,16)(18,19);(1,2)(3,11)(4,8)(5,9)(6,10)(7,12)(13,15)(14,16)(18,19)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,e^b=efg,h^b=h^2,d^c=df,e^d=eg33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2198, C2×#69140, #10949207, … |
| maximal normal subgroup of | D3×#2198, C2×#69140, #10949207, … |
| maximal quotient of | #10707229, #10707230, #10707256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1716);