Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#509 ⋊ C2 |
| Sylow | C3 ⋊ #2190 |
226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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)(6,14)(9,17)(12,19)(13,18);(1,2,3)(4,5)(6,13)(7,16)(8,10)(9,12)(11,15)(14,18)(17,19);(5,9)(6,12)(7,15)(10,17)(11,18)(13,16)(14,19)Polycyclic presentation:
2^7,3|d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,e^b=eg,f^b=fg,d^c=dg,h^c=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2190, C2×#71516, #10949080, … |
| maximal normal subgroup of | D3×#2190, C2×#71516, #10949080, … |
| maximal quotient of | #10707282, #10707287, #10707292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4092);