Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ #2192 |
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 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) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,6)(5,11)(7,16)(8,18)(9,19)(10,12)(13,29)(14,30)(15,25)(17,22)(20,27)(21,23)(24,33)(26,34)(28,31)(32,35);(2,3)(4,6)(5,10)(7,21)(8,17)(9,19)(11,12)(13,26)(14,28)(15,20)(16,23)(18,22)(24,32)(25,27)(29,34)(30,31)(33,35);(2,3)(4,5)(6,15)(7,20)(8,25)(9,14)(10,16)(11,17)(12,23)(13,22)(18,30)(19,29)(21,26)(24,34)(27,32)(28,33)(31,35)Polycyclic presentation:
2^7,3|d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^2,d^b=df,f^b=fg,h^b=h^2,e^c=eg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2192, C2×#69258, #10949144, … |
| maximal normal subgroup of | D3×#2192, C2×#69258, #10949144, … |
| maximal quotient of | #10707319, #10707330, #10707663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1834);