Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×#365 ⋊ C2 |
| Sylow | C3 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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)(4,6)(5,11)(7,17)(8,18)(9,15)(10,16)(12,19)(13,14);(2,3)(4,5,10,7,9,13,8,12)(6,11,16,17,15,14,18,19);(5,7)(6,14,15,11)(8,10)(12,13)(16,17,18,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=dfg,e^2=f,f^2=g,b^a=bdfg,c^a=ce,e^a=ef,f^a=fg,h^b=h^2,d^c=dg,e^c=efg,f^c=fg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2230, C2×#69315, #10949928, … |
| maximal normal subgroup of | D3×#2230, C2×#69315, #10949928, … |
| maximal quotient of | #10711287, #10711881, #10711885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1891);