Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#419 ⋊ C2 |
| Sylow | C3 ⋊ #1977 |
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(8,11,12,20,14,22,13,21)(9,15,17,19,16,23,10,18);(2,3)(4,6,7,5)(8,10,13,16,14,17,12,9)(11,18,21,23,22,19,20,15);(4,5,7,6)(8,9,13,17,14,16,12,10)(11,19,21,23,22,18,20,15)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,f^b=fg,h^b=h^2,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1977, C2×#70335, #10799193, … |
| maximal normal subgroup of | D3×#1977, C2×#70335, #10799193, … |
| maximal quotient of | #10694105, #10694132, #10694369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2911);