Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #1910 |
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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)(4,7)(5,10)(6,13)(8,17)(9,16)(11,19)(12,15)(14,18);(4,6,12,5,9,14,8,11)(7,13,15,10,16,18,17,19);(2,3)(4,5)(6,12)(7,10,16,19)(8,14)(9,11)(13,17,18,15)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1910, C2×#68713, #10797168, … |
| maximal normal subgroup of | D3×#1910, C2×#68713, #10797168, … |
| maximal quotient of | #10690691, #10690696, #10690711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1289);