Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#489 ⋊ C2 |
| Sylow | C3 ⋊ #1661 |
208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2)(4,5,7,9)(6,11,10,8)(12,14)(13,18)(15,23)(16,25)(17,24)(19,22)(20,27)(21,26);(2,3)(6,10)(8,11)(12,14)(13,18)(15,25)(16,23)(17,24)(19,27)(20,22)(21,26);(5,8)(6,10)(9,11)(12,13,17,21)(14,22,24,27)(15,20,16,19)(18,25,26,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,h^b=h^2,d^c=dg,e^c=efg,h^c=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1661, C2×#71245, #10776339, … |
| maximal normal subgroup of | D3×#1661, C2×#71245, #10776339, … |
| maximal quotient of | #10683984, #10683990, #10684007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3821);