Finite Group DatabasebetaFinite Group Databasebeta| order | 156 |
| isoclinism | isoclinic class of D3×D13 |
| automorphism | Aut(G) = D3×AGL(1,𝔽13) (order 936) · Inn(G) = G · Out(G) = C2×C3 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D13 |
| unambiguous semidirect product | (D3×C13)⋊C2 |
| unambiguous semidirect product | (C3×D13)⋊C2 |
| unambiguous semidirect product | D39⋊C2 |
| Fitting, socle, derived, Hall | C3×C13 ⋊ C22 |
| Sylow | C13 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 39 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16);(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,16)24 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#261, C2×D3×D13, D9×D13, … |
| maximal normal subgroup of | D3×#261, C2×D3×D13, D3×D13⋊C3, … |
| maximal quotient of | Dic3×D13, D3×Dic13, #64601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(156, 11);