Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#1055 |
| unambiguous semidirect product | C3⋊(C3×#1055) |
| derived | C3×C13 ⋊ C3×C8 |
| Hall | C32×C13 ⋊ C8 |
| Sylow | C13 ⋊ C3×C3⋊C8 |
| Sylow | C32 ⋊ #1055 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D39 |
| commutator, hypocenter | C3×C13 | C3×C8 |
| Frattini | C4 | C3×D39 |
| Fitting | C32×C4×C13 | C2 |
| socle, prime radical | C2×C32×C13 | C4 |
| cosocle | C3×C4×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C3×C4 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊C8×D13, C3×D3×#1055, C3×#10597592, … |
| maximal normal subgroup of | C3×C3⋊C8×D13, C3×D3×#1055, C3×#10597592, … |
| maximal quotient of | C3×C3⋊#6090, C2×C3×C3⋊#1055 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 51);