Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×Dic3×C13 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C4×C13) |
| derived | C3 ⋊ C2×C3×C4×C13 |
| Hall | C32×C13 ⋊ C2×C4 |
| Sylow | C32 ⋊ C2×C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C13 | D3 |
| commutator, hypocenter | C3 | C2×C3×C4×C13 |
| Frattini | C2 | C2×C3×D3×C13 |
| Fitting, socle, prime radical | C22×C32×C13 | C2 |
| cosocle | C2×C3 | C22×C3×C13 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C3×C13 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic3×Dic13, C3×#10597608, C3×#10597610, … |
| maximal normal subgroup of | C3×Dic3×Dic13, C3×#10597608, C3×#10597610, … |
| maximal quotient of | C2×C3×C13×C3⋊C8, C3×C13×#208, C3×C4×Dic3×C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 147);