Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3081 |
| unambiguous semidirect product | C3⋊(C3×Dic1027) |
| derived | C3×C13×C79 ⋊ C3×C4 |
| Hall | C32×C13×C79 ⋊ C4 |
| Hall | C13×C79 ⋊ C3×Dic3 |
| Hall | C32×C79 ⋊ Dic13 |
| Hall | C32×C13 ⋊ Dic79 |
| Sylow | C79 ⋊ C3×Dic39 |
| Sylow | C13 ⋊ C3×Dic237 |
| Sylow | C32 ⋊ Dic1027 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3081 |
| commutator, hypocenter | C3×C13×C79 | C3×C4 |
| Frattini | C2 | C3×D3081 |
| Fitting, socle, prime radical | C2×C32×C13×C79 | C2 |
| cosocle | C2×C3×C13×C79 | C2×C3 |
| LCS | G ▷ C3×C13×C79 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12324 |
9252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 143);