Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(Dic79⋊C13)) |
| unambiguous semidirect product | (C79⋊C13)⋊(C3⋊Dic3) |
| unambiguous semidirect product | (C3⋊Dic237)⋊C13 |
| derived, Hall | C32×C79 ⋊ C4×C13 |
| Hall | C32×C79⋊C13 ⋊ C4 |
| Hall | C3⋊Dic237 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C3⋊Dic3 |
| Sylow | C79 ⋊ C13×C3⋊Dic3 |
| Sylow | C32 ⋊ Dic79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(D79⋊C13)) |
| commutator, hypocenter | C32×C79 | C4×C13 |
| Fitting, socle, cosocle | C2×C32×C79 | C2×C13 |
| prime radical | C2×C32×C79⋊C13 | C2 |
| LCS | G ▷ C32×C79 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2844 |
Polycyclic presentation:
2,13,3^2,79,2|a^2=f,c^a=c^2,d^a=d^2,e^a=e^78,e^b=e^18210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 100);