Finite Group DatabasebetaFinite Group Databasebeta| order | 36972 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C79⋊C9)⋊C13) |
| unambiguous semidirect product | (C79⋊C13)⋊(C22⋊C9) |
| unambiguous semidirect product | (C22⋊(C79⋊C9))⋊C13 |
| derived, Hall | C22×C79 ⋊ C9×C13 |
| Hall | C22×C79⋊C13 ⋊ C9 |
| Hall | C22⋊(C79⋊C9) ⋊ C13 |
| Hall | C79⋊C13 ⋊ C22⋊C9 |
| Sylow | C79 ⋊ C13×C22⋊C9 |
| Sylow | C22 ⋊ (C79⋊C9)⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C79⋊C3)⋊C13) |
| commutator, hypocenter | C22×C79 | C9×C13 |
| Fitting, socle, cosocle | C22×C3×C79 | C3×C13 |
| prime radical | C22×C3×C79⋊C13 | C3 |
| LCS | G ▷ C22×C79 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1422 |
Polycyclic presentation:
3,13,2^2,79,3|a^3=f,c^a=d,d^a=cd,e^a=e^23,e^b=e^18180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36972, 35);