Finite Group DatabasebetaFinite Group Databasebeta| order | 36946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C13⋊(D29⋊C7)) |
| unambiguous semidirect product | C13⋊(C7⋊(D29⋊C7)) |
| unambiguous semidirect product | (C29⋊C7)⋊D91 |
| unambiguous semidirect product | D2639⋊C7 |
| Fitting, socle, derived | C7×C13×C29 ⋊ C2×C7 |
| Hall | C7×C13×C29⋊C7 ⋊ C2 |
| Hall | C7×C29⋊C7 ⋊ D13 |
| Hall | C13×C29 ⋊ C7×D7 |
| Sylow | C29 ⋊ C7×D91 |
| Sylow | C13 ⋊ C7⋊(D29⋊C7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C29 | C2×C7 |
| LCS | G ▷ C7×C13×C29 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2639 |
Polycyclic presentation:
2,7^2,13,29|c^a=c^6,d^a=d^12,e^a=e^28,e^b=e^16511 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36946, 19);