Finite Group DatabasebetaFinite Group Databasebeta| order | 37386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C31×C67 ⋊ C2×C32 |
| Hall | C31⋊C3×C67⋊C3 ⋊ C2 |
| Hall | D2077 ⋊ C32 |
| Sylow | C67 ⋊ C3×D31⋊C3 |
| Sylow | C31 ⋊ C3×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C67 | C2×C32 |
| LCS | G ▷ C31×C67 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2077 |
Polycyclic presentation:
2,3^2,31,67|d^a=d^30,e^a=e^66,e^b=e^29,d^c=d^5176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37386, 26);