Finite Group DatabasebetaFinite Group Databasebeta| order | 35372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C239⋊#3866 |
| Fitting, socle, derived, Hall | C37×C239 ⋊ C4 |
| Sylow | C239 ⋊ #3866 |
| Sylow | C37 ⋊ Dic239 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C239 | C4 |
| prime radical, cosocle | D37×C239 | C2 |
| LCS | G ▷ C37×C239 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8843 |
Polycyclic presentation:
2^2,37,239|a^2=b,c^a=c^31,d^a=d^238,c^b=c^362393 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35372, 7);