Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#27159929 |
| Fitting, socle, derived, Hall | C3×C13×C241 ⋊ C4 |
| Hall | C13×C241 ⋊ Dic3 |
| Hall | C3×C241 ⋊ Dic13 |
| Sylow | C241 ⋊ Dic39 |
| Hall | C3×C13 ⋊ #11757210 |
| Sylow | C13 ⋊ C3⋊#11757210 |
| Sylow | C3 ⋊ #27159929 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C241 | C4 |
| prime radical, cosocle | C3×C13×D241 | C2 |
| LCS | G ▷ C3×C13×C241 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9399 |
Polycyclic presentation:
2^2,3,13,241|a^2=b,c^a=c^2,d^a=d^12,e^a=e^64,e^b=e^2402382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 79);