Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#22627851 |
| Fitting, socle, derived, Hall | C22×C13×C241 ⋊ C3 |
| Hall | C13×C241 ⋊ A4 |
| Hall | C22×C241 ⋊ C13⋊C3 |
| Sylow | C241 ⋊ C22⋊(C13⋊C3) |
| Hall | C22×C13 ⋊ C241⋊C3 |
| Sylow | C13 ⋊ C22⋊(C241⋊C3) |
| Sylow | C22 ⋊ #22627851 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C13×C241 | C3 |
| LCS | G ▷ C22×C13×C241 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12532 |
Polycyclic presentation:
3,2^2,13,241|b^a=c,c^a=bc,d^a=d^3,e^a=e^2254180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 88);