Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #34037750⋊C2 |
| unambiguous semidirect product | #34037754⋊C2 |
| unambiguous semidirect product | #34037758⋊C2 |
| Fitting, socle, derived, Hall | C13×C241 ⋊ C22×C3 |
| Hall | D13×D241 ⋊ C3 |
| Hall | #22627850 ⋊ C22 |
| Sylow | C241 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×D241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C241 | C22×C3 |
| LCS | G ▷ C13×C241 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3133 |
Polycyclic presentation:
2^2,3,13,241|e^a=e^240,d^b=d^12,d^c=d^3,e^c=e^15336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 42);