Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D241 |
| unambiguous semidirect product | D723⋊D13 |
| unambiguous semidirect product | D3133⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C241 ⋊ C22 |
| Hall | C13×C241 ⋊ C2×D3 |
| Hall | C3×C241 ⋊ C2×D13 |
| Sylow | C241 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D241 |
| Sylow | C13 ⋊ D3×D241 |
| Sylow | C3 ⋊ D13×D241 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C241 | C22 |
| LCS | G ▷ C3×C13×C241 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9399 |
Polycyclic presentation:
2^2,3,13,241|d^a=d^12,e^a=e^240,c^b=c^2,d^b=d^122544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 84);