Finite Group DatabasebetaFinite Group Databasebeta| order | 37596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C241 ⋊ C3×C4 |
| Hall | C13×#11757210 ⋊ C3 |
| Hall | #22627851 ⋊ C4 |
| Hall | #11757210 ⋊ C13⋊C3 |
| Sylow | C241 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ #11757210⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C241 | C3×C4 |
| prime radical | #34037751 | C2 |
| cosocle | C13×D241 | C2×C3 |
| LCS | G ▷ C13×C241 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3133 |
Polycyclic presentation:
2,3,2,13,241|a^2=c,e^a=e^64,d^b=d^3,e^b=e^225,e^c=e^240288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37596, 49);