Finite Group DatabasebetaFinite Group Databasebeta| order | 37407 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C337 ⋊ C3 |
| Sylow | C337 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C337⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C337 | C3 |
| LCS | G ▷ C37×C337 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12469 |
Polycyclic presentation:
3,37,337|b^a=b^10,c^a=c^1284159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37407, 3);