Finite Group DatabasebetaFinite Group Databasebeta| order | 37070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊D337 |
| unambiguous semidirect product | C337⋊AGL(1,𝔽11) |
| unambiguous semidirect product | D3707⋊C5 |
| Fitting, socle, derived, Hall | C11×C337 ⋊ C2×C5 |
| Hall | C11⋊C5×C337 ⋊ C2 |
| Hall | D3707 ⋊ C5 |
| Sylow | C337 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ D337 |
| Sylow | C11 ⋊ C5×D337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C337 | C2×C5 |
| LCS | G ▷ C11×C337 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3707 |
Polycyclic presentation:
2,5,11,337|c^a=c^10,d^a=d^336,c^b=c^41187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37070, 12);