Finite Group DatabasebetaFinite Group Databasebeta| order | 37070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D337 |
| unambiguous semidirect product | C337⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×D337)⋊C5 |
| Fitting, socle, derived, Hall | C11×C337 ⋊ C2×C5 |
| Hall | C11⋊C5×C337 ⋊ C2 |
| Hall | C11×D337 ⋊ C5 |
| Sylow | C337 ⋊ C2×C11⋊C5 |
| 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 |
1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37070, 10);