Finite Group DatabasebetaFinite Group Databasebeta| order | 37860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C3×C631 ⋊ C4×C5 |
| Hall | C3×C631⋊C5 ⋊ C4 |
| Hall | Dic1893 ⋊ C5 |
| Hall | C631⋊C5 ⋊ Dic3 |
| Sylow | C631 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ Dic631⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D631⋊C5) |
| commutator, hypocenter | C3×C631 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C631 | C2×C5 |
| prime radical | C2×C3×C631⋊C5 | C2 |
| LCS | G ▷ C3×C631 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7572 |
Polycyclic presentation:
2,3,5,631,2|a^2=e,b^a=b^2,d^a=d^630,d^c=d^242408 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37860, 14);