Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C31×C61 ⋊ C4×C5 |
| Hall | #22628159 ⋊ C4 |
| Hall | Dic1891 ⋊ C5 |
| Sylow | C61 ⋊ Dic31⋊C5 |
| Sylow | C31 ⋊ Dic61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #34038672 |
| commutator, hypocenter | C31×C61 | C4×C5 |
| Fitting, socle, cosocle | C2×C31×C61 | C2×C5 |
| prime radical | C2×#22628159 | C2 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7564 |
Polycyclic presentation:
2,5,31,61,2|a^2=e,c^a=c^30,d^a=d^60,c^b=c^16,d^b=d^34398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 32);