Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C61 ⋊ C4×C5 |
| Hall | #22628160 ⋊ C4 |
| Hall | C31×#6923 ⋊ C5 |
| Hall | #6923 ⋊ ΓL(1,𝔽32) |
| Sylow | C61 ⋊ C4×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ #6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C61 | C4×C5 |
| prime radical | #34038658 | C2 |
| cosocle | C31×D61 | C2×C5 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1891 |
Polycyclic presentation:
2,5,2,31,61|a^2=c,e^a=e^50,d^b=d^16,e^b=e^20,e^c=e^60137 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 48);