Finite Group DatabasebetaFinite Group Databasebeta| order | 37107 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C19×C31 ⋊ C9 |
| Hall | C19×C31 ⋊ C7⋊C9 |
| Hall | C7×C31 ⋊ #4296 |
| Hall | C7×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ #11924780 |
| Sylow | C19 ⋊ #14519870 |
| Sylow | C7 ⋊ #19127106 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C19×C31 | C9 |
| prime radical, cosocle | C7×C31×C19⋊C3 | C3 |
| LCS | G ▷ C7×C19×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4123 |
Polycyclic presentation:
3^2,7,19,31|a^3=b,c^a=c^2,d^a=d^4,e^a=e^25,d^b=d^7659 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37107, 23);