Finite Group DatabasebetaFinite Group Databasebeta| order | 37107 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C19×C31 ⋊ C9 |
| Hall | C19×C31 ⋊ C7⋊C9 |
| Hall | C7×C31 ⋊ #4294 |
| Hall | C7×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ #11924776 |
| Sylow | C19 ⋊ #14519869 |
| Sylow | C7 ⋊ #19127101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #27136501 |
| commutator, hypocenter | C7×C19×C31 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C19×C31 | C3 |
| LCS | G ▷ C7×C19×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37107 |
Polycyclic presentation:
3,7,19,31,3|a^3=e,b^a=b^2,c^a=c^7,d^a=d^54131 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37107, 11);