Finite Group DatabasebetaFinite Group Databasebeta| order | 36925 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C211⋊C7)⋊C25 |
| unambiguous semidirect product | (C211⋊C25)⋊C7 |
| derived, Sylow | C211 ⋊ C7×C25 |
| Hall | C211⋊C25 ⋊ C7 |
| Hall | C211⋊C7 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (C211⋊C5)⋊C7 |
| commutator, hypocenter | C211 | C7×C25 |
| Fitting, socle, cosocle | C5×C211 | C5×C7 |
| prime radical | C5×C211⋊C7 | C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5275 |
Polycyclic presentation:
5,7,211,5|a^5=d,c^a=c^107,c^b=c^171205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36925, 2);