Finite Group DatabasebetaFinite Group Databasebeta| order | 30225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11925881⋊C25 |
| derived, Hall | C13×C31 ⋊ C3×C25 |
| Hall | C13×C31⋊C25 ⋊ C3 |
| Hall | #11925881 ⋊ C25 |
| Hall | C31⋊C25 ⋊ C13⋊C3 |
| Sylow | C31 ⋊ C25×C13⋊C3 |
| Sylow | C13 ⋊ (C31⋊C3)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #11925881⋊C5 |
| commutator, hypocenter | C13×C31 | C3×C25 |
| Fitting, socle, cosocle | C5×C13×C31 | C3×C5 |
| prime radical | C5×#11925881 | C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10075 |
Polycyclic presentation:
3,5,13,31,5|b^5=e,c^a=c^3,d^a=d^5,d^b=d^16305 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30225, 10);