Finite Group DatabasebetaFinite Group Databasebeta| order | 30225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#11925881 |
| Fitting, socle, derived, Hall | C52×C13×C31 ⋊ C3 |
| Hall | C52×C31 ⋊ C13⋊C3 |
| Hall | C13×C31 ⋊ C52⋊C3 |
| Hall | C52×C13 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C13⋊(C52⋊C3) |
| Sylow | C52 ⋊ #11925881 |
| Sylow | C13 ⋊ C52⋊(C31⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C31 | C3 |
| LCS | G ▷ C52×C13×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6045 |
Polycyclic presentation:
3,5^2,13,31|b^a=b^2c^2,c^a=b^4c^2,d^a=d^3,e^a=e^53361 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30225, 20);