Finite Group DatabasebetaFinite Group Databasebeta| order | 34025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1361⋊C25 |
| derived, Sylow | C1361 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C1361⋊C5 |
| commutator, hypocenter | C1361 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C1361 | C5 |
| LCS | G ▷ C1361 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34025 |
Polycyclic presentation:
5^2,1361|a^5=b,c^a=c^2111385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34025, 1);