Finite Group DatabasebetaFinite Group Databasebeta| order | 34450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D53⋊C13) |
| unambiguous semidirect product | (C53⋊C13)⋊D25 |
| unambiguous semidirect product | D1325⋊C13 |
| Fitting, derived, Hall | C25×C53 ⋊ C2×C13 |
| Hall | C25×C53⋊C13 ⋊ C2 |
| Hall | D1325 ⋊ C13 |
| Hall | C53⋊C13 ⋊ D25 |
| Sylow | C53 ⋊ C13×D25 |
| Sylow | C25 ⋊ D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C53 | C2×C13 |
| Frattini | C5 | C5⋊(D53⋊C13) |
| socle | C5×C53 | D5×C13 |
| LCS | G ▷ C25×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1325 |
Polycyclic presentation:
2,5,13,53,5|b^5=e^4,b^a=b^4e,d^a=d^52,e^a=e^4,d^c=d^16232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34450, 12);