Finite Group DatabasebetaFinite Group Databasebeta| order | 34450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(D53⋊C13)) |
| unambiguous semidirect product | (C53⋊C13)⋊(C5⋊D5) |
| unambiguous semidirect product | (C5⋊D265)⋊C13 |
| Fitting, socle, derived, Hall | C52×C53 ⋊ C2×C13 |
| Hall | C52×C53⋊C13 ⋊ C2 |
| Hall | C5⋊D265 ⋊ C13 |
| Hall | C53⋊C13 ⋊ C5⋊D5 |
| Sylow | C53 ⋊ C13×C5⋊D5 |
| Sylow | C52 ⋊ D53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C53 | C2×C13 |
| LCS | G ▷ C52×C53 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1325 |
Polycyclic presentation:
2,13,5^2,53|c^a=c^4,d^a=d^4,e^a=e^52,e^b=e^16232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34450, 17);