Finite Group DatabasebetaFinite Group Databasebeta| order | 34029 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C199 ⋊ C9 |
| Sylow | C199 ⋊ #4294 |
| Sylow | C19 ⋊ #13184226 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C199 | C9 |
| prime radical, cosocle | C19×C199⋊C3 | C3 |
| LCS | G ▷ C19×C199 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3781 |
Polycyclic presentation:
3^2,19,199|a^3=b,c^a=c^7,d^a=d^162,d^b=d^92445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34029, 17);