Finite Group DatabasebetaFinite Group Databasebeta| order | 34210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C311 ⋊ C2×C5 |
| Hall | #30686049 ⋊ C2 |
| Hall | C11×D311 ⋊ C5 |
| Hall | D311 ⋊ C11⋊C5 |
| Sylow | C311 ⋊ C2×C11⋊C5 |
| Sylow | C11 ⋊ D311⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C311 | C2×C5 |
| LCS | G ▷ C11×C311 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3421 |
Polycyclic presentation:
2,5,11,311|d^a=d^310,c^b=c^4,d^b=d^6355 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34210, 19);