Finite Group DatabasebetaFinite Group Databasebeta| order | 16124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C139⋊#1181 |
| Fitting, socle, derived, Hall | C29×C139 ⋊ C4 |
| Sylow | C139 ⋊ #1181 |
| Sylow | C29 ⋊ Dic139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C139 | C4 |
| prime radical, cosocle | D29×C139 | C2 |
| LCS | G ▷ C29×C139 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4031 |
Polycyclic presentation:
2^2,29,139|a^2=b,c^a=c^17,d^a=d^138,c^b=c^281115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16124, 7);