Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #23756305⋊C3 |
| Fitting, socle, derived, Hall | C41×C61 ⋊ C3×C4 |
| Hall | #23756305 ⋊ C3 |
| Hall | C41×C61⋊C3 ⋊ C4 |
| Hall | C61⋊C3 ⋊ Dic41 |
| Sylow | C61 ⋊ C3×Dic41 |
| Sylow | C41 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C61 | C3×C4 |
| prime radical | C41×D61⋊C3 | C2 |
| cosocle | C41×D61 | C2×C3 |
| LCS | G ▷ C41×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2501 |
Polycyclic presentation:
2,3,2,41,61|a^2=c,d^a=d^40,e^a=e^50,e^b=e^13,e^c=e^60337 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 19);