Finite Group DatabasebetaFinite Group Databasebeta| order | 34404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C47⋊#6923) |
| unambiguous semidirect product | C47⋊(C3⋊#6923) |
| Fitting, socle, derived, Hall | C3×C47×C61 ⋊ C4 |
| Hall | C47×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ Dic47 |
| Hall | C3×C47 ⋊ #6923 |
| Sylow | C61 ⋊ Dic141 |
| Sylow | C47 ⋊ C3⋊#6923 |
| Sylow | C3 ⋊ C47⋊#6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C47×C61 | C4 |
| prime radical, cosocle | C3×C47×D61 | C2 |
| LCS | G ▷ C3×C47×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8601 |
Polycyclic presentation:
2^2,3,47,61|a^2=b,c^a=c^2,d^a=d^46,e^a=e^50,e^b=e^602259 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34404, 25);