Finite Group DatabasebetaFinite Group Databasebeta| order | 19270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(D41⋊C5) |
| unambiguous semidirect product | (C41⋊C5)⋊D47 |
| unambiguous semidirect product | D1927⋊C5 |
| Fitting, socle, derived, Hall | C41×C47 ⋊ C2×C5 |
| Hall | C47×C41⋊C5 ⋊ C2 |
| Hall | D1927 ⋊ C5 |
| Hall | C41⋊C5 ⋊ D47 |
| Sylow | C47 ⋊ D41⋊C5 |
| Sylow | C41 ⋊ C5×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C47 | C2×C5 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1927 |
Polycyclic presentation:
2,5,41,47|c^a=c^40,d^a=d^46,c^b=c^10313 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D41⋊C5, C2×C47⋊(D41⋊C5) |
| maximal normal subgroup of | D47×D41⋊C5, C2×C47⋊(D41⋊C5) |
| maximal quotient of | C47⋊(Dic41⋊C5), C2×C47⋊(D41⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19270, 12);