Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊((C19⋊C3)⋊C4) |
| unambiguous semidirect product | (C19⋊C3)⋊Dic47 |
| unambiguous semidirect product | Dic893⋊C3 |
| derived, Hall | C19×C47 ⋊ C3×C4 |
| Hall | Dic893 ⋊ C3 |
| Hall | C47×C19⋊C3 ⋊ C4 |
| Hall | C19⋊C3 ⋊ Dic47 |
| Sylow | C47 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C47⋊(D19⋊C3) |
| commutator, hypocenter | C19×C47 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C47 | C2×C3 |
| prime radical | C2×C47×C19⋊C3 | C2 |
| LCS | G ▷ C19×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,47,2|a^2=e,c^a=c^18,d^a=d^46,c^b=c^7432 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 12);