Finite Group DatabasebetaFinite Group Databasebeta| order | 3978 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D663 |
| unambiguous semidirect product | C13⋊(C3⋊D51) |
| unambiguous semidirect product | C17⋊(C3⋊D39) |
| Fitting, socle, derived, Hall | C32×C13×C17 ⋊ C2 |
| Hall | C13×C17 ⋊ C3⋊D3 |
| Hall | C32×C17 ⋊ D13 |
| Hall | C32×C13 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D39 |
| Sylow | C13 ⋊ C3⋊D51 |
| Sylow | C32 ⋊ D221 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C17 | C2 |
| LCS | G ▷ C32×C13×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1989 |
Polycyclic presentation:
2,3^2,13,17|b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^16996 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3315, C5×C3⋊D663, C7×C3⋊D663, … |
| maximal normal subgroup of | C5×C3⋊D663, C7×C3⋊D663 |
| maximal quotient of | C3⋊D3315, C5×C3⋊D663, C7×C3⋊D663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3978, 32);