Finite Group DatabasebetaFinite Group Databasebeta| order | 2826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D471 |
| unambiguous semidirect product | C157⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C157 ⋊ C2 |
| Sylow | C157 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C157 | C2 |
| LCS | G ▷ C32×C157 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1413 |
Polycyclic presentation:
2,3^2,157|b^a=b^2,c^a=c^2,d^a=d^156708 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D2355, C5×C3⋊D471, C3⋊D3297, … |
| maximal normal subgroup of | C5×C3⋊D471, C7×C3⋊D471, C11×C3⋊D471, … |
| maximal quotient of | C3⋊D2355, C5×C3⋊D471, C3⋊D3297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2826, 16);