Finite Group DatabasebetaFinite Group Databasebeta| order | 51302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C113 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽227) |
| Fitting, socle, derived, Sylow | C227 ⋊ C2×C113 |
| Hall | C227⋊C113 ⋊ C2 |
| Hall | D227 ⋊ C113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C227 | C2×C113 |
| LCS | G ▷ C227 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,113,227|c^a=c^226,c^b=c^4227 conjugacy classes — view the full character table.
| holomorph of | C227 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(51302, 1);