Finite Group DatabasebetaFinite Group Databasebeta| order | 51302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C113 · Schur multiplier (H2) = C1 |
| direct product | C2×C227⋊C113 |
| Fitting, socle, Hall | C2×C227 ⋊ C113 |
| derived, Sylow | C227 ⋊ C2×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C227⋊C113 |
| commutator, cosocle, hypocenter | C227 | C2×C113 |
| Frattini | C1 | G |
| Fitting, socle | C2×C227 | C113 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(51302, 2);