Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C157⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C157⋊C3) |
| unambiguous semidirect product | (Dic3×C157)⋊C3 |
| derived | C3×C157 ⋊ C3×C4 |
| Hall | C3×C157⋊C3 ⋊ C4 |
| Sylow | C157 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C157⋊C3 |
| commutator, hypocenter | C3×C157 | C3×C4 |
| Fitting, socle | C2×C3×C157 | C2×C3 |
| LCS | G ▷ C3×C157 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic3×C157⋊C3, Dic15×C157⋊C3, ΓL(1,𝔽16)×C157⋊C3 |
| maximal normal subgroup of | C5×Dic3×C157⋊C3 |
| maximal quotient of | C5×Dic3×C157⋊C3, Dic15×C157⋊C3, ΓL(1,𝔽16)×C157⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 22);